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- Permanent Link:
- http://digital.auraria.edu/AA00003182/00001
## Material Information- Title:
- Stress distribution and yield zone definition of concrete barrier with anchor slab under traffic impact load
- Creator:
- Geng, Huali
- Publication Date:
- 2005
- Language:
- English
- Physical Description:
- xiii, 94 leaves : illustrations ; 28 cm
## Subjects- Subjects / Keywords:
- Stress concentration ( lcsh )
Roads -- Guard fences -- Design and construction ( lcsh ) Roads -- Safety measures -- Design and construction ( lcsh ) Bridges -- Safety measures -- Design and construction ( lcsh ) Concrete slabs -- Design and construction ( lcsh ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Bibliography:
- Includes bibliographical references (leaves 91-94).
- General Note:
- Department of Civil Engineering
- Statement of Responsibility:
- by Huali Geng.
## Record Information- Source Institution:
- |University of Colorado Denver
- Holding Location:
- Auraria Library
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 62873453 ( OCLC )
ocm62873453 - Classification:
- LD1193.E53 2005m G46 ( lcc )
## Auraria Membership |

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STRESS DISTRIBUTION AND YIELD ZONE DEFINITION OF CONCRETE BARRIER WITH ANCHOR SLAB UNDER TRAFFIC IMPACT LOAD by Huali Geng B.S., Wuhan University of Technology, 1982 A thesis submitted to the University of Colorado at Denver and Health Sciences Center in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering 2005 This thesis for the Master of Science degree by Huali Geng has been approved by Nien Y. Chang Trever Wang Brian Brady 2^^ Date Geng, Huali (M.S., Civil Engineering) Stress Distribution and Yield Zone Definition of Concrete Barrier with Anchor Slab under Traffic Impact Load. Thesis directed by Professor Nien Y. Chang. ABSTRACT Design of traffic safety barriers is complicated by its connection to moment (or anchor) slab and/or rigid wall, because of the lack of clarity in the definition of yield line for reinforced concrete design. Three-dimensional finite element analyses were performed to explore the yield line or zone via stress distributions of a concrete barrier-anchor slab-MSE wall system under the AASHTO impact test load. Several research models are used to compare their yield zones and stress distributions. The yield zones were found to extend from barrier to moment slab under a large test level impact load. The study result raises the issue of the effectiveness of yield line as defined in AASHTO 2003 LRFD Bridge Specifications. A sample design calculation was carried out using the finite element analysis results. The study provides some insight into the behavior characteristics of a concrete barrier-anchor slab-MSE wall system under impact load and identifies additional needs on the issue of the yield line or zone. This abstract accurately represents the content of the candidates thesis. I recommend its publication. IV DEDICATION I dedicate this thesis to my wife and son, for their unfaltering understanding and full support during the writing of this thesis. ACKNOWLEDGEMENT My thanks to my advisors, Nien Y. Chang, Trever Wang, for their advice, assistance and patience during the past years. I also wish to thank the staff of the University of Colorado at Denver Graduate School for their support and understanding. In addition, I wish to thank my employer, JR Engineering, LLC, and my colleagues for their support and help. CONTENTS Figures ....................................................................x Tables ..................................................................xiii Chapter 1. Introduction.............................................................1 1.1 Problem Statement.......................................................1 1.2 Research Objectives.....................................................2 1.3 Scope of Study..........................................................3 2. Review of Previous Studies..............................................10 2.1 History of the Highway Safety Research under Impact Load...............10 2.2 Yield Line Analysis Method............................................12 3. Model of Retaining System...............................................14 3.1 Reinforced Soil........................................................14 3.2 Yield Line Theory.....................................................15 3.3 About SAP2000.........................................................16 3.4 Establishment of the Research Model...................................17 3.4.1 Research Model Details...............................................18 3.4.2 Loading Details......................................................24 vii 3.5 Assumptions of the Research Model.................................28 3.6 Design Data.......................................................28 4. Analysis Results and Discussions...................................30 4.1 Yield Zone Pattern of the Concrete Barrier under Impact Load......31 4.1.1 Model AConcrete Barrier (Bottom Fixed).........................32 4.1.2 Model BConcrete Barrier on Bridge Deck.........................37 4.1.3 Research