Recommended Design Specifications for Live Load Distribution to Buried Structures (2010)

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67 Previous chapters have described the computer model basis for, development of, and assessment of the effect of new SDEs for live loads on buried structures. This chapter sum- marizes the SDEs, describes the recommended changes to the AASHTO LRFD Design Specifications, and discusses the over- all design and reliability margin. 3.1 SDEs This section summarizes the proposed live load SDEs. The form of the live load equations is similar for all types of pipe. 3.1.1 AASHTO LRFD Live Load Equations The live load equations for the AASHTO LRFD Specifica- tion are where LHS20 is the wheel load from the HS20 load case, 16,000 lb, and LL is the live load force, lb Determine the wheel interaction depth where Hint is the wheel interaction depth, ft sw is the wheel spacing, 6 ft wt is the tire patch width, 20 in. LLDFl is the live load distribution factor, 1.15 Determine the live load area and pressure For H H A w LLDF H l LLDFLL t l t l< = + ⎛⎝⎜ ⎞⎠⎟ +int • •12 12 • ( )H ⎛⎝⎜ ⎞⎠⎟ 3 H s w LLDF w t l int ( )= − 12 2 LL LHS= 20 1( ) where H is the culvert depth, ft lt is the tire patch length, 10 in. ALL is the live load area, sf WLL is the live load pressure, psf Determine the governing load length where Lt.gov is the governing load length, ft Determine the dynamic load allowance where IM is the dynamic load allowance Determine the service live load where MPF is the multiple presence factor, 1.2 Di is the inside diameter or span of the culvert, in. W MPF IM W D LL LL i t gov= +( ) ( )• • • min , ( ),1 12 11 For H ft IM≥ =8 0 10( ) For H ft IM H < = −⎛⎝⎜ ⎞⎠⎟8 33 1 8 100 9• ( ) For H L l LLDF Ht gov t l< = +0 833 12 8. ( ). • For H L lt gov t< =0 833 12 7. ( ). W LL ALL LL= 2 6• ( ) For H H A w s LLDF H l LL LL t w l l ≥ = + +⎛⎝⎜ ⎞⎠⎟ + int • 12 12 i DF Hl • ( ) ⎛⎝⎜ ⎞⎠⎟ 5 W LL ALL LL= ( )4 C H A P T E R 3 Interpretation, Appraisal, and Applications

3.1.2 Concrete Box Live Load Equations The proposed live load equations used for concrete box de- sign calculations are as presented in Section 3.1.1, except the interaction depth, live load area, and pressure are as follows. Determine the wheel interaction depth where Hint is the wheel interaction depth, ft sw is the wheel spacing, 6 ft wt is the tire patch width, 20 in. LLDFl is the live load distribution factor, 1.15 Di is the inside span of the culvert, in. where H is the culvert depth, ft wt is the tire patch width, 20 in. lt is the tire patch length, 10 in. LLDFl is the AASHTO LRFD live load distribution fac- tor, 1.15 3.1.3 Concrete Pipe Live Load Equations The proposed live load equations used for concrete pipe design calculations are as presented in Section 3.1.1, except as follows: where LLDFcp is the live load distribution factor for concrete pipe Determine the wheel interaction depth II s w D LLDF w t i cp int . ( )= − − 12 0 06 12 18 For D in LLDFi cp> =96 1 75 17. ( ) For 24 96 0 00833 0 95 16in D in LLDF Di cp i< ≤ = +. . ( )• For D in LLDFi cp≤ =24 1 15 15. ( ) For H H A w s LLDF H DLL t w l i≥ = + + + ⎛⎝⎜ ⎞int • •.12 0 06 12⎠⎟ + ⎛⎝⎜ ⎞⎠⎟i l LLDF Hl l 12 14• ( ) For H H A w LLDF H DLL t l i< = + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 12 i l LLDF Hl l 12 13+ ⎛⎝⎜ ⎞⎠⎟• ( ) H s w D LLDF w t i l int . ( )= − − 12 0 06 12 12 Determine the live load area and pressure Determine the governing load length where H is the culvert depth, ft wt is the tire patch width, 20 in. lt is the tire patch length, 10 in. Di is the inside span of the culvert, in. Lt.gov is the governing load length in inches 3.1.4 Corrugated Metal Pipe Equations 3.1.4.1 Live Load Equations The proposed live load equations used for corrugated metal pipe are as presented in Section 3.1.1, except the live load area is as follows. Determine the wheel interaction depth For H H A w s LLDF H D LL t w l i≥ = + + +⎛⎝⎜ ⎞int • •.12 0 06 12 ⎠⎟ + ⎛⎝⎜ ⎞⎠⎟i l LLDF Ht l 12 25• ( ) For H H A w LLDF H D LL t l i< = + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 12 i l LLDF Ht l 12 24+ ⎛⎝⎜ ⎞⎠⎟• ( ) H s w D LLDF w t i l int . ( )= − − 12 0 06 12 23 For H L l LLDF Ht gov t l< = +0 833 12 22. ( ). • For H L lt gov t< =0 833 12 21. ( ). For H H A w s LLDF H DLL t w cp i≥ = + + + ⎛⎝⎜int • •.12 0 06 12 ⎞⎠⎟ + ⎛⎝⎜ ⎞⎠⎟i l LLDF Ht cp 12 20• ( ) For H H A w LLDF H DLL t cp i< = + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 12 i l LLDF Ht cp 12 19+ ⎛⎝⎜ ⎞⎠⎟• ( ) 68

