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22-20 COPY NO 4753500 DESIGN OF ROADSIDE BARRIER SYSTEMS PLACED ON MSE RETAINING WALLS REVISED FINAL REPORT Prepared for National Cooperative Highway Research Program Transportation Research Board National Research Council TRANSPORTATION RESEARCH BOARD NAS-NRC PRIVILEGED DOCUMENT This report, not released for publication, is furnished only for review to members of or participants in the work of the National Cooperative Highway Research Program (NCHRP) It is to be regarded as fully privileged, and dissemination of the information included herein must be approved by NCHRP Roger P Bligh, Jean-Louis Briaud, Kang Mi Kim and Akram Abu-Odeh Texas Transportation Institute College Station, Texas TTI Project 475350 November 2009 ACKNOWLEDGMENT OF SPONSORSHIP This work was sponsored by the American Association of State Highway and Transportation Officials, in cooperation with the Federal Highway Administration, and was conducted in the National Cooperative Highway Research Program, which is administered by the Transportation Research Board of the National Research Council DISCLAIMER This is an uncorrected draft as submitted by the research agency The opinions and conclusions expressed or implied in the report are those of the research agency They are not necessarily those of the Transportation Research Board, the National Research Council, the Federal Highway Administration, the American Association of State Highway and Transportation Officials, or the individual states participating in the National Cooperative Highway Research Program REVISED FINAL REPORT NCHRP PROJECT 22-20 “DESIGN OF ROADSIDE BARRIER SYSTEMS PLACED ON MSE RETAINING WALLS” Prepared for National Cooperative Highway Research Program Transportation Research Board National Research Council Transportation Research Board NAS-NRC Privileged Document by Roger P Bligh Jean-Louis Briaud Kang Mi Kim and Akram Abu-Odeh Research Foundation Project 475350 Texas Transportation Institute Texas A&M University System College Station, Texas November 2009 TABLE OF CONTENTS Page TABLE OF CONTENTS v LIST OF FIGURES ix LIST OF TABLES xvii ABSTRACT 1 1 INTRODUCTION 3 1.1 1.2 1.3 1.4 2 STATE OF THE PRACTICE 7 2.1 2.1.1 2.1.2 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 3 RESEARCH PROBLEM STATEMENT 3 RESEARCH OBJECTIVE 3 RESEARCH APPROACH 3 REPORT SCOPE 5 DESIGN OF MSE WALL 7 External Stability 8 Internal Stability 9 DESIGN OF BARRIER 11 Background of Barrier Crash Testing Guidelines 11 Background of Barrier Design Loads 12 Barrier Design Practice 17 DESIGN OF THE BARRIER ON TOP OF THE MSE WALL 23 Design of MSE Wall for Barrier Impact 23 Comparison between ASD and LRFD 23 Previous Crash Test of Barrier on Edge of MSE Wall 24 SURVEY OF STATE DOTs 26 MSE Walls 27 Barriers 28 Barrier Connection to Wall/Pavement 31 Design 36 Performance 38 BARRIER STABILITY STUDY 41 DESCRIPTION OF BARRIER 42 3.1 3.2 STATIC ANALYSES AND STATIC TEST 43 3.2.1 Static Analytical Solution 43 3.2.2 Quasi-Static Finite Element Analysis 44 3.2.3 Full-Scale Static Test on Barrier 46 3.3 DYNAMIC ANALYSES AND DYNAMIC TEST 49 v TABLE OF CONTENTS (CONTINUED) Page 3.3.1 Full-Scale Dynamic Test (Bogie Test) on Barrier 49 3.3.2 Dynamic Analytical Simple Solution 60 3.3.3 Dynamic Finite Element Analysis 63 3.4 CONCLUSIONS 64 4 REINFORCEMENT PULLOUT TESTS 67 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5 ft HIGH MSE WALL AND BARRIER STUDY 83 5.1 5.1.1 5.1.2 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.4 5.5 6 RATE OF LOADING 67 SATURATION .67 FINES 67 REINFORCEMENT 70 NUMBER OF TESTS 70 PROCEDURE (SOIL INSTALLATION, RATE OF LOADING, TESTING) 71 RESULTS AND CONCLUSION 74 FT HIGH MSE WALL AND BARRIER TEST PLAN 83 Calculation of MSE Wall Capacity 84 Calculation of Barrier Capacity 85 FINITE ELEMENT ANALYSIS 87 Modeling Methodology 87 Finite Element Model: Boundary Conditions 98 Simulated Impact into Barrier Placed on MSE Wall with ft