Model..................................................44 4.1.4 Summary of the Yield Zone Pattern...............................56 4.2 Displacement of the Research Model................................61 4.3 Displacement on the Concrete Barrier and Anchor Slab..............66 5. Design Comparison..................................................67 5.1 Current Design Approach for Concrete Barrier......................67 5.2 Strength Calculation of Barrier Using Research Results............68 5.3 Design Results Comparison.........................................69 6. Conclusions and Recommendations....................................70 6.1 Conclusions.......................................................70 6.1.1 Yield Zone Pattern..............................................70 6.1.2 Displacement under Impact Load and Earth Pressure...............71 6.1.3 Stress Distributions on Concrete Barrier and Anchor Slab........71 6.2 Recommendations for Future Research...............................72 viii Appendix A. Conversional Calculations.............................................76 Calculation of Youngs Modular of Alternative Material.................77 Calculation of Strength of the Barrier using the AASHTO Design Method....................................................80 Critical Length of Yield Line on Barrier under TL-4, TL-5, and TL-6 of AASHTO.........................................83 Calculation of the Concrete Strength of the Barrier, Anchor Slab using the Research Results...........................84 B. National Cooperative Highway Research Program Report 350.......................................................87 Sequential Photographs.................................................88 Vehicle Longitudinal Accelerometer Trace...............................89 Vehicle Lateral Accelerometer Trace....................................90 References ...............................................................91 ix FIGURES Figure 1.1 Concrete Barrier with Anchor Slab on Modular Block Retaining Wall.....5 1.2 Empirical Curve for Estimating Anticipated Lateral Displacements during Construction of MSE Wall.........................................6 1.3 CDOT Standard DetailB (Bridge Rail Type 7) with Anchor Slab on Top of Retaining Wall....................................8 3.1 Typical Section of the Research Model.................................20 3.2 Finite Element Modeling of Retaining Wall System.....................20 3.3 3-D View of the Research Model.......................................21 3.4 Research Model Detail................................................23 3.5 Impact Load Factor vs. Time..........................................27 3.6 Directions of Three Load Components...................................30 4.1 Model ABarrier Fixed at the Bottom...................................33 4.2 Stress Contours (X-Direction) on the Outside Face of the Barrier under Transverse Load of TL-6 (Model A)..........................35 4.3 Stress Contours (X-Direction) on the Inside Face of the Barrier under Transverse Load of TL-6 (Model A)..........................36 4.4 Model BBarrier on Concrete Deck......................................38 4.5 Stress Contours (X-Direction) on the Outside Face of the Barrier under Transverse Load of TL-6 (Model B)...............................40 4.6 Stress Contours (X-Direction) on the Inside Face of Barrier under Transverse Load of TL-6 (Model B)...............................41 4.7 Stress Contours (X-Direction) on the Top of Deck under Transverse Load of TL-6 (Model B)...............................42 4.8 Stress Contours (X-Direction)..............................................43 4.9 Stress Contours (Z-Direction)..............................................43 4.10 Maximum and Minimum Stresses (X-Direction) on the Outside Top of Barrier under TL-6.................................................45 4.11 Sequential Stress Distributions (Three Directions) at 0.10 s, and 0.15s under TL-6.......................................47 4.12 Sequential Changes of Stress Distribution under TL-6.....................48 4.13 Stress Contours (X-Direction) of the Outside Face of the Barrier under TL-6............................................................50 4.14 Stress Contours (X-Direction) on the Outside Face of the Barrier under Increased Lateral Load................................................51 4.15 Stress Contours (Z Direction) on the Barrier and Anchor Slab.............51 4.16 Stress Contours (X-Direction) on the Top Face of the Anchor Slab under TL-6............................................................53 XI 4.17 Sliding Deformation of the Research Model.........................55 4.18 Yield Zone on Outside Face of Model A.............................58 4.19 Yield Zone on Inside Face of Model A..............................58 4.20 Yield Zone on Outside Face of the Research Model..................59 4.21 Yield Zone on Inside Face of the Research Model...................59 4.22 Yield Zone on Outside Face of Model B.............................60 4.23 Yield Zone on Top Face of Anchor Slab of Model B..................60 4.24 Displacement of Retaining System under TL-4, TL-5, and TL-6.......62 4.25 Displacement of the Wall under TL-4, TL-5, and TL-6...............64 4.26 Horizontal Displacement at the Top of Barrier under TL-4, TL-5, and TL-6.. 