Structural Design of Culvert Joints (2012) / Chapter Skim
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From page 41... ...
Appendix A Literature review A.1 Literature Review Table of Contents A.1 Introduction .............................................................................................................. 2 A.2 Pipe joint standards.
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Appendix A Literature review A.2 A.1 Introduction This literature review covers a. existing standards including joint design and joint testing protocols b.
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Appendix A Literature review A.3 Sealing systems for joints include: i. O ring, sleeve gaskets, strip gaskets and wraps, Figure A.2a and Figure A.2b ii.
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Appendix A Literature review A.4 A.2 Pipe joint standards. A.2.1 Introduction A series of ASTM standards exist providing specifications for design, geometry and testing of jointed culvert and pipe products.
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Appendix A Literature review A.5 Field testing of joint leakage is described in ASTM F 1417, based on air pressure. Joint assembly is covered in ASTM F 1668, the standard guide to polymer pipe burial (construction)
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Appendix A Literature review A.6 Table A.1 Summary of relevant concrete pipe standards. Standard Title Pipe types Joint type Joint design, testing or other requirements ASTM C 76-08 (AASHTO M 170)
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Appendix A Literature review A.7 Low-Pressure Air Test Method ASTM C 969-02 Standard Practice for Infiltration and Exfiltration Acceptance Testing of Installed Precast Concrete Pipe Sewer Lines Precast concrete Any preformed flexible joint sealants to prevent solid (soil) flow through joint Water infiltration of exfiltration tests of joints: infiltration rate is measured or exfiltration rate (after filling pipe with water to specific head and measuring water loss)
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Appendix A Literature review A.8 Sewer Pipe, Using Rubber Gaskets gaskets – either O rings or profile gaskets. Deflected position test: deflect to create 1 ⁄2-in.
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Appendix A Literature review A.9 Table A.2 Summary of relevant corrugated metal pipe standards. Standard Title Pipe types(s)
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Appendix A Literature review A.10 Table A.3 Summary of relevant polymer pipe standards Standard Title Pipe types(s) Joint type(s)
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Appendix A Literature review A.11 A.3 Design and performance of jointed pipes A.3.1 Design requirements for joints Kurdziel (2002, 2004) , Romer and Kienow (2004)
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Appendix A Literature review A.12 - consideration of the Reissner effect (ovaling that occurs in the cross-section due to longitudinal bending) - ability to resist prying open (lever action)
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Appendix A Literature review A.13 A.3.2 Testing procedures A.3.2.1 Concrete pipe testing ASTM C443 (2005) specifies requirements for hydrostatic pressure testing of joints in concrete pipes.
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Appendix A Literature review A.14 Figure A.3 Configuration of the off-center hydrostatic joint test (from ASTM C 497, 2005)
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Appendix A Literature review A.15 Figure A.4 Pressure test for polymer pipes in straight alignment according to ASTM D 3212. Figure A.5 Pressure test for polymer pipes after distortion with a 5% decrease in vertical diameter, ASTM D 3212.
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Appendix A Literature review A.16 Figure A.6 Compatibility test for polymer and gaskets ASTM F 477-08. Issues of compatibility between the polymer used to manufacture the pipe and the gasket material are examined using a compatibility test for polymer and gaskets defined by ASTM F 477-08.
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Appendix A Literature review A.17 a. Test arrangement b.
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Appendix A Literature review A.18 A.3.3 Longitudinal bending in buried pipes and culverts Jeyapalan and Abdel-Magid (1987) studied failures in reinforced polymer mortar pipes using finite element analysis.
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Appendix A Literature review A.19 - A hard point under the invert, Figure A.9a; - Pipeline passing between regions with different soil stiffness, Figure A.9b (see also Elachachi et al.
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Appendix A Literature review A.20 Figure A.10 Analysis of jointed water pipe with region of scour (void) under the pipe, Rajani and Tesfamariam (2004)
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Appendix A Literature review A.21 Table A.4 Embedment cases considered by Buco et al.
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Appendix A Literature review A.22 A.4 Methods of analysis A.4.1 Analysis of jointed pipes While Kurdziel (2004) concluded that "there does not appear to be any means for mathematically estimating this performance without using physical testing similar to that used in this study", recent finite element analyses have demonstrated the ability to provide effective representations of joint behavior.
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Appendix A Literature review A.23 effect of that local contact on the stresses in the thermoplastic structure. This type of analysis is able to study the local behavior (distributions of stress, for example)
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Appendix A Literature review A.24 modeled slip at specially designed joints in corrugated metal culverts, which compress when hoop thrust across the joint reaches some thresh-hold, promoting positive arching in deeply buried structures (redistribution of earth loads away from the culvert as a result of decreases in the circumference or perimeter of the metal culvert)
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Appendix A Literature review A.25 yx z q df/2 = 3d c L/2 b d a. Problem geometry b.
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Appendix A Literature review A.26 0.000 0.005 0.010 0.015 0.020 0.025 0 1 2 3 4 5 6 7 8 9 10 c/d ρmax/d 0 10-5 10-4 10-3 10-2 10-1 0 10-1 10-2 10-3 10-4 10-5 Values of Kr ANSYS Poulos a. Maximum deflection: L/d=25, νs=0.3 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0 2 4 6 8 10 c/d M/Esd3 10-1 10-5 10-4 10-3 10-2 10-1 10-2 10-3 10-4 10-5 Values of Kr Poulos ANSYS b.
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Appendix A Literature review A.27 Buco (2007) then employed this joint model in calculations of buried pipe behavior, as illustrated in Figure A.16.
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Appendix A Literature review A.28 Figure A.17 Comparison of bending along the pipe over the void for void length of 30cm, and void angle under the invert of 60° (a) void under the spigot, (b)
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Appendix A Literature review A.29 This approach makes no attempt to model the local circumferential stresses around the pipe circumference, but represents all stresses in the form of stress resultants, that is the total vertical shear force acting across the pipe wall, the total longitudinal bending moment, and sometimes the axial force (where the model is also representing axial force and deformation)
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Appendix A Literature review A.30 Table A.6 Individual spring values used by Jeyapalan and Abdel-Migid (1987)
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Appendix A Literature review A.31 In the three-dimensional finite element study of Trickey and Moore (2007) , the performance of the Poulos approach was examined in comparisons to their three-dimensional elastic finite element solutions, and this shows that the Poulos solution has some shortcomings.
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Appendix A Literature review A.32 • capacity of the joint to resist moment, perhaps expressed as a percentage of the capacity of the pipe barrel to resist moment • capacity of the joint to resist axial tension, perhaps expressed as a percentage of the total required axial force capacity of the pipe barrel There do not appear to be any generic requirements for the joint to tolerate specific amounts of movement across the joint: • vertical displacement • rotation (except that joint leakage tests in the laboratory based on ASTM C443-05a, for example, examines leakage after rotation opening the joint by 0.5 in.
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Appendix A Literature review A.33 A.5.2 Laboratory testing A.5.2.1 Standard tests for joint leakage (undistorted and distorted) Tests like ASTM C969.
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Appendix A Literature review A.34 American Society of Testing and Materials (ASTM) A798-07 Practice for Installing FactoryMade Corrugated Steel Pipe for Sewers and Other Applications ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA, 19428-2959 USA American Society of Testing and Materials (ASTM)
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Appendix A Literature review A.35 American Concrete Pipe Association (ACPA) Concrete Pipe Design Manual (accessed September 2009)
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Appendix A Literature review A.36 Kienow, K.K., 1998. Pipe Joint Failure Caused by an Inadequately Specified Constructed Environment, Proceedings, Pipelines in the Constructed Environment, ASCE Pipeline Division Conference, San Diego CA, 433-450.
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Appendix B Survey of DOTs B.1 Survey of Culvert and Joint Usage and Performance, US DOTs Contents B.1 Survey input ............................................................................................................. 1 B.2 Culvert usage.
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Appendix B Survey of DOTs B.2 B.3 Joints in reinforced concrete pipes Two joint types were predominant for reinforced concrete pipes: i. bell and spigot with gasket is common or the dominant joint type used in seven states; only five states indicate no usage of this joint option; ii.
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Appendix B Survey of DOTs B.3 B.6 Choices for buried pipe testing in the laboratory Two laboratory tests were undertake for reinforced concrete pipes, two for corrugated steel, and one each for HDPE and PVC. These were chosen as follows: I
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Appendix B Survey of DOTs B.4 Table B.1 Survey respondents Jurisdiction Name Position Type Performance % area % pop. Alabama Butch Bolling Materials Engineer Yes No 1.5% 1.5% Arizona Ken Akoh-Arrey Chief Drainage Engineer Yes Yes 3.2% 2.2% Arkansas Michael C
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Appendix B Survey of DOTs B.5 Table B.2 Culvert usage: y=yes (extent not indicated) , m=most; c=common; s=some; r=rare; n=never State AL AR AZ CA CO CT DE FL IL KS LA MA MN MO NH OH ON PA SC SD TN TX UT VA WS RCP m y y y y y m c y y m c m y y y y s y m c y y c c CSP c y y y y y s r y y s r s y r y y m n c c s y c c CAP r y n y y y r s y y s r r y y/n y r y n r r y cr1 r HDPE y sdo2 y y y y s s y y s n s y y y y r y r s r y c-r c PVC y sdo y y y y r s y y s n r y y/n y y r y n r r y c-r r Table B.3 RCP joints usage: x=used but frequency not indicated; m=most; c=common; s=some; r=rare; n=never performance: (g)
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Appendix B Survey of DOTs B.6 Table B.4 CSP joints usage: y=used but frequency not indicated; a=all; m=most; c=common; r=rare; n=never performance: (g) =good; (s)
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Appendix B Survey of DOTs B.7 Table B.5 HDPE: y=used; m=most; c=common; r=rare; n=never; performance: g=good; s=satisfactory; v=variable; p=poor State AL AR AZ CA CO CT DE FL IL KS LA MA MN MO NH OH ON PA SC SD TN TX UT VA WS bell & spigot & gasket y m (g)
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Appendix B Survey of DOTs B.8 B.7 Other input. CO RCP: Joint type: If contractor takes care with applying mastic sealant or o-ring and precautions when fitting together, most joints function properly.