Long Strip 101 Simulated Impact into Barrier Placed on MSE Wall with 16 ft Long Strip 110 BOGIE TEST 119 FT High MSE Wall Construction and Test Installation .119 Bogie Test 1: New Jersey Barrier with 16 ft Strips 123 Bogie Test 2: Vertical Concrete Barrier with ft Bar Mats 142 Bogie Test 3: Vertical Concrete Barrier with ft Strips 162 Bogie Test 4: Vertical Concrete Barrier with 16 ft Strips .179 Damage of Moment Slab after Test .196 SUMMARY OF BOGIE TESTS 200 COMPARISON OF TEST AND NUMERICAL SIMULATION 202 10 FT HIGH MSE WALL AND BARRIER STUDY 211 10 FT HIGH MSE WALL AND BARRIER STUDY DESCRIPTION 211 6.1 6.1.1 Calculation of MSE Wall Capacity 211 6.1.2 Calculation of Barrier Capacity .212 6.2 FINITE ELEMENT ANALYSIS 213 6.2.1 Barrier Damage and Displacement 218 6.2.2 Loads and Displacements in Reinforcement Strips .221 vi TABLE OF CONTENTS (CONTINUED) Page 6.2.3 Panel Analysis 225 6.3 TL-3 CRASH TEST 226 6.3.1 10 ft High MSE Wall Construction and Test Installation .226 6.3.2 Impact Conditions 228 6.3.3 Test Vehicle 228 6.3.4 Test Description .235 6.3.5 Test Article and Vehicle Damage 235 6.3.6 Occupant Risk 235 6.3.7 Data from Accelerometers 241 6.3.8 Photographic Instrumentation 245 6.3.9 Load on the Strip from Strain Gages 246 6.3.10 Panel analysis 249 6.3.11 Other Instrumentations 249 6.3.12 Damage of Moment Slab after Test .250 6.4 CONCLUSIONS .251 6.5 COMPARISON OF TEST AND SIMULATION 253 7 DESIGN GUIDELINES 261 7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.3 7.4 7.4.1 7.4.2 8 GUIDELINES FOR THE BARRIER 261 Sliding of the Barrier .262 Overturning of the Barrier .262 Rupture of the Coping in Bending 262 GUIDELINES FOR THE WALL REINFORCEMENT 264 Pullout of the Wall Reinforcement 264 Rupture of the Wall Reinforcement 267 GUIDELINES FOR THE WALL PANEL 269 DATA TO BACK-UP GUIDELINES 270 Barrier 270 Wall Reinforcement .277 SUMMARY AND CONCLUSION 282 8.1 SUMMARY OF CHAPTERS 282 8.1.1 Chapter 282 8.1.2 Chapter 282 8.1.3 Chapter 282 8.1.4 Chapter 283 8.1.5 Chapter 283 8.1.6 Chapter 283 8.1.7 Chapter 284 8.2 CONCLUSION 284 vii TABLE OF CONTENTS (CONTINUED) Page REFERENCES 287 APPENDIX A: DESIGN OF MSE WALL ………………………………………………A-1 APPENDIX B: STATE-OF-PRACTICE SURVEY ………………………………………B-1 APPENDIX C: DETAILED DRAWING OF MSE WALL FOR BOGIE TEST …………C-1 APPENDIX D: BOGIE TEST MSE WALL CONSTRUCTION PROCEDURE ………D-1 APPENDIX E: DETAILED DRAWING OF MSE WALL FOR TL-3 TEST ……………E-1 APPENDIX F: TL-3 MSE WALL CONSTRUCTION PROCEDURE …………………F-1 APPENDIX G: CRASH TEST VEHICLE PROPERTIES AND INFORMATION ……G-1 APPENDIX H: CRASH TEST SEQUENTIAL PHOTOGRAPHS ………………………H-1 APPENDIX I: AASHTO LRFD FORMAT DESIGN GUIDELINE APPENDIX J: EXAMPLE OF DESIGN GUIDELINE viii ……………………I-1 …………………………………J-1 LIST OF FIGURES Page Figure 2.1.1 Figure 2.1.2 Figure 2.1.3 Figure 2.1.4 Figure 2.1.5 Figure 2.2.1 Figure 2.2.2 Figure 2.2.3 Figure 2.2.4 Figure 2.2.5 Figure 2.2.6 Figure 2.2.7 Figure 2.2.8 Figure 2.3.1 Figure 2.3.2 Figure 2.3.3 Figure 2.4.1 Figure 2.4.2 Figure 2.4.3 Figure 2.4.4 Figure 2.4.5 Figure 2.4.6 Figure 2.4.7 Figure 2.4.8 Figure 2.4.9 Figure 2.4.10 Figure 2.4.11 Figure 2.4.12 Figure 2.4.13 Figure 2.4.14 Figure 2.4.15 Figure 2.4.16 Figure 2.4.17 Figure 2.4.18 Figure 2.4.19 Figure 2.4.20 Figure 2.4.21 Figure 2.4.22 Principal elements of MSE wall (4) 7 Construction of MSE wall (4) 7 External stability considerations (4) 8 Internal stability considerations (2) 9 Default values for the pullout friction factor, F * (AASHTO LRFD Figure 11.10.6.3.2-1) (2) 10 Instrumented wall (12) 14 Magnitude and location of average resultant force 15 Distribution of contact pressure (12) 16 Longitudinal distribution for initial and final impacts 16 Idealized span based failure mechanisms (15) 18 Idealized mid-span failure mechanism (2) 20 Failure mechanism at barrier joint or end (2) (17) 21 Typical failure pattern for safety shaped barriers (17) 22 Distribution of stress from concentrated horizontal loads (AASHTO LRFD Figure 3.11.6.3-2 a) (2) 23 Precast