65 6.1 Recommended Detail of Concrete Barrier with Anchor Slab............73 xii TABLES Table 3.1 Properties of Material...............................................29 3.2 Test Load Magnitude..................................................29 3.3 Test Load Length.....................................................30 4.1 Critical Length of the Yield Line....................................31 4.2 Displacement at the Top of Barrier...................................61 4.3 Displacement at the Top of Wall......................................63 5.1 Comparison of Concrete Barrier Designs...............................69 5.2 Comparison of Anchor Slab Designs....................................69 xiii 1. Introduction 1.1 Problem Statement The American Association of State Highway & Transportation Officials (AASHTO) LRFD Design Specifications, the nationally-accepted specification for bridge design, stipulates the design method for a barrier that is used for barrier on a cantilever concrete slab such as concrete bridge deck. A process for the design of crash test specimens to determine their crashworthiness is described in Appendix A. The AASHTO Specification states: The procedures of Appendix A are not applicable to traffic railings mounted on the rigid structures, such as retaining walls or spread footings when the crashing pattern is expected to extend to the supporting components. (AASHTO LRFD Bridge Design Specifications, 2003, 3rd Edition, Section 13.1, p. 13-1). AASHTO has adopted the analysis method of yield line as the design method for concrete barriers. The deformation and stress distribution of barrier with anchor slab are complex, but very important with respect to the structural analysis. When a concrete barrier is under a lateral load, the deformation of the barrier will have an effect on all adjacent 1 components. Therefore, lateral load on the concrete barrier will affect the barrier itself as well as the entire supporting structure. When an impact load acts on the concrete barrier, each component of the retaining wall system will undergo deflections. The following questions are pertinent to the barrier problem statement: 1. What are the displacement patterns of the concrete barrier w/anchor slab on MSE retaining wall if the retaining system is under AASHTO test loads? 2. Is the current design theory of yield line of a concrete barrier specified by AASHTO appropriate for a barrier with anchor slab on a retaining system? 3. How does the stresses distribute to throughout the structural components of a barrier with anchor slab if the AASHTO test load level 4, 5, or 6 forces is applied on the system? 4. How do we evaluate a limited usage of the design theory of yield line adopted by the AASHTO Specification when the structure is under an impact load, and if the AASHTO design method of yield line analysis could apply to the analysis of a barrier with anchor slab properly? 1.2 Research Objectives This research is a combination of geo-technical engineering and structural 2 engineering concepts. It not only deals with problems of geo-technical engineering, such as the behavior of retaining wall systems under impact loads, but also deals with structural engineering concept such as stress distribution and deflection of concrete members. By analyzing 3-dimensional finite element models, the research will investigate the following issues: 1. The applying limitations of the yield line theory for concrete barriers design described in the AASHTO Specifications under different impact loads. 2. Stress (longitudinal) distributions and yield zones on concrete barrier with anchor slab under lateral loads that are specified by AASHTO. 3. Displacements of the retaining system combined with the barrier and anchor slab under lateral impact loads that are specified by AASHTO and earth pressure. 1.3 Scope of Study Along with the development of technology, more and more new types of structures are used in the modem world. This phenomenon brings out the issue of safety for engineers designing these structures. The retaining wall structure is still a common type of structure in the civil engineering field, even if many new alternative 3 structures are used (Figure 1.1) However, the 3-dimensional displacement of a retaining structure is a complex problem when it is under an impact loading condition. AASHTO presents a figure for Empirical Curve for Estimating Anticipated Lateral Displacement during Construction of MSE Walls (AASHTO interim 1999 Figure Cl 1.10.4.2-1, p.l 1-44). The figure provided by AASHTO is only used in very limited cases (Figure 1.2). However, the use of this figure above is not sufficient in many cases. Traffic rails should normally provide a smooth continuous face of rail on the traffic side. It generally provides protection of the occupants of a vehicle in the event of a collision with a railing. The purpose of using concrete barriers, in the event of a collision by a vehicle, is to redirect the vehicle in a controlled manner. The vehicle should not overturn or rebound into traffic lanes. The barrier should have sufficient strength to survive the initial impact of the collision and to remain effective in redirecting the vehicle. 