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Appendix B Survey of DOTs B.9 Pipe type: MTO through the introduction of its MTO Gravity Pipe Design Guidelines May 2007 accepts the following pipe types for use on its highways provided that the pipe materials satisfy the following design parameters: Serviceability as defined by the Design Service Life (DSL) criteria; Durability defined by the Estimated Material Service Life (EMSL)
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Appendix B Survey of DOTs B.10 - Based on industry recommendations, a rubber gasketted pipe achieving a 13 psi pressure rating under laboratory conditions would be more suitable for locations where infiltration/exfiltration is a concern. AASHTO M 315 joints for RCP correspond to this configuration.
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Appendix B Survey of DOTs B.11 B.8 Survey form used to solicit information Survey : Usage of specific culvert joints.
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Appendix B Survey of DOTs B.12 Further details of experience with specific joint types (repeat page as needed) Pipe type Joint type Performance (give details if possible when performance is poor)
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Appendix B Survey of DOTs B.13 4. inspect pipes and pipe joints using laser ring profilers and video micrometer inspection measuring gaps across the joints; many producers do not meet the specification The DOT is developing joint gap measurement protocols.
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Appendix B Survey of DOTs B.14 B.9.4 Issues affecting joints in corrugated steel pipes Flexible (steel and thermoplastic) pipe deformations are limited to 5%.
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Appendix C Laboratory testing of culvert joints C.1 Laboratory testing of culvert joints Table of Contents C.1 INTRODUCTION .........................................................................................................................................
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Appendix C Laboratory testing of culvert joints C.2 C.1 Introduction This appendix describes laboratory testing of the six culvert products examined during the project. The objectives of these tests were to: • Produce measurements of jointed pipe response under controlled laboratory conditions • Examine pipe response under live loads as well as earth loads • Determine three dimensional behavior under simulated vehicle loading at service and ultimate loads levels • Examine shallow buried pipe response at two different cover depths • Examine pipe response under different quality (good and poor)
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Appendix C Laboratory testing of culvert joints C.3 a. 24 inch (610mm)
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Appendix C Laboratory testing of culvert joints C.4 C.2 Reinforced concrete pipes Both 24 in.
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Appendix C Laboratory testing of culvert joints C.5 a. View of experimental configuration in the GeoEngineering laboratory.
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Appendix C Laboratory testing of culvert joints C.6 Table C.1. Pressures for the articulation test of the 24 in (610mm)
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Appendix C Laboratory testing of culvert joints C.7 Figure C.4. Load versus deflection measured during articulation testing of the 24 in (610mm)
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Appendix C Laboratory testing of culvert joints C.8 Figure C.6. Maximum pipe deformations during articulation testing of the 24 in (610mm)
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Appendix C Laboratory testing of culvert joints C.9 Figure C.7. Strain gage locations in the 24 in (610mm)
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Appendix C Laboratory testing of culvert joints C.10 Figure C.9. View of the prisms after placement in the 24 in (610mm)
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Appendix C Laboratory testing of culvert joints C.11 C.2.2.2 Test configuration Two burial qualities were used to examine the 24 in.
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Appendix C Laboratory testing of culvert joints C.12 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.13 (a) Longitudinal section (a)
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Appendix C Laboratory testing of culvert joints C.14 (a) Longitudinal section (a)
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Appendix C Laboratory testing of culvert joints C.15 Figure C.15. Grid with Geosynthetic used for the end-wall treatment for all burial testing (shown here with 4ft of cover soil over the 24 in diameter specimen)
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Appendix C Laboratory testing of culvert joints C.16 C.2.2.3 Results Tables C.2 and C.3 provide the circumferential response of the bell, spigot and barrels for the tests performed on the 24 in.
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Appendix C Laboratory testing of culvert joints C.17 Table C.2. Circumferential strain in the bell and spigot; recorded at incremental load of 80 kN (17.9 kips)
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Appendix C Laboratory testing of culvert joints C.18 (a)
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Appendix C Laboratory testing of culvert joints C.19 (a)
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Appendix C Laboratory testing of culvert joints C.20 Figure C.19. Vertical crown displacements of the 24 in (610mm)
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Appendix C Laboratory testing of culvert joints C.21 (a)
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Appendix C Laboratory testing of culvert joints C.22 Figure C.21. Vertical crown displacements of the 48 in (1220mm)
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Appendix C Laboratory testing of culvert joints C.23 C.2.3.2 Test configuration Both reinforced concrete pipe specimens were tested at 2 ft (610mm) of cover, with good burial conditions according to AASHTO guidelines and with the load applied directly over the joint.
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Appendix C Laboratory testing of culvert joints C.24 (a)
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Appendix C Laboratory testing of culvert joints C.25 (a)
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Appendix C Laboratory testing of culvert joints C.26 Figure C.25. Circumferential crack about mid-span in one of the 24 in.
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Appendix C Laboratory testing of culvert joints C.27 Figure C.27. Close-up of the crown of the 24 in.
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Appendix C Laboratory testing of culvert joints C.28 Figure C.29. Incremental crown displacement of the 24 in.
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Appendix C Laboratory testing of culvert joints C.29 (a) Invert (b)
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Appendix C Laboratory testing of culvert joints C.30 Figure C.31. Incremental diameter changes in the joint elements of the 48 in.
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Appendix C Laboratory testing of culvert joints C.31 C.3 Corrugated steel pipes Two 36 in.
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Appendix C Laboratory testing of culvert joints C.32 Figure C.33. Strain gage scheme for the 36 in.
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Appendix C Laboratory testing of culvert joints C.33 Figure C.36. Reflective prism and string potentiometer scheme for the 36 in.
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Appendix C Laboratory testing of culvert joints C.34 details of one of these tests. The load was applied with an actuator placed above the pit mounted on beams while a string potentiometer placed at the top of the joint measured the displacement; set to 1 in (25mm)
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Appendix C Laboratory testing of culvert joints C.35 (a) Support condition.
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Appendix C Laboratory testing of culvert joints C.36 Therefore, incremental strain response during cyclic loading is illustrated in Figure C.41. Preliminary analysis of these strains indicates that the pattern of incremental circumferential strains implies ovaling in the band during vertical loading (decrease in vertical diameter and increase in horizontal diameter that produces tensile strain on the outside of the band at springlines, and compressive strain at crown and invert)
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Appendix C Laboratory testing of culvert joints C.37 Figure C.41. Measured strains at some locations at the band during bending test; 36 in.
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Appendix C Laboratory testing of culvert joints C.38 Figure C.43. Measured strains at some locations of the band during bending test; 36 in.
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Appendix C Laboratory testing of culvert joints C.39 C.3.2.2 Test configuration The corrugated steel pipe without O-rings was buried in accordance with AASHTO guidelines (Type 1 backfill compacted to 90 to 95 % of maximum standard Proctor dry density) in the configuration show in Figure C.44, and then was subjected to surface loads.
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Appendix C Laboratory testing of culvert joints C.40 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.41 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.42 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.43 (a)
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Appendix C Laboratory testing of culvert joints C.44 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.45 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.46 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.47 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.48 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.49 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.50 The data from the reflective prisms was also employed to plot vertical displacements of the springlines in the pipe while the live load was applied over pipes at different burial depths, burial conditions and load locations. Springline displacements rather than crown displacements were employed since they represent a global response of the pipe while the crown movements include localized responses due to the flexibility of the pipe (vertical diameter change)
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Appendix C Laboratory testing of culvert joints C.51 (a)
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Appendix C Laboratory testing of culvert joints C.52 (a) Void under joint (b)
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Appendix C Laboratory testing of culvert joints C.53 (a)
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Appendix C Laboratory testing of culvert joints C.54 (a)
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Appendix C Laboratory testing of culvert joints C.55 C.3.3 Ultimate limit state test The 36 in.
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Appendix C Laboratory testing of culvert joints C.56 Figure C.58. Configuration of the ultimate limit state test for the 36 in.
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Appendix C Laboratory testing of culvert joints C.57 (a) Strains in the corrugated pipe barrel at section S03 (b)
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Appendix C Laboratory testing of culvert joints C.58 (a) Strains in band at section S05 (b)
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Appendix C Laboratory testing of culvert joints C.59 (a) Strains in the corrugated pipe barrel at section S03 (b)
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Appendix C Laboratory testing of culvert joints C.60 (a) Strains in band at section S05 (b)
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Appendix C Laboratory testing of culvert joints C.61 The diameter changes in the joint registered by the reflective prisms and string potentiometer during the ultimate limit state test of the corrugated steel pipe without O-rings can be seen in Figure C.63. Due to excessive distortion, the reflective prisms in the joint could only register changes until 45 kips (200kN)
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Appendix C Laboratory testing of culvert joints C.62 Figure C.64. Incremental diameter changes of the joint during the ultimate limit state test of the 36 in.
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Appendix C Laboratory testing of culvert joints C.63 Figure C.65. Incremental springline vertical displacement during the ultimate limit state test of the 36 in.
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Appendix C Laboratory testing of culvert joints C.64 (a) Internal view (b)
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Appendix C Laboratory testing of culvert joints C.65 (a) Internal view (b)
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Appendix C Laboratory testing of culvert joints C.66 C.4 Thermoplastic pipes Two thermoplastic pipes were examined under burial conditions with fully factored service loads at different burial depths, loading locations and burial qualities in some cases. Bending tests were performed prior to burial for one of the specimens.
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Appendix C Laboratory testing of culvert joints C.67 (a) Reflective prisms (b)
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Appendix C Laboratory testing of culvert joints C.68 (a) Schematic (b)
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Appendix C Laboratory testing of culvert joints C.69 C.4.1.3 Results Figure C.71 shows the response registered by the string potentiometer mounted on one of the loading points. During initial loading, sliding of the joint was observed after 1300 lbf.ft (1.75kN.m)
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Appendix C Laboratory testing of culvert joints C.70 Figure C.72. Diameter change of the joint during the bending test of the 36 in.
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Appendix C Laboratory testing of culvert joints C.71 (a) Reflective prisms (b)
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Appendix C Laboratory testing of culvert joints C.72 C.4.2.2 Test configuration The 36 in.