barrier and coping with cast-in-place slab 25 Barrier damage after RECO crash test (18) 26 Type of reinforcement in MSE walls (Question 1) 28 Type of facing panels in MSE walls (Question 2) 28 Type of Facing Panel Connection (Question 3) 28 Percentage of states using different barrier categories (Question 4) 29 Category of barriers (Question 4) 30 Type of guardrail (Question 5) 30 Type of bridge rail (Question 6) 30 Precast barrier vs cast-in-place barrier (Question 7) 31 Use of different pavement types on MSE walls (Question 9) 31 Pavement type (Question 9) 32 Continuous or jointed barrier slab/footing (ACP, Question 13) 33 Barrier flush or offset from face of wall (ACP, Question 13) 33 Wall panel coped/recessed (ACP, Question 17) 33 Lateral and vertical barrier movement connected or disconnected/Isolated from wall panel (ACP, Question 19) 33 Continuous or jointed barrier/slab footing (RCP, Question 22) 35 Flush or offset barrier from face of wall (RCP, Question 24) 35 Wall panel coped/recessed (RCP, Question 26) 36 Lateral and vertical barrier movement connected or disconnected/Isolated from wall panel (RCP, Question 28) 36 Integrally poured or doweled into pavement (RCP, Question 29) 36 NHCRP Report 350 test level 37 Use of AASHTO LRFD Bridge Specification for rail design (Question 32) 37 Calculation of bending moment in pavement slab due to barrier impact load (Question 38) 38 ix LIST OF FIGURES (CONTINUED) Page Figure 2.4.23 Failures of MSE walls or barriers atop MSE walls due to vehicular impact (Question 39) 39 Figure 2.4.24 Other performance issues associated with MSE walls or barriers atop MSE walls (Question 40) 39 Figure 3.2.1 Required static force to induce sliding or overturning 44 Figure 3.2.2 Quasi-static finite element model (a) at rest and (b) end of the time 45 Figure 3.2.3 Comparison of static test and finite element static model 46 Figure 3.2.4 Static test (a) beginning of test (b) end of test (note crack) 47 Figure 3.2.5 Static test installation 48 Figure 3.2.6 Results of static test of (a) D1 and (b) D2 48 Figure 3.3.1 Bogie test photo 50 Figure 3.3.2 Horizontal displacement of barrier measured from the film of the (a) 13 mph and (b) 18 mph impact test 51 Figure 3.3.3 (a) Force, (b) acceleration, (c) velocity and (d) displacement of bogie of 13 mph dynamic test 51 Figure 3.3.4 (a) Acceleration, (b) velocity, and (c) displacement of barrier of 13 mph dynamic test 52 Figure 3.3.5 (a) Acceleration, (b) velocity, and (c) displacement of moment slab of 13 mph dynamic test 53 Figure 3.3.6 (a) Force, (b) acceleration, (c) velocity and (d) displacement of bogie of 18 mph dynamic test 54 Figure 3.3.7 (a) Acceleration and (b) displacement of barrier of 18 mph dynamic test 55 Figure 3.3.8 (a) Acceleration and (b) displacement of moment slab of 18 mph dynamic test 55 Figure 3.3.9 Comparison of static and dynamic overturning tests 56 Figure 3.3.10 Cracking of coping and moment slab after 18-mph impact 57 Figure 3.3.11 Cracks observed on top of moment slab after 18-mph impact 58 Figure 3.3.12 Analytical solution for sliding; (a) force, (b) acceleration, (c) velocity, and (d) displacement 61 Figure 3.3.13 Comparison of analytical simple solution and advanced solution for overturning; (a) impact force, (b) acceleration, (c) velocity, and (d) displacement 62 Figure 3.3.14 Variations of (a) h and (b) l 63 Figure 3.3.15 Finite element model for overturning at (a) at rest and (b) at impact 64 Figure 4.3.1 Grain size distribution of the sand used in the pullout experiments 68 Figure 4.3.2 Compaction curve for the sand tested 69 Figure 4.6.1 Test set-up with steel strip 72 Figure 4.6.2 Test set-up with bar mat 73 Figure 4.7.1 Load displacement curve obtained (tie back strip, unsaturated) 75 Figure 4.7.2 Load displacement curve obtained (tie back strip, saturated) 76 Figure 4.7.3 Load displacement curve obtained (bar mat) 78 Figure 4.7.4 Pullout load at failure versus time to failure for all tests 81 