where H is the culvert depth, ft wt is the tire patch width, 20 in. lt is the tire patch length, 10 in. LLDFl is the AASHTO LRFD live load distribution fac- tor, 1.15 Di is the inside span of the culvert, in. sw is the wheel spacing, 6 ft 3.1.4.2 Thrust Calculations For the proposed live load equations, the following live load adjustment is required: 3.1.5 Thermoplastic Pipe (Profile Wall) Equations 3.1.5.1 Live Load Equations The proposed live load equations used for profile wall thermoplastic pipe are as presented in Section 3.1.1, except the live load area is as follows. Determine the wheel interaction depth where H is the culvert depth, ft wt is the tire patch width, 20 in. lt is the tire patch length, 10 in. LLDFl is the AASHTO LRFD live load distribution fac- tor, 1.15 For H H A w s LLDF H D LL t w l i≥ = + + +⎛⎝⎜ ⎞int • •.12 0 06 12 ⎠⎟ + ⎛⎝⎜ ⎞⎠⎟i l LLDF Ht l 12 31• ( ) For H H A w LLDF H D LL t l i< = + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 12 i l LLDF Ht l 12 30+ ⎛⎝⎜ ⎞⎠⎟• ( ) H s w D LLDF w t i l int . ( )= − − 12 0 06 12 29 T DL LL F t d l = + ( )γ γ• • • ( ) 1 2 28 F D L LLDF H i t l 1 0 75 12 12 = + ⎛ ⎝⎜ ⎞ ⎠maximum F1,lim , . • • ⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ ( )27 F Di1 15 1 26,lim , ( )= ( )maximum Di is the inside span of the culvert, in. sw is the wheel spacing, 6 ft 3.1.5.2 Thrust Calculations For the proposed live load equations, the following live load adjustments are proposed: 3.1.6 Corrugated Metal Arch Equations 3.1.6.1 Live Load Equations The proposed live load equations used for corrugated metal arches are as presented in Section 3.1.1, except the live load area is as follows. Determine the wheel interaction depth where H is the culvert depth, ft wt is the tire patch width, 20 in. lt is the tire patch length, 10 in. S is the culvert span, ft LLDFl is the AASHTO LRFD live load distribution fac- tor, 1.15 sw is the wheel spacing, 6 ft The service live load is determined from W MPF IM W S LL LL t gov= +( ) ( )• • • min , ( ),1 39 For H H A w s LLDF H SLL t w l≥ = + + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 i l LLDF Ht l 12 38+ ⎛⎝⎜ ⎞⎠⎟• ( ) For H H A w LLDF H S l LL t l t < = + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 1 i 2 37+ ⎛⎝⎜ ⎞⎠⎟LLDF Hl • ( ) H s w S LLDF w t l int . ( )= − − 12 0 06 36 T DL LL F Fd l 1 1 2 2 35= +γ γ• • • • ( ) F Sh 2 0 95 1 0 6 34= + . . ( ) • F D L LLDF H i t l 1 0 75 12 12 = + ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜max F1,lim , . • • ⎞ ⎠⎟ ( )33 F Di1 15 1 32,lim , ( )= ( )max 69