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Appendix C Laboratory testing of culvert joints C.73 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.74 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.75 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.76 (a) Longitudinal section (b)
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Appendix C Laboratory testing of culvert joints C.77 Figure C.78. Steel loading plate, loading column and 2000 kN (220US ton)
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Appendix C Laboratory testing of culvert joints C.78 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.79 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.80 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.81 (a) Joint (b)
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Appendix C Laboratory testing of culvert joints C.82 kN 0 20 40 60 80 100 m m -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 kips 0 5 10 15 20 in -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 Dv - Bell Dh - Bell Dv - Spigot Dh - Spigot (a) Joint kN 0 20 40 60 80 100 m m -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 kips 0 5 10 15 20 in -0.015 -0.010 -0.005 0.000 0.005 Dv - 3ft - Pipe A Dh - 3ft - Pipe A Dv - 3ft - Pipe B Dh - 3ft - Pipe B Dv - 6ft - Pipe B Dh - 6ft - Pipe B (b)
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Appendix C Laboratory testing of culvert joints C.83 kN 0 20 40 60 80 100 m m -10 -8 -6 -4 -2 0 2 kips 0 5 10 15 20 in -0.4 -0.3 -0.2 -0.1 0.0 Dv -Bell Dh -Bell Dv -Spigot Dh -Spigot (a) Joint kN 0 20 40 60 80 100 m m -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 kips 0 5 10 15 20 in -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 Dv - 3ft - Pipe A Dh - 3ft - Pipe A Dv - 3ft - Pipe B Dh - 3ft - Pipe B Dv - 6ft - Pipe A Dh - 6ft - Pipe A Dv - 6ft - Pipe B Dh - 6ft - Pipe B (a)
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Appendix C Laboratory testing of culvert joints C.84 Vertical displacements of the springlines while the live load was applied were obtained from the reflective prisms data. Springline displacements rather that crown displacements were used since they represent the global response of the pipe while the crown values represent a local response including ovaling of the flexible thermoplastic pipe.
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Appendix C Laboratory testing of culvert joints C.85 (a) Void under joint (b)
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Appendix C Laboratory testing of culvert joints C.86 (a)
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Appendix C Laboratory testing of culvert joints C.87 Figure C.86. Vertical springline displacements comparison for the 36 in.
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Appendix C Laboratory testing of culvert joints C.88 (a)
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Appendix C Laboratory testing of culvert joints C.89 Figure C.89. Vertical springline displacements comparison for the 60 in.
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Appendix C Laboratory testing of culvert joints C.90 C.4.3.2 Test configuration Both thermoplastic pipes were tested at 2 ft (610mm) of cover, with good burial conditions (satisfying AASHTO guidelines)
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Appendix C Laboratory testing of culvert joints C.91 C.4.3.3 Results Diameter changes were register by the reflective prisms and by the string potentiometers during the ultimate limit state tests. Figure C.92 shows the vertical and horizontal diameter changes recorded for the joint elements of the 36 in.
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Appendix C Laboratory testing of culvert joints C.92 Figure C.93. Incremental diameter changes of the joint during the ultimate limit state test of the 60 in.
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Appendix C Laboratory testing of culvert joints C.93 Figure C.94. Incremental springline vertical displacement during the ultimate limit state test of the 36 in.
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Appendix C Laboratory testing of culvert joints C.94 Figure C.96. PVC pipe after ultimate limit state test.
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Appendix D Field testing D.1 Field testing Contents Introduction ..................................................................................................................................... 2 Description of Field Test Culverts ...................................................................................................
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Appendix D Field testing D.2 Culvert Rotation about the Springline ....................................................................................... 36 Joint Rotations of CMP-D4-F1.8 ..........................................................................................
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Appendix D Field testing D.3 RC-D4.5-F2 4.5 2.0 Tongue & Groove 6 6 HDPE-D3-F4.7 3.0 4.7 Bell-Spigot - 19.5 HDPE-D3.5-F3.5 3.5 3.5 Bell-Spigot - 20 Description of Test Culvert CMP-D4-F1.8 This is a circular corrugated metal culvert located in Pike County in Southern Ohio on County Road 76 with straight-line-mileage (SLM)
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Appendix D Field testing D.4 Description of Test Culvert CMP-D3-F2.5 This is a corrugated metal culvert located in Pike County in Southern Ohio on County Road 76 with SLM of 1.60. This culvert with a diameter of 3 ft (0.9 m)
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Appendix D Field testing D.5 Figure D.2 Testing of CMP-D3-F2.5 under static truck loading Description of Test Culvert RC-D7-F4.7 This reinforced concrete culvert is located in central Ohio in Logan County on State Route 274 with SLM of 15.00. This relatively large culvert consists of concrete sections 5 ft (1.52 m)
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Appendix D Field testing D.6 a) Instrumentation setup inside the culvert b)
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From page 191... ...
Appendix D Field testing D.7 a) Close-up view of instrumentation b)
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From page 192... ...
Appendix D Field testing D.8 a) Instrumentation b)
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From page 193... ...
Appendix D Field testing D.9 a) Instrumentation b)
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From page 194... ...
Appendix D Field testing D.10 described in Figure D and the wheel locations shown in Figure D..
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Appendix D Field testing D.11 Figure D.8 Static and live load cases (rear end view) Dynamic Loading Loaded trucks were driven over the culvert at a series of speeds.
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Appendix D Field testing D.12 be driven. This series of speeds was repeated for load cases C and S from Figure D..
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Appendix D Field testing D.13 Instrumentation Schemes Instrumentation consisted of linear displacement sensors and strain gauges. Seven of the eight linear displacement sensors had a precision of 0.001 in.
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Appendix D Field testing D.14 other culverts, the longitudinal sensor was offset by up to 15 degrees from the crown in the direction of B to facilitate placement of the instrumentation frame structure. The instrumentation frame structure was secured to the culvert segment opposite of the truck loading in load case S shown in Figure D..
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Appendix D Field testing D.15 Figure D.11 Close-up of upstream side view of sensor placement (RC-D7-F4.7)
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Appendix D Field testing D.16 Figure D.12 Upstream side view of location A (RC-D4.5-F2) Figure D.13 Position of instrumentation frame relative to truck loading scheme
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Appendix D Field testing D.17 CMP Culvert Instrumentation Scheme Testing of the metal culverts CMP-D4-F1.8 and CMP-D3-F1.5 consists of a slightly different setup than the one above. Six linear displacement sensors were used on the metal culverts.
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Appendix D Field testing D.18 Figure D.15 Arrangement of strain gauges in the CMP culverts
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Appendix D Field testing D.19 Experimental Test Results Introduction This section presents data gathered from tests of five in-service culverts and one pipe installation. The in-service culverts include two CMP (corrugated metal pipe)
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Appendix D Field testing D.20 Figure D.16 Deformed shape of a pipe culvert under loading. Horizontal and Vertical Deflection of CMP-D4-F1.8 The vertical and horizontal response of CMP-D4-F1.8 under dynamic loading is shown in Figure D.17 through Figure D.20.
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Appendix D Field testing D.21 Under S loading, the increase in truck speed had no discernible effect on the change in horizontal radius (Figure D.19)
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Appendix D Field testing D.22 Figure D.17 Vertical change in diameter of CMP-D4-F1.8 under dynamic loading case S, measured at the upstream and downstream sensors -1.524 -1.016 -0.508 0.000 0.508 -0.06 -0.04 -0.02 0.00 0.02 0 1 2 3 4 5 6 7 C ha ng e in D ia m et er (m m )
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Appendix D Field testing D.23 Figure D.18 Vertical change in diameter of CMP-D4-F1.8 under dynamic loading case C, measured at the upstream and downstream sensors -1.524 -1.016 -0.508 0.000 0.508 -0.06 -0.04 -0.02 0.00 0.02 0 1 2 3 4 5 6 7 C ha ng e in D ia m et er (m m )
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Appendix D Field testing D.24 Figure D.19 Horizontal change in radius of CMP-D4-F1.8 under dynamic loading case S, measured at the upstream and downstream sensors -0.102 0.000 0.102 0.203 0.305 0.406 0.508 -0.004 0.000 0.004 0.008 0.012 0.016 0.020 0 1 2 3 4 5 6 7 C ha ng e in R ad iu s (m m )
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Appendix D Field testing D.25 Figure D.20 Horizontal change in radius of CMP-D4-F1.8 under dynamic loading case C, measured at the upstream and downstream sensors.
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Appendix D Field testing D.26 Static Response of CMP-D4-F1.8 The measured static response of CMP-D4-F1.8 is shown in Figure D.21 and Figure D.23. A close-up of the static response is shown in Figure D.22 to help the reader better understand the results.
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Appendix D Field testing D.27 Figure D.22 Close-up of the measured static displacement history shown in Figure D.21 Figure D.23 Horizontal change in radius of CMP-D4-F1.8 measured at the upstream and downstream sensors.
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Appendix D Field testing D.28 Horizontal and Vertical Deflections of the Other Four In-Service Culverts All of the tested culverts exhibited a decrease in vertical diameter and increase in horizontal diameter as a result of loading. The smallest deflections were measured during the test of RC-D7F4.7.
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Appendix D Field testing D.29 Figure D.25 Vertical change in diameter during construction equipment loading of HDPE-D3.5F3.5 Figure D.26 Horizontal change in radius during the complete testing of HDPE-D3.5-F3.5 -4.064 -3.556 -3.048 -2.540 -2.032 -1.524 -1.016 -0.508 0.000 0.508 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 1500 1900 2300 2700 3100 3500 3900 C ha ng e in D ia m et er (m m )
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Appendix D Field testing D.30 Figure D.27 Horizontal change in radius during construction equipment loading of HDPE-D3.5F3.5 Strain Measurements Strain measurements were taken during the test of the two CMP culverts. Strain histories measured at eleven locations on culvert CMP-D4-F1.8 during static loading are shown in Figure D.28.