Figure 4.7.5 Values of apparent coefficient of friction (f*) from pullout tests (23) 81 x APPENDIX I: AASHTO LRFD FORMAT DESIGN GUIDELINE SECTION DESIGN GUIDELINES 1.1 SCOPE This section provides guidelines to design three components: the barrier-moment slab, the MSE wall reinforcement, and the wall panel The guidelines are applicable for TL-3 and TL-4 criteria as defined in Section 13 of AASHTO LRFD Bridge Design Specifications, and for inextensible MSE wall reinforcement (e.g., strips, bar mats) Depending on the design, two points of rotation are possible as shown in Figure 1.1 The point of rotation should be determined based on the interaction between the barrier coping and top of the wall panel With reference to Figure 1.1, the point of rotation should be taken as Point A if the top of the wall panel is isolated from contact with the coping by the presence of an air gap or a sufficiently compressible material The point of rotation should be taken as Point B if there is direct bearing between the bottom of the coping and the top of the wall panel or level up concrete Traffic Barrier Coping C.G Leveling pad Overburden Soil Moment Slab Panel Rotation Point, A Rotation Point, B Figure 1.1 Barrier-moment slab system for design guideline I-1 1.2 DEFINITIONS Rotation Point A—The rotation point of a barrier-moment slab system if the top of the wall panel is isolated from contact with the coping by the presence of an air gap or a sufficiently compressible material as shown in Figure 1.1 Rotation Point B—The rotation point of a barrier-moment slab system if there is direct bearing between the bottom of the coping and the top of the wall panel or level up concrete as shown in Figure 1.1 1.3 NOTATION Η point hb point hc Ld Ls l lA lB M Md Mi Mu P Pr pd Qd R t V W top γ φ φr φs σv = horizontal shear load on top of the panel (kips) = moment arm taken as the vertical distance between the point of impact of the dynamic force and the of rotation A (ft) = moment arm taken as the vertical distance between the point of impact of the dynamic force and the of rotation B (ft) = moment arm taken as the vertical distance between the point of impact of the dynamic force and the middle of the weakest section of the coping (ft) = dynamic load (kips) = static load equivalent to the dynamic impact force (kips) = vertical distance from the top of the panel to the uppermost reinforcement layer (ft) = horizontal distance from the center of gravity of the weight to the point of rotation A (ft) = horizontal distance from the center of gravity of the weight to the point of rotation B (ft) = static moment resistance to overturning of the barrier-moment slab system (kips-ft) = Ultimate moment resistance of the coping of the barrier-moment slab system in bending (kips-ft) = moment applied to the panel during impact (kips-ft) = ultimate moment resistance of the wall panel (kips-ft) = static resistance to sliding of the barrier-moment slab system (kips) = static resistance to pullout of the reinforcement (kips) = dynamic pressure diagram for pullout or rupture of the reinforcement (psf) = dynamic line load diagram for pullout or rupture of the reinforcement (lb/ft) = resistance for rupture of the reinforcement (kips) = thickness of the panel (ft) = vertical load transferred from the barrier to the panel during the impact (kips) = weight of the monolithic section of barrier and moment slab between joints plus any material laying on of the moment slab (kips) = load factors = resistance factors = friction angle of the soil – moment slab interface (°) = friction angle of the soil (°) = vertical soil stress (ksf) I-2 1.4 GUIDELINES FOR THE BARRIER 1.4.1 General C1.4.1 The barrier, the coping, and moment slab should be safe against structural failure Any section along the coping and moment slab should not fail in bending when the barrier is subjected to the design impact load Two modes of stability failure are possible in addition to structural