where S is the culvert span, ft, and the other factors are as defined in previous sections. 3.1.6.2 Thrust Calculations For the proposed live load equations, the following live load adjustments are required: 3.1.7 Concrete Arch Equations The proposed live load equations used for concrete arches are as presented in Section 3.1.1, except the live load area is as follows. Determine the wheel interaction depth For H H A w s LLDF H SLL t w l≥ = + + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 i l LLDF Ht l 12 44+ ⎛⎝⎜ ⎞⎠⎟• ( ) For H H A w LLDF H S l LL t l t < = + + ⎛⎝⎜ ⎞⎠⎟int • •.12 0 06 1 i 2 43+ ⎛⎝⎜ ⎞⎠⎟LLDF Hl • ( ) H s w S LLDF w t l int . ( )= − − 12 0 06 42 T DL LL F i d l m arch = +γ γ• • • , ( ) 2 41 F S w LLDF H S m arch t l , . . ( ) • • • = + + 0 54 12 0 03 40 where H is the culvert depth, ft wt is the tire patch width, 20 in. lt is the tire patch length, 10 in. S is the culvert span, ft LLDFl is the AASHTO LRFD live load distribution fac- tor, 1.15 sw is the wheel spacing, 6 ft The service live loads were determined from where S is the culvert span, ft, and the other factors are as defined in previous sections. 3.2 Recommended Changes to the AASHTO LRFD Bridge Design Specifications Recommended changes to the 4th Edition AASHTO LRFD Bridge Design Specifications are presented in Appendix C. The research team has recommended changes to Sections 3 and 12. Table 3-1 summarizes the changes to each section for the six culvert types. 3.3 Overall Design and Reliability Margin Section 2.4 described the research team’s assessment of the effect of the proposed SDEs on the culvert forces pertinent to design. The results are presented as graphs of design forces from the SDEs versus either Standard or LRFD design forces. These graphs are useful for a detailed assessment of the effect W MPF IM W S LL LL t gov= +( ) )(• • • min , ( ),1 45 70 Culvert Type Section 3 Changes Section 12 Changes All types Eliminate LLDF dependence on soil type Effect of fill ignored < 1 ft for round culverts Effect of fill ignored for < 2 ft for flat-top and 3-sided culverts Added equations for rectangular area calculation N.A. Concrete Box Add 0.06 iD factor (e.g. Eqns (2) & (3)) None Concrete Pipe LLDF varies from 1.15 to 1.75 Add 0.06 iD factor Add ,t govL factor Change live load bedding factor for indirect design to 2.2 Corrugated Metal Pipe Add 0.06 iD factor Eqn (147)–(149) Thermoplastic Pipe (profile wall) Add 0.06 iD factor Eqn (153)–(155) Corrugated Metal Arch Add 0.06 iD factor Eqn (161)–(162) Concrete Arch Add 0.06 iD factor None Table 3-1. Proposed changes to AASHTO LRFD Bridge Design Specifications.

of the SDEs and give a general impression of the relative effect of the SDEs on design margin and reliability. In this section, the research team presents statistics about the ratio of SDE design forces to Standard design forces, and the ratio of SDE to LRFD design forces. Table 3-2 lists the numerical values of the maximum, minimum, average, stan- dard deviation, and coefficient of variation of the design force ratios. The culvert forces listed in the table are those specified in the code and vary according to the culvert type. Some cul- vert types have two design forces and others have only one. The maximum, minimum, and average design force ratios are also shown in Figure 3-1. In the figure, the square repre- sents the average ratio and the ends of the vertical bars repre- sent the minimum and maximum ratios. For most design forces, the ratio of SDE to LRFD is between 0.9 and 1.1. Ex- ceptions to these limits are the RCP crown moment at 0.888, 71 Table 3.2. Design for statistics, SDE/Standard and SDE/LRFD ratios. Figure 3.1. Maximum, minimum and average design force ratio.

the corrugated metal arch peak thrust at 1.460, and the rein- forced concrete arch peak moment at 0.882. The range of design force ratios is generally larger for the SDE/Standard ratio. This reflects that the SDEs, like the LRFD design methods, spread the loads from a finite-size wheel patch (typically 20 by 10 inches), rather than a point load. Figure 3-1 illustrates that, except for a few structure forces, the proposed SDEs do not significantly affect the design mar- gin or reliability on average. However, the relatively large spread in the ratios does mean that there are some combina- tions of soil type, diameter, and depth where the SDEs are sig- nificantly different than the LRFD design forces. Where there is a significant variation between the proposed SDEs and current practice, the differences are not random— rather the SDEs model behavior not captured in the current standards. For example, in corrugated metal pipe, the ratio gets larger as depth of fill decreases. As noted earlier in this report, this is the result of the high thrust occurring in the crown of these culverts, which occurs because of the low bending stiff- ness and high axial stiffness. Based on this study, the current AASHTO load spreading method provides a neutral or conservative approach for all culvert types, except corrugated metal arches. The proposed SDEs are a better fit to the modeling results produced in this study and are generally less conservative than the current AASHTO load-spreading method. For most reinforced concrete pipe diameters and depths considered, the SDEs generally predict much lower crown moments than the Standard method and moderately lower crown moments than the LRFD method. However, the SDEs are still quite conservative relative to the ACPA Handbook methods that have been used without issue for a substantial number of years. The research team believes that the proposed SDEs reflect an improvement in the distribution of live load with depth and better culvert designs. 72