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Appendix D Field testing D.31 Longitudinal strain indicates the presence of longitudinal forces pulling apart or pushing together the jointed pipes. The maximum longitudinal strains (gauges #9 through #12 and #15 through #18)
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Appendix D Field testing D.32 Figure D.28 Strain measurements during static loading of CMP-D4-F1.8 -250 -200 -150 -100 -50 0 50 100 150 200 0 300 600 900 1200 1500 1800 St ra in (µ s) Gauge #7 Gauge #8 S-R2 SC-R2 C-R2 S-F2 C-F2 SC-R1 SC-R3 C-R3 C-R1 C-F3 C-F1 S-F1 S-F3 S-R3 S-R1 -300 -200 -100 0 100 200 300 400 0 300 600 900 1200 1500 1800 St ra in (µ s)
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Appendix D Field testing D.33 Figure D.28 Continued -100 -50 0 50 100 0 300 600 900 1200 1500 1800 St ra in (µ s) Gauge #9 Gauge #10 -100 -80 -60 -40 -20 0 20 40 60 80 100 0 300 600 900 1200 1500 1800 St ra in (µ s)
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Appendix D Field testing D.34 Figure D.29 Strain measurements during dynamic loading of CMP-D4-F1.8 -200 -150 -100 -50 0 50 100 150 0 100 200 300 400 500 600 St ra in (µ s) Gauge #7 Gauge #8 S-5mph S-30mph S-20mph S-10mph C-5mph C-30mph C-20mph C-10mph -200 -150 -100 -50 0 50 100 150 200 0 100 200 300 400 500 600 St ra in (µ s)
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Appendix D Field testing D.35 Figure D.29 Continued -50 -40 -30 -20 -10 0 10 20 30 40 0 100 200 300 400 500 600 St ra in (µ s) Gauge #11 Gauge #12 -120 -100 -80 -60 -40 -20 0 20 40 60 0 100 200 300 400 500 600 St ra in (µ s)
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Appendix D Field testing D.36 Culvert Rotation About the Springline When loaded, the culverts tend to be pushed downward beneath the loading. Away from the load location, the culverts can have little or no downward movement.
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Appendix D Field testing D.37 Joint Rotations of CMP-D4-F1.8 The joint rotations of culvert CMP-D4-F1.8 under dynamic loading cases S and C are shown in Figure D.32 and Figure D.34, respectively. The original measurements from the longitudinal sensors near crown and the invert are shown in Figure D.31 and Figure D.33.
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Appendix D Field testing D.38 Figure D.31 Longitudinal movement across the joint of CMP-D4-F1.8 under dynamic load case S, measured at the ‘top' and ‘bottom' locations -0.0762 -0.0508 -0.0254 0.0000 0.0254 0.0508 -0.003 -0.002 -0.001 0.000 0.001 0.002 0 1 2 3 4 5 6 7 M ov em en t a cr os s t he Jo in t ( m m )
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Appendix D Field testing D.39 Figure D.32 Joint rotation of CMP-D4-F1.8 under dynamic loading case S
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Appendix D Field testing D.40 Figure D.23 Longitudinal movement across the joint of CMP-D4-F1.8 under dynamic load case C, measured at the ‘top' and ‘bottom' locations -0.254 -0.127 0.000 0.127 -0.010 -0.005 0.000 0.005 0 1 2 3 4 5 6 7 M ov em en t a cr os s t he Jo in t ( m m )
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Appendix D Field testing D.41 Figure D.34 Joint rotation of CMP-D4-F1.8 under dynamic loading case C
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Appendix D Field testing D.42 Figure D.35 Joint rotation of CMP-D4-F1.8 under static loading. Joint Rotation of Pipe HDPE-D3.5-F3.5 During Its Installation The joint rotation was measured during three distinct portions of the test.
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Appendix D Field testing D.43 Figure D.36 Joint rotation during the complete testing of HDPE-D3.5-F3.5 Figure D.37 Joint Rotation of HDPE-D3.5-F3.5 during the placement of backfill. The joint rotation during the compaction of the backfill is shown in Figure D.38.
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Appendix D Field testing D.44 directly above the joint was the greatest cause of rotation during the test and resulted in a total of -0.29 degrees of rotation. The placement of the backfill resulted in large rotations.
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From page 229... ...
Appendix D Field testing D.45 Figure D.39 Joint Rotation of HDPE-D3.5-F3.5 during the construction equipment loading. The Effect of Dynamic Loading It is necessary to investigate whether dynamic loading or static loading produces larger deflections in the buried pipe culverts.
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Appendix D Field testing D.46 a) Vertical Deflection b)
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Appendix D Field testing D.47 Conclusions Results are presented for the testing of five in-service culverts and one culvert installation. Movements measured during the culvert installation are significantly larger than movements measured during any of the surface loading tests.
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From page 232... ...
Appendix E Simplified design and design examples E.1 Appendix E Explanation of simplified design approach and design examples Contents Introduction .....................................................................................................................................
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From page 233... ...
Appendix E Simplified design and design examples E.2 been drafted to consider for inclusion in the AASHTO LRFD Bridge Design Specifications. The last section of this appendix presents example calculations for: i.
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From page 234... ...
Appendix E Simplified design and design examples E.3 II. Changes in pipe diameter in the ends of corrugated steel pipes, and in the bells of the HDPE and PVC test pipes Both of these issues is examined in turn.
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From page 235... ...
Appendix E Simplified design and design examples E.4 where ܫ ൌ ݐ ଷ 12 ൌ ݏ݁ܿ݊݀ ݉݉݁ݐ ݂ ܽݎ݁ܽ E = Representative modulus of elasticity M = Moment at a given location ρ = Radius of curvature at a given location t = pipe wall thickness The differences between internal and external strains are then calculated employing eq.
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From page 236... ...
Appendix E Simplified design and design examples E.5 between observations and the simplified design calculations based on [E.1 to E.4] are due to the soil-pipe interaction captured in the finite element solutions, but more approximately represented in the design equations.
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From page 237... ...
Appendix E Simplified design and design examples E.6 Ms = Tangent constrained modulus of soil DL = Deflection lag factor (1) KB = Bedding coefficient (0.1)
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From page 238... ...
Appendix E Simplified design and design examples E.7 that the vertical deformations of the two pipes at the joint are the same. Appendix F presents the formulation of the solutions for shear force and pipe deformations (including rotation across the joint)
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From page 239... ...
Appendix E Simplified design and design examples E.8 E.1 presents those values in units of force per unit displacement per unit of horizontal area (pipe length and pipe width)
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Appendix E Simplified design and design examples E.9 Design for earth load It was recognized at the commencement of this project that no rotation or shear force occurs across a joint connecting pipes subjected to uniform earth loads, if they are constructed to have uniform soil support (under these circumstances, both pipes settle downward equal amounts, so no load transfer or rotation occurs across the joint)
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From page 241... ...
Appendix E Simplified design and design examples E.10 an increase in soil density from 90% to 95% of the maximum value from a standard Proctor test approximately doubles soil modulus)
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From page 242... ...
Appendix E Simplified design and design examples E.11 Surface load positions leading to peak shear force and peak rotation or moment across joints connecting flexible pipes are also different. Just as it did for rigid pipes, peak shear force across a joint connecting flexible pipes also results when the edge of the loaded rectangle over which the load has spread at depth H just touches the joint.
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From page 243... ...
Appendix E Simplified design and design examples E.12 Figure 6 presents example calculations for a 36 inch (0.9 m) diameter corrugated steel pipe with moment release joint at burial depth of 4 ft (1.2 m)
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From page 244... ...
Appendix E Simplified design and design examples E.13 Table E.1. Strains ε1- ε2 in pipe barrels (units of μ strain)
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From page 245... ...
Appendix E Simplified design and design examples E.14 Table E.4. Calculated versus measured changes in diameter in mm (1 inch = 25.4mm )
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From page 246... ...
Appendix E Simplified design and design examples E.15 Table E.8 Summary of simplified design requirements (shear force and rotation) for three flexible pipes with moment release joints at four burial depths.
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From page 247... ...
Appendix E Simplified design and design examples E.16 depth (m) 0.0 0.5 1.0 1.5 2.0 2.5 k s oi l M N /m 3 0 20 40 60 80 100 120 140 160 180 200 depth (ft)
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From page 248... ...
Appendix E Simplified design and design examples E.17 Figure E.2. Values of back-calculated soil stiffness ksoil in MN/m3 obtained using finite element analysis of the first three sets of buried pipe experiments and use of closed for equations for all six pipes (1MN/m3 = 6.3 kips/ft3; 1m=40 in.)
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From page 249... ...
Appendix E Simplified design and design examples E.18 US customary SI Internal diameter ID 2 ft 0.61 m Pipe geometry Outside diameter OD 2.625 ft 0.80 m Pipe geometry Depth to pipe crown h 2 ft 0.61 m Burial condition Depth to pipe springline H 3.3125 ft 1.01 m Burial condition Soil unit weight γS 140 pcf 22 kN/m3 Burial condition Vertical arching factor VAF 1.4 1.4 AASHTO LFRD Table 12.10.2.1-3 Section 12 Earth load factor γE 1.3 1.3 AASHTO LFRD Table 3.4.1-2 Section 3 Earth load per unit length WE 2213 lb/ft 32.3 kN/m [F.41] Appendix F Live load distribution factor LLDF 1.15 1.15 AASHTO LFRD Section 3.6.1.2.6 Width of standard wheel pair W0 1.67 ft 0.51 m AASHTO LFRD Section 3.6.1.2.5 Distribution width at depth H W0+LLDF*
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From page 250... ...
Appendix E Simplified design and design examples E.19 US customary SI Internal diameter ID 4 ft 1.22 m Pipe geometry Outside diameter OD 5.0 ft 1.51 m Pipe geometry Depth to pipe crown h 20 ft 6.10 m Burial condition Depth to pipe springline H 22.5 ft 6.85 m Burial condition Soil unit weight γS 139.9 pcf 22 kN/m3 Burial condition Vertical arching factor VAF 1.4 1.4 AASHTO LFRD Table 12.10.2.1-3 Section 12 Earth load factor γE 1.3 1.3 AASHTO LFRD Table 3.4.1-2 Section 3 Earth load per unit length WE 28369.7 lb/ft 414.6 kN/m [F.41] Appendix F Live load distribution factor LLDF 1.15 1.15 AASHTO LFRD Section 3.6.1.2.6 Width of standard wheel pair W0 1.67 ft 0.51 m AASHTO LFRD Section 3.6.1.2.5 Distribution width at depth H W0+LLDF*
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From page 251... ...