failure of the barrier system They are sliding and overturning of the barrier-moment slab system The equivalent static load defined in this section should be used for sizing the moment slab The design for structural capacity of the barrier, coping, and moment slab should follow the design recommended in Section 13 of AASHTO LRFD Bridge Design Specifications including the loads Width of moment slabs should range between 4.5 ft to 10 ft Length of moment slabs should range between 20 ft to 60 ft Dimensions outside these ranges can be used provided it is shown that sufficiently rigid body behavior is achieved Much of the knowledge and experience with MSE structures and traffic barriers have been with design as specified in Section 11 and Section 13 AASHTO LRFD Bridge Design Specifications In these recommendations it is assumed that a barrier-moment slab design would generate in movement or less at the top of the barrier during impact This inch dynamic movement is considered acceptable as it would likely require little or no repair and should not affect the impact performance of the barrier system 1.4.2 Sliding of the Barrier C1.4.2 The factored static resistance (φ P) to sliding of the barrier-moment slab system along its base should satisfy the following condition (Figure 1.4.1): The equivalent static load should be applied to the length of the moment slab between joints Any coupling between adjacent moment slabs or friction that may exist between free edges of the moment slab and the surrounding soil should be neglected φ P ≥ γ Ls (1.4.2-1) Ls = equivalent static load (10 kips) φ = resistance factor (0.8) (AASHTO LRFD Bridge Design Specifications Table 10.5.5-1) γ = load factor (1.0) [extreme event] P = static resistance (kips) The static force P should be satisfy the following condition: P = W tan φr (1.4.2-2) where: W = weight of the monolithic section of barrier and moment slab between joints (with an upper limit of 60ft) plus any material laying on top of the moment slab φr = friction angle of the soil–moment slab interface(°) I-3 If the soil – moment slab interface is rough, φr is equal to the friction angle of the soil φs (cast in place) If the soil – moment slab interface is smooth, φr ⎛2 ⎞ should be reduced accordingly ⎜ tan φs ⎟ (precast) ⎝3 ⎠ 1.4.3 Overturning of the Barrier The factored static moment resistance (φ M) of the barrier-moment slab system to overturning should satisfy the following condition (Figure 1.4.1): φ M ≥ γ Ls (hA or hB) (1.4.3-3) where: Ls = equivalent static load (10 kips) φ = resistance factor (0.9) γ = load factor (1.0) [extreme event] = moment arm taken as the vertical distance from the point of impact due to the dynamic force to the point of rotation A hb = moment arm taken as the vertical distance from the point of impact due to the dynamic force to the point of rotation B M = static moment resistance (kips-ft) M should be calculated as: M = W (lA or lB) (1.4.3-4) where: W = weight of the monolithic section of barrier and moment slab plus any material laying on top of the moment slab lA = horizontal distance from the center of gravity of the weight W to the point of rotation A lB = horizontal distance from the center of gravity of the weight W to the point of rotation B 1.4.4 Design of the Coping The critical section of the coping must be designed to resist the applicable impact load conditions for the appropriate test level as defined in Section 13 of AASHTO LRFD Bridge Design Specifications (Figure 1.4.2) I-4 The moment contribution due to any coupling between adjacent moment slabs, shear strength of the overburden soil, or friction which may exist between the backside of the moment slab and the surrounding soil should be neglected Traffic Barrier Ls W He lB hB lA hA Coping C.G Leveling pad Overburden Soil Moment Slab Panel Rotation Point, B Rotation Point, A Fs He = effective height of the impact force (AASHTO LRFD Bridge Design Specifications Figure A13.2-1) Figure 