4 Figure 1.1 Concrete Barrier with Anchor Slab on Modular Block Retaining Wall (KeyStone Retaining Wall System, Inc) 5 L/H Bated on 20 ft high wails, relative displacement Inorsasss approximately 20% for every 400 psf of surcharge. Experience Indicates that for higher watts, the surcharge effect may be greater. Note: This figure Is only a guide. Actual displacement wit depend, In addition to the parameters addressed In the figure, on so! characteristics, compaction effort and contractor workmanship. Figure 1.2 Empirical Curve for Estimating Anticipated Lateral Displacements during Construction of MSE Wall (AASHTO Interim 1999) 6 The critical length of yield line pattern of impact force is a central design factor for the strength of a concrete barrier. It defines the failure zone on the concrete barrier when impacted by a vehicle. The design factors are based on the dimensions of the barrier, location of the impact load, magnitude of the impact load, and properties of the materials of the barrier. To distribute the barriers reactions to the supporting retaining structure, a concrete anchor slab is constructed on top of the reinforced soil wall, and connected to the barrier. The concrete anchor slab, or moment slab, will function as a structural element to restrict movement of soil and reduce the displacement and moment that are produced by the concrete barrier under impact load. A typical detail of the barrier and moment slab is shown on of CDOTs Standard (Figure 1.3). This study investigates the stress distributions throughout the concrete barrier and the anchor slab under a combination of AASHTO impact test loads and earth pressure load, and discusses the yield zone patterns by comparing stress contours on several models to the character of the yield zone of plate. SAP2000 is used to analyze the computer model. SAP2000 is a software application used in the structural engineering field. This application has been developed to make 7 TYPICAL SECTION Sol construction joint p*r ^vJ M-412-1. St* 0*g. No. B404A1 for aipbolt roodtoy olt*mot*. Figure 1.3 CDOT Standard DetailB (Bridge Rail Type 7) with Anchor Slab on Top of Retaining Wall 8 \\ the definition, solution and modification of the 3D problem data as fast and easy as possible. It uses the Finite Element Method (FEM) to analyze structural models and is able to represent deflection and stress for each structural member. It is a Graphic User Interface application. SAP2000 has very good illustrations of element analysis and readable outputs. The SAP2000 application is widely used in the structural field by designing firms, both small and large. The application is very popular amongst many practicing structural engineers. The outputted results will be complied in database format. Results for the critical area will be collected and included in this research. Microsoft Excel spreadsheets will be used to present the data. 9 2. Review of Previous Studies 2.1 History of the Highway Safety Research under Impact Load Each year more than 6 million motor vehicle crashes occur on our Nation's roads resulting in 3 million human injuries and 42,000 premature deaths. Crash data indicates that more than 40% of highway fatalities involve vehicles hitting objects on the roadside, including barriers. Thus, highway safety, particularly the crashworthiness of barriers, is an important study in the transportation field. The National Cooperative Highway Research Program (NCHRP), U.S. Department of Transportation Federal Highway Administration, and Transportation Research Board National Research Council have completed a great deal of research on Roadside Safety. However, most of their effort has been full-scale testing research. Finite element analysis (FEA) is an extremely efficient and cost-effective tool to assist in the design of safer highway guardrails, bridge supports, signposts, and other roadside structures. Computer simulation programs are provided by few institutes such as the Center of Excellence for Finite Element Crash Analysis, and the National Crash Analysis Center (NCAC). 10 NCHRP Report 350, Recommended Procedures for the Safety Performance Elevation of Highway Features was issued in 1993. This document includes six different Test Levels, all of which differ in some way from previous NCHRP Report 230 (Recommended Procedures for the safety Performance Evaluation of Highway Appurtenances, 1981) basic test matrix as well as from the Performance Level contained in the Guide Specifications. AASHTO issued its 1994 LRFD [Load and Resistance Factor Design] Bridge Design Specifications as an alternate to the long- standing Standard Specifications for Highway Bridges. Section 13 contains recommendations on railing designs and a crash test matrix that differs from NCHRP Report 350 and AASHTO Guide Specifications. (Reference 17, Bridge Railing Design and Testing) Other research includes Simplified Impact Testing of Traffic Barrier System (Phase I) (U.S. Transportation), and the Performance of Roadside Barriers (National Cooperative Highway Research Program, Project 22-13, FY 1996). Most of this research focuses on