Appendix E Simplified design and design examples E.20 US customary SI Internal diameter ID 3.00 ft 0.91 m Pipe geometry Diameter in contact with soil OD 3.04 ft 0.93 m Pipe geometry Modulus of pipe material E 4166921622 psf 200000000 kPa Pipe property Second moment of area in axial direction I 0.000405513 ft4 0.0000035 m4 Pipe geometry Flexural rigidity of whole pipe along axis EI 1689741 lbf.ft^2 700 kN.m2 Vertical arching factor VAF 1.00 1.00 Implicit in AASHTO LFRD Section 12.7.2.2 Depth to pipe crown h 4 ft 1.22 m Burial condition Depth to pipe springline H 5.5 ft 1.68 m Burial condition Soil unit weight γS 140 pcf 22.00 kN/m3 Burial condition Earth load factor γE 1.95 1.95 AASHTO LFRD Table 3.4.1-2 Section 3 Earth load per unit length WE 4579.50 lb/ft 66.93 kN/m [F.74] Appendix F Live load distribution factor LLDF 1.15 1.15 AASHTO LFRD Section 3.6.1.2.6 Width of standard wheel pair W0 1.67 ft 0.51 m AASHTO LFRD Section 3.6.1.2.5 Distribution width at depth H W0+LLDF*
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From page 252... ...
Appendix E Simplified design and design examples E.21 Figure E.5 Design calculations for 36 in.
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From page 253... ...
Appendix E Simplified design and design examples E.22 US customary SI Internal diameter ID 3.00 ft 0.91 m Pipe geometry Diameter in contact with soil OD 3.04 ft 0.93 m Pipe geometry Modulus of pipe material E 4.167E+09 psf 200000000 kPa Pipe property Second moment of area in axial direction I 0.0004055 ft4 0.0000035 m4 Pipe geometry Flexural rigidity of whole pipe along axis EI 1689741 lbf.ft2 700 kN.m2 Vertical arching factor VAF 1.00 1.00 Implicit in AASHTO LFRD Section 12.7.2.2 Depth to pipe crown h 4.00 ft 1.22 m Burial condition Depth to pipe springline H 5.52 ft 1.68 m Burial condition Soil unit weight γS 139.85 pcf 22.00 kN/m3 Burial condition Earth load factor γE 1.95 1.95 AASHTO LFRD Table 3.4.1-2 Section 3 Earth load per unit length WE 4579.50 lb/ft 66.93 kN/m [24] Appendix C Live load distribution factor LLDF 1.15 1.15 AASHTO LFRD Section 3.6.1.2.6 Width of standard wheel pair W0 1.67 ft 0.51 m AASHTO LFRD Section 3.6.1.2.5 Distribution width at depth H W0+LLDF*
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From page 254... ...
Appendix E Simplified design and design examples E.23 Figure E.6 Design calculations for 36 in.
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From page 255... ...
Appendix E Simplified design and design examples E.24 US customary SI Internal diameter ID 3.00 ft 0.91 m Pipe geometry Diameter in contact with soil OD 3.09 ft 0.94 m Pipe geometry Modulus of pipe material E 57503518 psf 2760000 kPa AASHTO LFRD Table 12.12.3.3-1 Flexural rigidity of whole pipe along axis EI 1448349 lbf.ft2 600 kN.m2 Area in hoop direction per unit length A 0.0144357 ft2/ft 0.0044 m2/m Pipe geometry Hoop stiffness per unit length EA 830102 lbf/ft 12144 kN/m Constrained modulus of the soil MS 66302 lbf/ft2 3200 kPa AASHTO LFRD Table 12.12.3.4-1 Normalized hoop stiffness SH 0 0 AASHTO LFRD Equation 12.12.3.4-4 Vertical arching factor VAF 1.00 1.00 AASHTO LFRD Equation 12.12.3.4-3 Depth to pipe crown h 2.00 ft 0.61 m Burial condition Depth to pipe springline H 3.54 ft 1.08 m Burial condition Soil unit weight γS 139.85 pcf 22.00 kN/m3 Burial condition Earth load factor γE 1.95 1.95 AASHTO LFRD Table 3.4.1-2 Section 3 Earth load per unit length WE 2998.24 lb/ft 43.81 kN/m [F.74] Appendix F Live load distribution factor LLDF 1.15 1.15 AASHTO LFRD Section 3.6.1.2.6 Width of standard wheel pair W0 1.67 ft 0.51 m AASHTO LFRD Section 3.6.1.2.5 Distribution width at depth H W0+LLDF*
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From page 256... ...
Appendix E Simplified design and design examples E.25 Earth load contribution to rotation 0.0918 WEλ/(OD ksoil) 0.00026 radians 0.00026 radians [F.83]
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From page 257... ...
Appendix E Simplified design and design examples E.26 US customary SI Internal diameter ID 5 ft 1.52 m Pipe geometry Diameter in contact with soil OD 5.26 ft 1.60 m Pipe geometry Modulus of pipe material E 15792633 psf 758000 kPa AASHTO LFRD Table 12.12.3.3-1 Flexural rigidity of whole pipe along axis EI 6396875 lbf.ft2 2650 kN.m2 Area in hoop direction per unit length A 0.0480833 ft2/ft 0.0146558 m2/m Pipe geometry Hoop stiffness per unit length EA 759362 lbf/ft 11109 kN/m Constrained modulus of the soil MS 93237 lbf/ft2 4500 kPa AASHTO LFRD Table 12.12.3.4-1 Normalized hoop stiffness SH 0 0 AASHTO LFRD Equation 12.12.3.4-4 Vertical arching factor VAF 0.95 0.94 AASHTO LFRD Equation 12.12.3.4-3 Depth to pipe crown h 20.00 ft 6.10 m Burial condition Depth to pipe springline H 22.63 ft 6.90 m Burial condition Soil unit weight γS 139.85 pcf 22.00 kN/m3 Burial condition Earth load factor γE 1.95 1.95 AASHTO LFRD Table 3.4.1-2 Section 3 Earth load per unit length WE 30706.11 lb/ft 448.52 kN/m [F.74] Appendix F Live load distribution factor LLDF 1.15 1.15 AASHTO LFRD Section 3.6.1.2.6 Width of standard wheel pair W0 1.67 ft 0.51 m AASHTO LFRD Section 3.6.1.2.5 Distribution width at depth H W0+LLDF*
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From page 258... ...
Appendix E Simplified design and design examples E.27 Earth load contribution to rotation 0.0918 WEλ/(OD ksoil) 0.00125 radians 0.00125 radians [F.83]
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From page 259... ...
Appendix F Analytical solutions for response of joints F.1 Appendix F Analytical solutions for response of joints.
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From page 260... ...
Appendix F Analytical solutions for response of joints F.2 moment or rotation using three dimensional finite element analysis. Instead, the use of beam-onelastic-spring modeling is adopted.
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From page 261... ...
Appendix F Analytical solutions for response of joints F.3 vR ൌ FROD LR kR [F.2] where the spring stiffness for the soil under the left and right hand pipes, in units of force per unit deflection, are OD LL kL and OD LR kR respectively.
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From page 262... ...
Appendix F Analytical solutions for response of joints F.4 ∆θR ൌ െ6 VJkROD LRଶ [F.10] which produces relative vertical displacement across the joint ∆vJ ൌ ൬∆vL ∆θL LL2 ൰ െ ൬∆vR െ ∆θR LR 2 ൰ [F.11]
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From page 263... ...
Appendix F Analytical solutions for response of joints F.5 RGିଵ ൌ 1 0.125 OD L kୱ୭୧୪kG [F.19] Calculations for shear force across the joint will always be conservative when the gasket is assumed rigid and so most of the remaining discussion in this appendix is based on that assumption (i.e.
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From page 264... ...
Appendix F Analytical solutions for response of joints F.6 Now, only the pressures that fall within the external pipe diameter OD act across the pipe, so the force per unit length along the pipe at depth H, is FH ൌ w PLL LLDF .
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From page 265... ...
Appendix F Analytical solutions for response of joints F.7 The value of eR is immaterial when xR ൌ 0 so there is no need to adjust the expression for eR when right force is zero. Now, consider a surface load placed directly over the joint, the load position expected to produce maximum joint rotation, Figure F.4b.
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From page 266... ...
Appendix F Analytical solutions for response of joints F.8 and eL ൌ eR ൌ 0 [F.42] Substitution of these into the expressions for shear force and rotation across the joint yields VJ ൌ 0.25 RG WE ሾ 1kL െ 1 kRሿ1 LL kL 1 LR kR [F.43]
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From page 267... ...
Appendix F Analytical solutions for response of joints F.9 A range of results are shown in Table F.1 for other values of ୩R ୩L. These indicate that even for the right hand side pipe sitting on rigid bedding, maximum shear is limited to one quarter of the total overburden load applied to the pipe.
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From page 268... ...
Appendix F Analytical solutions for response of joints F.10 stiffness, and so small moments will be transferred across the joint that reduce rotations and therefore the shear force being transferred; however, the effect of the ‘zero moment approximation' is likely small.
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From page 269... ...
Appendix F Analytical solutions for response of joints F.11 a. geometry and loading conditions b.
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From page 270... ...
Appendix F Analytical solutions for response of joints F.12 a. Linear distribution of deflections b.
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From page 271... ...
Appendix F Analytical solutions for response of joints F.13 a. undeformed position, showing three pipe segments on either side of the central joint b.
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From page 272... ...
Appendix F Analytical solutions for response of joints F.14 d. provide simplified expressions suitable for the AASHTO LFRD Bridge Design Specifications for maximum shear force and maximum rotation or moment transferred across the joint resulting from wheel loading acting at the ground surface e.
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From page 273... ...
Appendix F Analytical solutions for response of joints F.15 dM dc ൌ V ൌ 0 [F.59] This occurs at the central position where a=b, and so MJ ൌ FH݁ିሺ ఒಹଶ ሻ sinሺߣܮு2 ሻ 2λଶ [F.60]
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From page 274... ...
Appendix F Analytical solutions for response of joints F.16 and shear ܸሺݔሻ ܧܫ ൌ ݀ଷݕ ݀ݔଷ ൌ FH 2kS ሾ4λ ଷሺ1 B െ CሻD௫ െ 2λଷሺ1 2B െ CሻA௫ െ ൫2λଷC௫ െ 2λଷCሺ୶ିሻ൯ሿ [F.67] where A௫ ൌ eି௫ሺcos λݔ sin λݔሻ [F.68]
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From page 275... ...