1.4.1 Barrier-moment slab system for barrier design guideline (sliding and overturning) Traffic Barrier Critical section Coping C.G Leveling pad Overburden Soil Moment Slab Panel Rotation Point, A Rotation Point, B Figure 1.4.2 Coping and possible critical section I-5 1.5 GUIDELINES FOR THE SOIL REINFORCEMENT 1.5.1 General C1.5.1 The reinforcement guidelines should ensure that the reinforcement does not pullout or break during the impact of the chosen vehicle In this section, the recommendations for the load in the reinforcement due to the impact are based on a pressure diagram and line load diagram back calculated by using the design loads in excess of static earth pressure loads recorded in the tests The design load for pull out is different from the design load for rupture The reason is that the design load for pullout is an equivalent static load while the design load for rupture is a measured dynamic load 1.5.2 Pullout of the Soil Reinforcement 1.5.2.1 Pressure distribution approach C1.5.2.1 The factored ultimate static resistance (φ Pr) to pullout of the reinforcement should satisfy the following condition: φ Pr ≥ γs p s At+ γd pd At (1.5.2-1) where, φ = resistance factor (1.0) The reinforcement resistance Pr should be calculated by the equation shown in AASHTO 11.10.6.3.2-1 The traffic surcharge should not be added as it is already include in the measured load during the experiments γs = load factor for static load (1.0) ps = static earth pressure At = the tributary area of the reinforcement unit pd = dynamic pressure distribution to pullout of the reinforcement (Figure 1.5.1) γd = load factor for dynamic load (1.0) 1.5.2.2 C1.5.2.2 Line load approach The factored static resistance (φ Pr) to pullout of the reinforcement should satisfy the following condition: φ Pr ≥ γ s p s A t + γ d Q d SL The reinforcement resistance Pr should be calculated by the equation shown in AASHTO 11.10.6.3.2-1 (1.5.2-2) where, φ = resistance factor (1.0) γs = load factor for static load (1.0) ps = static earth pressure At = the tributary area of the reinforcement unit I-6 γd = load factor for dynamic load (1.0) Qd = dynamic line load to pullout of the reinforcement (Figure 1.5.2) Traffic Barrier Coping Moment Slab Top Row of Reinforcement pd = 315 psf 1.8 ft ps pd = 230 psf 2.5 ft Second Row of Reinforcement Figure 1.5.1 Pressure distribution pd for reinforcement pullout Traffic Barrier Coping Moment Slab Qd=575 lb/ft < 2.7 ft Qd=575 lb/ft < ft Top Row of Reinforcement ps Second Row of Reinforcement Figure 1.5.2 Line load pd for reinforcement pullout I-7 1.5.3 Rupture of the Soil Reinforcement C1.5.3 In this section, the recommendations for the load in the reinforcement due to the impact are based on a pressure diagram and line load diagram back calculated by using the design loads in excess of static earth pressure loads recorded in the tests 1.5.3.1 Pressure distribution approach C1.5.3.1 The factored resistance (φR) to rupture of the reinforcement should satisfy the following condition : φR ≥ γs ps At + γd pd At + γLL p LL At (1.5.3-1) where, φ = The factored resistance φR to rupture of the reinforcement is specified in Article 11.10.6.4 The cross section of the reinforcement can be subject to corrosion in the long term, depending on the expected time of burial and the composition of the soil, sand, or aggregate (AASHTO LRFD 11.10.6.4.2) resistance factor (1.0) γs = load factor for static load (1.0) ps = static earth pressure At = the tributary area of the reinforcement unit pd = dynamic pressure distribution to rupture of the reinforcement (Figure 1.5.3) γd = load factor for dynamic load (1.0) Traffic Barrier Coping Moment Slab 1.8 ft Top Row of Reinforcement pd = 1200 psf ps 2.5 ft pd = 230 psf Second Row of Reinforcement Figure 1.5.3 Pressure diagram pd for reinforcement rupture 1.5.3.1 C1.5.3.2 Line load approach The factored resistance (φR) to rupture of the reinforcement should satisfy the following condition: φR ≥ γs p s At + γd Qd SL + γLL p LL At (1.5.3-2) I-8 The resistance φR to rupture of the reinforcement should be calculated by the equation shown in Article 11.10.6.4 The cross section of the reinforcement can be subject to corrosion in the long term, depending on the expected time of burial and the composition of the soil, sand, or aggregate (AASHTO LRFD 11.10.6.4.2) where, φ = resistance factor (1.0) γs = load factor for static load (1.0) ps = static earth pressure At = the tributary area of the reinforcement unit γd = load factor for dynamic load (1.0) Qd = dynamic line load to rupture of the reinforcement (Figure 1.5.4) SL = longitudinal spacing of the reinforcement unit Traffic Barrier Coping Moment Slab Qd=2160 lb/ft < 2.7 ft Qd=575 lb/ft < ft Top Row of Reinforcement ps Second Row of Reinforcement Figure 1.5.4 Line load Qd for reinforcement rupture 1.6 GUIDELINES FOR THE WALL PANEL The wall panels must be designed to resist the dynamic pressure distributions defined in Figure 1.5.3, Section 1.5.3.1 I-9 The wall panel should have sufficient structural capacity to resist the maximum design rupture load for the wall reinforcement The static load is not included because it is not located at panel connection APPENDIX J: EXAMPLE OF DESIGN GUIDELINE 10-ft high MSE wall with 10-ft long strips design Guidelines for the barrier 1.1 Sliding φ P ≥ γLs γLs = P = W tan φ r φP= × 10 kips = × 32.39 kips 32.39 kips = = 0.8 10 kips 25.91 kips > 10 kips OK 56.10 kips for three10ft long barrier and 30ft long moment slab and overburden soil 30 assumed this is the same as retained fill tan φr = 0.58 W= φr = Detail of calculation of weight for three10ft long barrier and 30ft long moment slab and overburden soil 0.15 kcf He = 24 in concrete unit weight= soil unit weight= 0.125 kcf Length of section = 30 ft Ls (1) 32" 4.5" hB (9) Overburden Soil (2) (10) (3) 24" Rotation Point, B (5) (11) 4.25" 6" 48" 4.75" Overburden Soil C.G ho 9" (8) (6) lB lO 9" (7) (4) 5" W He Rotation Point, B Rotation Point, O Section x y Area(in2) weight (k) x from O y from O y*weight x*weight Barrier 12.00 32.00 384.00 12.00 6.00 40.00 480.00 72.00 Coping 12.00 9.00 108.00 3.38 6.00 19.50 65.81 20.25 4.50 9.00 20.25 0.63 13.50 18.00 11.39 8.54 16.50 10.00 165.00 5.16 8.25 10.00 51.56 42.54 4.25 5.00 21.25 0.66 2.13 2.50 1.66 1.41 4.75 5.00 23.75 0.74 14.13 2.50 1.86 10.48 48.00 6.00 144.00 4.50 32.50 11.00 49.50 146.25 48.00 9.00 432.00 13.50 40.50 4.50 60.75 546.75 Moment Slab Soil 4.50 9.00 20.25 0.53 15.00 21.00 11.07 7.91 10 48.00 9.00 432.00 11.25 40.50 19.50 219.38 455.63 11 48.00 6.00 144.00 3.75 48.50 13.00 48.75 181.88 1894.50 56.10 Total h o and l o = 1001.73 1493.64 17.86 26.63 lB = 21.13 in 1.2 Overturning φ M ≥ γ Ls h B γ Ls hB = × 10 kips × M = W lB = = = 0.9 φM= 43.00 in hB = 43.00 in = = 21.13 in = 56.10 kips × 1185.10 kips-in 98.76 kips-ft 98.76 = × > 430.00 kips-in 35.83 kips-ft 88.88 kips-ft 35.83 kips-ft OK 1.3 Rupture of the coping in bending (AASHTO LRFD Section 5) ' ksi 60 ksi fy = fc = Ld He hC Overburden Soil C.G h 10" 5" Rotation Point, B Mimpact = γ = = 2052.00 × × kip-in ⎡ ⎛ k ⎞⎤ φ M ult = φ ⎢ As f y d ⎜ − ⎟ ⎥ ⎠⎦ ⎝ ⎣ Ld 54.00 = × kips × 171.00 φ= hc 38.00 kip-ft 0.90 in (for flexure) ' k = Asfy /0.85fc bd The thickness of the critical section on the coping = Use # bars @ 10.00 in o.c 0.75 in Ab = db = d= 11.18 in 2.00 in use d= 9.00 in 11.18 0.44 0.38 in in in = 8.81 in Impact is resisted by the 10 ft length of a barrier unit at the moment slab ft / 0.83 ft per bar × As = 10.00 = ρ= = k= φ Mult = = = 0.44 in 5.30 in 5.30 0.00491 0.08662 in / 0.90 ×[ 2464.90 kips-in 205.41 kips-ft 120.00 5.30 ( in / 9.00 60 ksi × 0.08662 / in × > in 1- 171.00 kips-ft 9.00 in × ) OK Guidelines for the soil reinforcement 2.1 Pullout of the soil reinforcement φ P ≥ γ s p s At+ γ d pd At + γ LL p LL At (traffic live load has been neglected in this example) Please refer to Appendix A, Example (pages A-15 to A-23) for detailed calculations of