Appendix F Analytical solutions for response of joints F.17 Response to earth loads The loading per unit length WE along a flexible pipe of external diameter OD at depth H in soil of unit weight γS, given load factor γE and vertical arching factor VAF, is WE ൌ γEVAF H γS OD [F.74] Consider two pipes with different levels of ground support, Figure F.7a.
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From page 276... ...
Appendix F Analytical solutions for response of joints F.18 θJ ൌ WE 1 kL െ 1 kR λLkL λRkR ሺλL ଶ kL െ λRଶ kRሻ [F.81] For the specific case of kR kL ൌ 2 [F.82]
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From page 277... ...
Appendix F Analytical solutions for response of joints F.19 2VJλL kL 2VJλR kR െ 2MଵλLଶ kL െ 2MଵλRଶ kR ൌ WE ሾ 1 kL െ 1 kRሿ [F.90] and these actions also produce rotations of equal magnitude െ 2VJλLଶ kL െ 4MଵλLଷ kL ൌ െ 2VJλRଶ kR 4MଵλRଷ kR [F.91]
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From page 278... ...
Appendix F Analytical solutions for response of joints F.20 shear force in the beam over the lower stiffness soil are assembled from Hetényi's expressions for these stress resultants due to the shear force P1 and moment M1 at that transition point V ൌ െPଵC୶ െ 2 λLMଵB୶ [F.96]
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From page 279... ...
Appendix F Analytical solutions for response of joints F.21 under the center of the loaded region of length LH can be employed.
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From page 280... ...
Appendix F Analytical solutions for response of joints F.22 moment release joint are calculated using equations [F.83]
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From page 281... ...
Appendix F Analytical solutions for response of joints F.23 a. surface load on two buried pipes b.
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From page 282... ...
Appendix F Analytical solutions for response of joints F.24 a. earth loads b.
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From page 283... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.1 12.5.3 STRENGTH LIMIT STATE Buried structures and tunnel liners shall be investigated for construction loads and at Strength Load Combinations I and II, as specified in Table 3.4.1-1, as follows: For metal structures: … add • joint failure For concrete structures: … add • joint failure of pipes only For thermoplastic pipe: … add • joint failure 12.5.5 Resistance Factors …
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From page 284... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.2 Table 12.5.5-1 Resistance factors for buried structures Structure Type Resistance Factor Metal Pipe, Arch, and Pipe Arch Structures Helical pipe with lock seam or fully welded seam: … • • Minimum pipe joint strength – simplified design model Minimum pipe joint strength – design using beam on spring model 0.671 Reinforced Concrete Pipe 0.67 Direct Design Method … • • Minimum pipe joint strength – simplified design model Minimum pipe joint strength – design using beam on spring model Thermoplastic Pipe 0.67 0.67 PE and PVC pipe … • • Minimum pipe joint strength – simplified design model Minimum pipe joint strength – design using beam on spring model 1 Value is that already used for longitudinal seam strength.
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From page 285... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.3 12.6.2 Service Limit State … add 12.6.2.2 Settlement 12.6.2.2.1 General • The effect of longitudinal differential settlement on structural requirements of joints shall be determined as specified in Article 12.6.2.2.2.
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From page 286... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.4 12.15 DESIGN OF PIPE JOINTS 12.15.1 Moment release and moment transfer joints I
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From page 287... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.5 12.15.4 Capacity to accommodate shear and rotation The joint shall accommodate deformations associated with longitudinal differential settlement.
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From page 288... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.6 W for 0 = width of load transverse to pipe axis (ft, m)
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From page 289... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.7 v = ቚ0.5 െ ଷሺL0LLDF .Hሻ଼LP ቚ Design value of rotation across the joint is j-d = 180 గ ሼ0.25 WE ୩౩ౢ LP OD+ ୵ PL ୰ ୩౩ౢ LPయ OD ሽ (degrees)
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From page 290... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.8 Design values for shear force and bending moment across a moment transfer joint are: Vj-d = 0.154 WE + ୵ PL v LబାLLDF H (lbf, kN)
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From page 291... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.9 12.15.7 Beam-on-Elastic-Spring Analysis 12.15.7.1 Geometry Finite element analysis is performed using any conventional structural analysis program, with the buried pipes and their joints represented by a series of beam elements, Figure 12.15.7.1.
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From page 292... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.10 EIpipe = Epipe π (OD4-ID4)
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From page 293... ...
Appendix G Draft changes to AASHTO LFRD Bridge Design Specifications G.11 Spring stiffness used under each node in the finite element analysis has units of force per unit deformation.
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From page 294... ...
Appendix H Joint testing frame H.1 Appendix H Joint testing frame for measuring the structural capacity of joints.
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From page 295... ...
Appendix H Joint testing frame H.2 than unity (reductions in circumferential bending moment relative to those generated in a D-load test at a specific value of vertical applied force)
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From page 296... ...
Appendix H Joint testing frame H.3 ends of the two halves of the test frame (which both rest on the laboratory floor) , produces some rotation and moment in addition to the shear force which is applied.
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From page 297... ...
Appendix H Joint testing frame H.4 - The moment versus rotation characteristics of the gasketted bell and spigot joint in the PVC pipe shown in Figure H.14 are rather complex, with various changes in stiffness; this is interpreted as being associated with stick-slip characteristics of the gasket distorting, then sliding inside the bell, in repeated cycles (stiffness is higher when the gasket is distorting, and it is reduced during a period of sliding)
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From page 298... ...
Appendix H Joint testing frame H.5 Table H.1 Comparison of factored shear resistance to factored demand (resistance factor 0.67) Product Max.
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From page 299... ...
Appendix H Joint testing frame H.6 Figure H.1 Plan view of the half of the loading frame anchored to the test floor; the other half is similar, but without steel supports anchoring the frame to the floor.
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From page 300... ...
Appendix H Joint testing frame H.7 Figure H.2 Elevation view looking at one end of the loading frame; frame designed for pipes 24 inch to 60 inch internal diameter.
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From page 301... ...
Appendix H Joint testing frame H.8 Figure H.3 Side view of the half of the frame anchored to the floor.
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From page 302... ...
Appendix H Joint testing frame H.9 Figure H.4 Test frame in position for shear force testing; this arrangement shows additional longitudinal ties connecting the top corners of the end frames; these ties carry end reactions when sealing plates cover the pipe ends, these are tied to the end frames, and pipe has internal pressure or vacuum (future project)
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From page 303... ...
Appendix H Joint testing frame H.10 c Figure H.6 Loading system used to apply shear force (2000 kN actuator restrained by reaction frame anchored to the rock below; actuator fitted with 200 kN load cell)
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From page 304... ...
Appendix H Joint testing frame H.11 Figure H.7 Detail of connection between the two frames; the left hand frame is anchored to the floor of the laboratory; for moment (or rotation) testing, the two parts are connected by a hinge pin at the centre, and the actuator is used to hold the other end of the right hand frame; for shear testing, the hinge pin is removed, and the other end of the right hand frame is supported on a removable timber block.
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From page 305... ...
Appendix H Joint testing frame H.12 Figure H.10 Instrumentation used during shear testing of the corrugated metal pipe. Figure H.11 Pin inserted for moment and rotation testing of the PVC pipe.
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From page 306... ...
Appendix H Joint testing frame H.13 Figure H.14 Moment versus frame rotation for PVC pipe (1 kN.m = 737 ft.lb)
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From page 307... ...
Appendix H Joint testing frame H.14 Figure H.15 Axial movements between the crowns and inverts of the two pipe ends for the corrugated steel pipe during articulation testing; shown versus uncorrected moment (1 mm = 0.04 in.; 1 kN.m = 737 ft.lb)
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From page 308... ...
Appendix H Joint testing frame H.15 Figure H.16 Moment versus rotation for corrugated steel pipe; rotation based on frame movement and rotation between the pipe ends at the joint (measurements shown on Figure H.15)
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From page 309... ...
Appendix H Joint testing frame H.16 Figure H.17 Uncorrected moment versus change in diameter for corrugated steel pipe (1 kN.m = 737 ft.lb)
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From page 310... ...
Appendix H Joint testing frame H.17 Figure H.18 Shear force versus stroke for PVC, corrugated steel and reinforced concrete pipes.
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From page 311... ...
Appendix I Flexural rigidity of flexible pipes I.1 Appendix I Flexural Rigidity of Flexible Pipes Contents Introduction ......................................................................................................................... 1 Flexural rigidity of Corrugated Steel Pipe ..........................................................................
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From page 312... ...
Appendix I Flexural rigidity of flexible pipes I.2 effective I value for any pipe, the corrugation profile (Figure I.1a) is modeled as a straight section with an effective thickness, teff (Figure I.1b)
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From page 313... ...
Appendix I Flexural rigidity of flexible pipes I.3 Figure I.2 Mathematical models of the corrugated section Figure I.3 Mathematical model of discretized element i. The following variables are used in the derivation of an effective thickness.
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From page 314... ...
Appendix I Flexural rigidity of flexible pipes I.4 F = Small force per unit length into the page applied axially to the corrugation. (force/length)
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From page 315... ...
Appendix I Flexural rigidity of flexible pipes I.5 ൌ ܯܮܧܫ ܨ ܮଶsin ߚ 2ܧܫ (I.4) The horizontal deflection of element i is caused four kinds of movement.
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From page 316... ...
Appendix I Flexural rigidity of flexible pipes I.6 ݐ ൌ ܨܼ4ܧ∆ (I.10) This equation can be used to determine the effective thickness of an equivalent straight section that has the same amount of axial displacement as the original corrugation when subjected to axial load F
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From page 317... ...
Appendix I Flexural rigidity of flexible pipes I.7 Pipe) used in this project was measured, as described in Appendix C
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From page 318... ...
Appendix I Flexural rigidity of flexible pipes I.8 Many pipes consist of helically wrapped corrugation. Helix angles can vary from 6 degrees to 33 degrees for small diameter pipes (Havens 1993)
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From page 319... ...
Appendix I Flexural rigidity of flexible pipes I.9 A = Cross-sectional area of the corrugation (length2) A1 = Area of section 1 in Figure I.2b, per unit width into the page (length2 / length into the page)
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From page 320... ...
Appendix I Flexural rigidity of flexible pipes I.10 longitudinally to the pipe (<1%)
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From page 321... ...