ps (static earth pressure) 1) Top layer of reinforcement * P= 2b × L × σv × F = × φP = 0.688 kips p s At = p d At = 2.052 kips 2.052 kips > (See Appendix A, Example 3) 313.00 psf × γs p s At + γ d pd At = = 1.602 kips 2.920 ft2 = 0.914 kips × 0.688 kips + 2) Second layer of reinforcement * P= 3.413 kips 2b × L × σv × F = × 3.413 kips > φP = 1.205 kips (See Appendix A, Example 3) p s At = p d At = 230.00 psf × γs p s At + γ d pd At = = 2.111 kips 1.602 kips (using pressure diagram) × 2.111 kips 3.940 ft2 = 0.91 kips × 1.205 kips + OK 0.914 kips OK (using pressure diagram) × 0.906 kips 2.1 Rupture of the soil reinforcement φ R ≥ γ s p s At+ γ d pd At + γ LL p LL At (traffic live load has been neglected in this example) Please refer to Appendix A, Example (pages A-15 to A-23) for detailed calculations of ps (static earth pressure) 1) Top layer of reinforcement σt × b × Ec = 60 ksi × R= σt As = = 9.226 kips × 9.226 kips > φR = p s At = 0.688 kips (See Appendix A, Example 3) p d At = 1200.00 psf × 4.380 ft2 = 50 mm × 1.984 mm= for 100 year corrosion 5.944 kips OK 5.256 kips (using pressure diagram) γs p s At + γd pd At = × 5.944 kips = 0.688 kips + 2) Second layer of reinforcement σt × b × Ec = 60 ksi × R= σt As = = 9.226 kips = × 9.226 kips > φR p s At = 1.205 kips (See Appendix A, Example 3) p d At = 3.940 ft2 = 230.00 psf × γs p s At + γd pd At = × 2.111 kips = × 5.256 kips 50 mm × 1.984 mm= for 100 year corrosion 2.111 kips OK 0.906 kips 1.205 kips + (using pressure diagram) × 0.906 kips Guidelines for the wall panel φ Mu ≥ γ Mi 3.1) Find M u b= 12 in h= 5.5 in Ey = ' f c= 4000 psi d= As= 0.22 in (unit length) fy = 60000 psi 29000000 psi 2.75 in 3.1.1) Cracking M cr = C φcr I g fr cb h h/2 T εcr b fr Stress Strain Ig (2nd moment of area) = y= h/2= f r = 7.5 f c' = bh /12= 166.38 in 2.75 in 474.34 psi Mcr= Ig*fr/y= Ecr= ' 57000*sqrt(f c)= 3.60E+06 psi = ε cr= fr/Ecr= 1.32E-04 strain φ cr= ε cr/y= 4.78E-05 strin/in = 28697.67 lbs-in/ft = 2.39 kips-ft/ft 3605.00 ksi 5.74E-04 strain/ft Force εc 3.1.2) yield k⎞ ⎛ M n = As f y d ⎜ − ⎟ 3⎠ ⎝ fc' C φy x=kd h d As T ρ= As/Ac= 0.3333 % n= ρn= Es/Ec= 8.04 k= fs = fy εs = εsy ε > ε cr Strain b More cracking Stress Force 0.027 0.21 ( ρ n) + ρ n − ρ n = My = Asfy d(1-k/3) = ε s= fy/Es = φ cr= ε s/(d-kd) = 33803.618 lbs-in/ft = 2.82 kips-ft/ft 0.00207 strain 0.0009479 strin/in = 1.14E-02 strain/ft εcr = 0.003 3.1.3) Ultimate φcr kd β 0.85fc' kd kd C h d As Yielding h/2 εs > εy b More cracking ⎛ C = T → 0.85 f c' kdb = As f y M n = As f y d ⎜ − ⎟ 2⎠ ⎝ ' k= Asfy /0.85fc bd = 0.1176471 Mn = Asfy d(1-k/2) = 34164.706 lbs-in/ft = ε cu= β1 = φ n= Stress Strain k⎞ T fy 2.85 kips-ft/ft 0.003 strain 0.85 0.0078818 strin/in = ε cu/(kd/β 1) = 9.46E-02 strain/ft Moment (kip-ft/ft) Ultimate Yielding 2.5 Cracking 1.5 0.5 0 0.02 0.04 0.06 0.08 0.1 Curvature (strain/ft) φ Mu = 0.9 × 2.85 kips-ft/ft = > 2.56 kips-ft/ft 1.25 kips OK Force 3.2) Find M i P1=1200 psf P2=230 psf A l1=0.54 ft B l2=2.5 ft l3=1.2 ft F1=1848.62 lb F2=862.88 lb 1200.6 276 -299.98 -586.88 -648 425.66388.31 -174.96 -165.6 Mi has been selected maximum positive moment γ Mi = 3.3) Check shear × 1.25 kips-ft/ft 0.90 = 3756.79 1/2φ Vult = 1.25 kips-ft/ft 1/2φ Vult ≥ Vimpact, φVult = φ f c' bw d φ Vult = = φ= × lbs 1.88 2.00 = kips 0.90 × 3.76 > (for shear) 63.25 × kips 0.44 kips 12 OK Vi has been selected maximum positive shear × 2.75 ... and damping of the MSE wall in steady state condition 97 System weight of the MSE wall model 97 System reaction force of the MSE wall model 98 Comparison of simulation with different... Concrete damage profile on frontside of (a) test and (b) simulation 203 Concrete damage profile on side view of (a) test and (b) simulation 204 Impact load 205 Displacement of. .. damage profile on (a) frontside and (b) backside of the barrier 104 Raw data of load on the strip 105 50-msec average load on the strip 106 Distribution of load on the strip
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