Appendix I Flexural rigidity of flexible pipes I.11 The relationship in Equation I.21 exists between the reduced cross-section in Figure I.2b and the crosssection with an effective thickness teff. Note that Aeff , A1 and A2 are the areas of section 1 and 2 into the length of the page.
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From page 322... ...
Appendix I Flexural rigidity of flexible pipes I.12 CONCLUSIONS Methods are presented for determining the flexural rigidity of standard corrugated sections of corrugated steel pipes and HDPE pipes. The corrugated steel pipe method can be used with many of the currently manufactured corrugated steel pipe culverts.
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From page 323... ...
Appendix J Finite element analyses J.1 Finite element analyses CONTENTS Development of Beam-on-Springs Model using Experimental Data ............................................... 2 Development of FE Based Beam-on-Springs Model Using the Laboratory Test Data.................
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From page 324... ...
Appendix J Finite element analyses J.2 Contours of stress and displacement ........................................................................................ 52 Comparison of analyses using "expected" soil moduli with experimental data .......................
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From page 325... ...
Appendix J Finite element analyses J.3 This is representative of the test setup.
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From page 326... ...
Appendix J Finite element analyses J.4 However, the flexibility of the HDPE and CMP culvert pipes causes vertical displacements to be different at each measurement location. This is problematic because a simple beam-on-springs model assumes that there is only one measurement of vertical displacement at any location along the beam elements.
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From page 327... ...
Appendix J Finite element analyses J.5 predicted by a simple beam-on-springs model. Attempts were made to use beam-on-springs modeling to match the invert data, but modeling always predicted the maximum vertical displacement directly beneath the loading.
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From page 328... ...
Appendix J Finite element analyses J.6 Figure J.3 The effect of LLDF on the calculated vertical displacements for the RC laboratory test pipe with loading centered on the joint (1 in.
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From page 329... ...
Appendix J Finite element analyses J.7 Table J.1 Modeling data for the laboratory test pipes.
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From page 330... ...
Appendix J Finite element analyses J.8 ground. The circular shape of the pipe culverts may affect how the soil vertically supports the culvert.
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From page 331... ...
Appendix J Finite element analyses J.9 of ksi. It should be noted that values in this table cannot be compared between the different pipes because the effect of the pipe diameter is not accounted for.
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From page 332... ...
Appendix J Finite element analyses J.10 calculated parameters show better agreement with each other when then 0.7 reduction factor is used for the flexible pipes. Table J.3 Comparison of back‐calculated soil stiffness parameters (Es and ks1) with and without the 0.7 factor proposed for flexible pipes. Outliers identified in Table J.2 are ignored. (1 psi = 6.9 kPa; 1 pci = 0.27 MN/m3)
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From page 333... ...
Appendix J Finite element analyses J.11 Table J.4 Back-calculated soil stiffness parameters (Es and ks1) for all laboratory tests using the Biot, Vesic, and Terzaghi methods (1 ksi = 6.9 MPa; 1 pci = 0.27 MN/m3; 1 ft = 0.30 m)
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From page 334... ...
Appendix J Finite element analyses J.12 a) Back-calculated Es values from the Biot and Vesic models b)
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From page 335... ...
Appendix J Finite element analyses J.13 average of the back-calculated values from the Vesic and Terzaghi methods show the best agreement with the expected value. The Terzaghi method is the most accurate and yields backcalculated values that have the smallest range.
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From page 336... ...
Appendix J Finite element analyses J.14 The shear stiffness is dependent upon E, Ap, and ν. The only measured joint stiffness parameter is the flexural stiffness of the concrete pipe joint.
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From page 337... ...
Appendix J Finite element analyses J.15 Figure J.5 Theoretical versus measured vertical movement of the RC laboratory test pipe at 2 ft burial and load directly above the joint (1 ft = 0.3 m) Figure J.6 Theoretical versus measured vertical movement of the RC laboratory test pipe at 2 ft burial and load offset 3 ft north of joint (1 ft = 0.3 m)
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From page 338... ...
Appendix J Finite element analyses J.16 Figure J.7 Theoretical versus measured vertical movement of the RC laboratory test pipe at 2 ft burial and load offset 3 ft south of joint (1 ft = 0.3 m) Figure J.8 Theoretical versus measured vertical movement of the RC laboratory test pipe at 4 ft burial and load directly above the joint (1 ft = 0.3 m)
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From page 339... ...
Appendix J Finite element analyses J.17 Figure J.9 Theoretical versus measured vertical movement of the RC laboratory test pipe at 4 ft burial and load offset 3 ft north of joint (1 ft = 0.3 m) Figure J.10 Theoretical versus measured vertical movement of the RC laboratory test pipe at 4 ft burial and load offset 3 ft south of joint (1 ft = 0.3 m)
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From page 340... ...
Appendix J Finite element analyses J.18 Figure J.11 Theoretical versus measured vertical movement of the CMP laboratory test pipe at 2 ft burial and load directly above the joint (1 ft = 0.3 m) Figure J.12 Theoretical versus measured vertical movement of the CMP laboratory test pipe at 2 ft burial and load offset 3 north ft of joint (1 ft = 0.3 m)
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From page 341... ...
Appendix J Finite element analyses J.19 Figure J.13 Theoretical versus measured vertical movement of the CMP laboratory test pipe at 2 ft burial and load offset 3 ft south of joint (1 ft = 0.3 m) Figure J.14 Theoretical versus measured vertical movement of the CMP laboratory test pipe at 4 ft burial and load directly above the joint (1 ft = 0.3 m)
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From page 342... ...
Appendix J Finite element analyses J.20 Figure J.15 Theoretical versus measured vertical movement of the CMP laboratory test pipe at 4 ft burial and load offset 3 ft north of joint (1 ft = 0.3 m) Figure J.16 Theoretical versus measured vertical movement of the CMP laboratory test pipe at 4 ft burial and load offset 3 ft south of joint (1 ft = 0.3 m)
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From page 343... ...
Appendix J Finite element analyses J.21 Figure J.17 Theoretical versus measured vertical movement of the HDPE laboratory test pipe at 2 ft burial and load directly above the joint (1 ft = 0.3 m) Figure J.18 Theoretical versus measured vertical movement of the HDPE laboratory test pipe at 2 ft burial and load offset 3 ft north of joint (1 ft = 0.3 m)
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From page 344... ...
Appendix J Finite element analyses J.22 Figure J.19 Theoretical versus measured vertical movement of the HDPE laboratory test pipe at 2 ft burial and load offset 3 ft south of joint (1 ft = 0.3 m) Figure J.20 Theoretical versus measured vertical movement of the HDPE laboratory test pipe at 4 ft burial and load directly above the joint (1 ft = 0.3 m)
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From page 345... ...
Appendix J Finite element analyses J.23 Figure J.21 Theoretical versus measured vertical movement of the HDPE laboratory test pipe at 4 ft burial and load offset 3 ft north of joint (1 ft = 0.3 m) Figure J.22 Theoretical versus measured vertical movement of the HDPE laboratory test pipe at 4 ft burial and load offset 3 ft south of joint (1 ft = 0.3 m)
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From page 346... ...
Appendix J Finite element analyses J.24 Table J.6 Measured versus theoretical shear displacements for all 18 laboratory tests (1 in = 2.54 cm; 1 ft = 0.3 m) Shear displacement across the pipe joint 2 ft burial depth 4 ft burial depth No loading offset Loading offset 3 ft North Loading offset 3 ft South No loading offset Loading offset 3 ft North Loading offset 3 ft South RC Measured (in.)
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From page 347... ...
Appendix J Finite element analyses J.25 Table J.7 Measured versus theoretical joint rotations for all 18 laboratory tests (1 ft = 0.3 m) Relative rotation of connected pipes 2 ft burial depth 4 ft burial depth No Loading Offset Loading Offset 3 ft North Loading Offset 3 ft South No Loading Offset Loading Offset 3 ft North Loading Offset 3 ft South RC Measured (deg)
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From page 348... ...
Appendix J Finite element analyses J.26 Evaluation of the Model using Field Test Data The most interesting challenge in getting the beam-on-springs model to match the field test data is the large number of unknowns including soil condition, pipe and joint deterioration, and the effect of the road surface. There are two sets of data that are relied on when performing the beam-on-springs analysis.
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From page 349... ...
Appendix J Finite element analyses J.27 Table J.8 Modeling data for the field test pipes (1 in.
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From page 350... ...
Appendix J Finite element analyses J.28 ks1 (pci)
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From page 351... ...
Appendix J Finite element analyses J.29 Some information learned from the laboratory tests sheds light on the accuracy of the shear displacements. Laboratory tests showed that the vertical displacement at the crown and invert in flexible pipes is too affected by local bending to effectively match the results from a beam-on-springs model.
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From page 352... ...
Appendix J Finite element analyses J.30 seem to be greatly affected by the additional bending at the crown that is observed in the flexible laboratory test pipes. This is expected, and is shown by the fact that the predicted shear displacements are smaller than the measured shear displacements for all of the flexible test pipes.
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From page 353... ...
Appendix J Finite element analyses J.31 Table J.10 Relative rotation of connected pipes for all in-service culvert tests, loaded with the truck's rear wheels. Relative Rotation of Connected Pipes (radians)
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From page 354... ...
Appendix J Finite element analyses J.32 model. In the RC pipe model, pipe segments are 5 ft (1.5 m)
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From page 355... ...
Appendix J Finite element analyses J.33 Figure J.23 Continued c. Load placed 10 ft from the joint d.
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From page 356... ...
Appendix J Finite element analyses J.34 a. Load placed 10 ft from joint b.
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From page 357... ...
Appendix J Finite element analyses J.35 Figure J.25 Springs beneath a buried RC pipe culvert system The calibration of the beam-on-springs model is performed using a spring spacing of 3 in.
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From page 358... ...
Appendix J Finite element analyses J.36 a. Effect of spring spacing on the flexible HDPE model b.
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From page 359... ...
Appendix J Finite element analyses J.37 s. These spring stiffness values cover most pipe diameters up to 5 ft (1.5 m)
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From page 360... ...
Appendix J Finite element analyses J.38 more than 9% when compared to the 3 in.
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From page 361... ...
Appendix J Finite element analyses J.39 indicates that soil stiffness values obtained from the laboratory tests can yield conservative results when used in design. The way in which surface loading spreads as it attenuates through the soil was investigated.
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From page 362... ...
Appendix J Finite element analyses J.40 k = Individual spring stiffness beneath the modeled beam (force/length) ks = Modulus of subgrade reaction of the soil (force/length3)
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From page 363... ...
Appendix J Finite element analyses J.41 Figure J.28 Illustration of load spreading represented by Equation J.3 Step #2: Determine Pipe Lengths in the Model The purpose of this model is to determine and examine movement at a particular joint. This section provides guidance as to how far the pipes should extend on either side of the joint.
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From page 364... ...
Appendix J Finite element analyses J.42 2. Spring spacing should not be greater than 15 inches (0.38 m)
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From page 365... ...
Appendix J Finite element analyses J.43 Ap values is much more complex. Appendix I provides guidelines for calculating Ip values for CMP and HDPE pipes. Calculation of Ap for HDPE pipes is also presented in Appendix I. Calculation of Ap for CMP pipes is presented in Equation J.10. ܣ,௧ ൌ ߨ4 ൫݀ ଶ െ ݀ଶ൯ (J.8)
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From page 366... ...
Appendix J Finite element analyses J.44 the beams and springs are modeled, the loading should be applied to the model. Then let the software analyze the model and calculate joint rotations and shear displacement at the joint.
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From page 367... ...
Appendix J Finite element analyses J.45 Elastic soil modeling has been used in these calculations of pipe response under factored service load. Additional work will be performed in Phase 2 of the project to - examine the choice of soil parameters, and to determine whether elasto-plastic soil response needs to be modeled to improve calculations - examine jointed pipe response to earth loads - model the band connector on the corrugated steel pipes and examine performance of the analysis in calculations of measured deformation and strain - examine the response of the lined-corrugated HDPE test pipe - examine the pipes to be tested in Phase 2 of the project Problem description Given the geometry of the bell and spigot joint employed in the reinforced concrete test pipes, and the nature of jointed pipe response to surface loading, three dimensional analysis has been developed.
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From page 368... ...
Appendix J Finite element analyses J.46 (a) Lateral view (b)
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From page 369... ...
Appendix J Finite element analyses J.47 (b) Frontal view Figure J.30 Schematic of the good burial condition Modeling Program used The general purpose Finite Element code ABAQUS version 6.7 was used to perform the numerical analyses.
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From page 370... ...
Appendix J Finite element analyses J.48 Figure J.30 Geometry of the pipe Figure J.32 Geometry of the gasket Figure J.33 Geometry of the bell-gasket-spigot assembly
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From page 371... ...
Appendix J Finite element analyses J.49 Figure J.34 Geometry of the soil for the poor burial condition at 4 ft of cover Figure J.35 Geometry of the soil for the good burial condition Figure J.36 Assembly for the poor burial condition at 4 ft of cover
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From page 372... ...
Appendix J Finite element analyses J.50 Material properties As mentioned before, the material properties for the elements employed in the simulations were defined as linear elastic, characterized by Elastic Modulus and Poisson's Ratio. Five materials were defined as presented and described in Table J.14.
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From page 373... ...
Appendix J Finite element analyses J.51 experiments. While maximum surface load of 100 kN (22,400 lbf)
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From page 374... ...
Appendix J Finite element analyses J.52 Mesh design Due to the complexity of the geometry, tetrahedral elements were employed to discretize the model. These elements feature quadratic displacements to provide approximations better than those of the four node tetrahedral element (where displacement would be linear)
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From page 375... ...
Appendix J Finite element analyses J.53 Figure J.39 Vertical displacement for the poor burial condition at 4 ft of cover (1m = 39.4 in.) Figure J.40 Stress σyy for the poor burial condition at 4 ft of cover (1000 Pa = 0.14 psi)
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From page 376... ...
Appendix J Finite element analyses J.54 Figure J.41 Stress σxx for the poor burial condition at 4 ft of cover (1000 Pa = 0.14 psi) Figure J.42 Vertical displacement for the poor burial condition at 2 ft of cover (1m = 39.4 in.)
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From page 377... ...
Appendix J Finite element analyses J.55 Figure J.43 Stress σyy for the poor burial condition at 2 ft of cover (1000 Pa = 0.14 psi) Figure J.44 Stress σxx for the poor burial condition at 2 ft of cover (1000 Pa = 0.14 psi)
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From page 378... ...
Appendix J Finite element analyses J.56 Figure J.45 Vertical displacement for the good burial condition at 2 ft of cover (1m = 39.4 in.) Figure J.46 Stress σyy for the good burial condition at 4 ft of cover (1000 Pa = 0.14 psi)
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From page 379... ...
Appendix J Finite element analyses J.57 Figure J.47 Stress σxx for the good burial condition at 4 ft of cover (1000 Pa = 0.14 psi) Figure J.48 Vertical displacement for the good burial condition at 2 ft of cover (1m = 39.4 in.)
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From page 380... ...
Appendix J Finite element analyses J.58 Figure J.49 Stress σyy for the good burial condition at 2 ft of cover (1000 Pa = 0.14 psi) Figure J.50 Stress σxx for the good burial condition at 2 ft of cover (1000 Pa = 0.14 psi)
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From page 381... ...
Appendix J Finite element analyses J.59 Figure J.51. Comparison points in the bell and spigot Table J.15 Comparison of experimental results and calculations for the poor burial case at 4 ft Point ID Location/description Experimental result με Simulation result με 1 Spigot region, inside the pipe, Crown location, hoop direction 7 5 2 Spigot region, inside the pipe, Invert location, hoop direction 6 5 3 Spigot region, inside the pipe, Springline location, hoop direction -4 -5 4 Bell region, inside the pipe, Crown location, hoop direction 12 11 5 Bell region, inside the pipe, Invert location, hoop direction 21 10 6 Bell region, inside the pipe, Springline location, hoop direction -14 -13
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From page 382... ...
Appendix J Finite element analyses J.60 Table J.16 Comparison of experimental results and calculations for the poor burial case at 2 ft Point ID Location/description Experimental result με Simulation result με 1 Spigot region, inside the pipe, Crown location, hoop direction 14 13 2 Spigot region, inside the pipe, Invert location, hoop direction 12 13 3 Spigot region, inside the pipe, Springline location, hoop direction -12 -11 4 Bell region, inside the pipe, Crown location, hoop direction 38 34 5 Bell region, inside the pipe, Invert location, hoop direction 40 26 6 Bell region, inside the pipe, Springline location, hoop direction -35 -34 Table J.17 Comparison of experimental results and calculations for the good burial case at 4 ft Point ID Location/description Experimental result με Simulation result με 1 Spigot region, inside the pipe, Crown location, hoop direction 7 7 2 Spigot region, inside the pipe, Invert location, hoop direction 3 6 3 Spigot region, inside the pipe, Springline location, hoop direction -5 -7 4 Bell region, inside the pipe, Crown location, hoop direction 3 13 5 Bell region, inside the pipe, Invert location, hoop direction 4 10 6 Bell region, inside the pipe, Springline location, hoop direction -10 -14
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From page 383... ...
Appendix J Finite element analyses J.61 Table J.18 Comparison of experimental results and calculations for the good burial case at 2 ft Point ID Location/description Experimental result με Simulation result με 1 Spigot region, inside the pipe, Crown location, hoop direction 10 14 2 Spigot region, inside the pipe, Invert location, hoop direction 8 12 3 Spigot region, inside the pipe, Springline location, hoop direction -8 -13 4 Bell region, inside the pipe, Crown location, hoop direction 13 36 5 Bell region, inside the pipe, Invert location, hoop direction 12 23 6 Bell region, inside the pipe, Springline location, hoop direction -25 -32 Tables J.15 and J.16 providing results for the poor burial condition indicate that the simulations at both burial depths provide very effective estimates of the local strain values measured in the experiments; not only are the patterns of strain captured in the analysis, but most magnitudes of these strains were close. Only strains calculated at point 5 (circumferential strain on the inside of the bell at the invert)
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From page 384... ...
Appendix J Finite element analyses J.62 Table J.19 Vertical displacements in the joint at the crown 4 ft poor burial Bell– analysis -0.15 mm Spigot– analysis -0.15 mm Bell – test -1.2 mm Spigot – test -1.3 mm 2 ft poor burial Bell – analysis -0.27 mm Spigot – analysis -0.23 mm Bell – test -0.93 mm Spigot – test -1.1 mm 4 ft good burial Bell– analysis -0.14 mm Spigot– analysis -0.13 mm Bell – test -0.37 mm Spigot – test -0.38 mm 2 ft good burial Bell– analysis -0.21 mm Spigot– analysis -0.18 mm Bell – test -0.38 mm Spigot – test -0.39 mm
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From page 385... ...
Appendix J Finite element analyses J.63 Table J.19 provides calculated values of vertical deflection in the bell and spigot of the central joint (at the pipe crown)
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From page 386... ...
Appendix J Finite element analyses J.64 Effect of gasket modulus Table J.21 provides values of pipe strain calculated after changing the characteristics of the gasket (and thereby the resistance to rotation across the joint)
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From page 387... ...
Appendix J Finite element analyses J.65 Table J.21 Strains at 4 ft of cover and poor burial Test 4 ft of Central joint με Simulation Central loading με Harder Gasket με Softer Gasket με S06-Cro-Ins-θ 7 5 5 5 S06-Sp1-Ins-θ -4 -5 -5 -6 S06-Inv-Ins-θ 6 5 6 5 S06-Sp2-Ins-θ N/A -5 5 -6 S10-Cro-Ins-θ 12 11 11 11 S10-Sp1-Ins-θ -14 -13 -13 -13 S10-Inv -Ins-θ 21 10 10 10 S10-Sp2-Ins-θ -12 -13 -13 -13 Table J.22 Strains at 2 ft of cover and poor burial Test 2 ft of Central joint με Simulation Central loading με Harder Gasket με Softer Gasket με S06-Cro-Ins-θ 14 13 12 13 S06-Sp1-Ins-θ -12 -11 -11 -12 S06-Inv-Ins-θ 12 13 14 12 S06-Sp2-Ins-θ N/A -11 -11 -12 S10-Cro-Ins-θ 38 34 34 34 S10-Sp1-Ins-θ -35 -34 -35 -34 S10-Inv -Ins-θ 40 26 26 27 S10-Sp2-Ins-θ -33 -34 -35 -34
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Key Terms
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