full-scale tests on concrete barriers and connections. However, most of the current research models are barriers fixed at their base, or portable barriers. So far, little research has been done on concrete barriers on MSE retaining wall systems by using the FEM analysis method. The barrier with anchor slab on the top of a MSE retaining wall was researched in a research project sponsored by the Colorado Department of Transportation Three- Dimensional Load Transfer of Colorado Type 7 and Type 10 Rails on Independent Moment Slab under Test Level Impact Load (Chang and Fatih, 2003; Chang, et al, 2004). The model was analyzed by using the Nike-3D program. The research focused on displacement, earth pressure, inclusion stresses and safety length for barrier with anchor slab. Some additional research is currently underway. A research project entitled Design of Roadside Barrier System Placed on MSE Retaining Walls is on the research list of the National Cooperative Highway Research Program (NCHRP 22-20). The scheduled completion date is June 30, 2007. It focuses on the analysis and design method of barriers. The research model will include the development of a methodology for the design of roadside barrier systems placed on MSE retaining walls, preliminary procedures for the design of roadside barrier systems, and development of the justification for and the details of a full-scale crash testing plan for validating the preliminary procedures. 2.2 Yield Line Analysis Method Ingerslev first proposed the concept of yield line analysis of concrete slabs in 1921- 12 1923. K.W. Johansen developed modem yield line theory in Yield-Line Theory (1962). This type of analysis is widely used for slab design in the Scandinavian countries. Early publications were mainly in Danish, and it is not until Hognestads English language summary of Johansens work that the method received wide attention. Since that time, a number of important publications on the method have been published, such as Yield Line Analysis of Slabs by Leonard L. Jones and Randal H. Wood (1967), Reinforced Concrete Slabs by Robert Park and William L. Gamble (1980) and so on. For solid concrete barriers, the concept of lateral load carrying capacity was established by Hirsh (1978). The expression developed for the strength of the barrier is based on the formation of yield lines at the limit state. In this study, the assumed yield line pattern is caused by a truck-banier collision force. The force is distributed over a length along the barrier. An assumed yield line pattern is consistent with the geometry and boundary conditions of the barrier. A solution is obtained by equating the external work due to the applied loads to the internal work done by the resisting moments along the yield lines. 13 3. Model of Retaining System 3.1 Reinforced Soil Reinforced soil (RS) was introduced to contemporary civil engineering by the French engineer H. Vidal, who initiated systematic worldwide research in the field of mechanics of RS and extensive engineering applications of this material, in the late 1950s. Vidal invented a particular form of RS using metallic strips as reinforcement. Applications of RS include retaining walls, bridge abutments, embankments, foundations, and so on. In recent years, RS is more widely used than conventional concrete retaining walls due to its low cost and ease of construction. Laboratory tests (1989) and full-scale loading tests (1994) showed that a GRS-RW with a FHR facing (Full-Height Rigid Facing) could support very large vertical and lateral load acting immediately behind the crest of the wall without exhibiting noticeable deformation. When the facing is considered a deformable element, the measurement and evaluation of elements can be highly complex. 14 3.2 Yield Line Theory A yield line analysis uses rigid plastic theory to compute the failure loads corresponding to given plastic moment resistances in various part of the slab. Under overloading condition in a slab failing in flexure, the reinforcement will yield first in a region of high moment. When this occurs, this portion of the slab acts as a plastic hinge, and is able to resist its hinging moment, but no more. When the load is increased future, the hinging region rotates plastically and the moments due to additional loads are redistributed to adjacent sections, causing them to yield. In the thesis, we call the hinging region as yield zone. Assumed failure shapes and minimization of energy principles can give values for particular cases that can differ slightly from one author to another depending on the mathematical assumptions made with respect to the failure shape. The assumed failure patterns and the types of loads are fundamental principles of the yield line method. A location of yield zone is at a region of the maximum moment on a structural member. When a structure member is under the maximum moment, the location of yield zone of the maximum principal moment is the location of the maximum principal stress. It is a guideline for us to determine a location of yield zone on a concrete member later on. 15 Yield line analysis is a fundamental concept of the critical length of yield line pattern of various impact loads, as specified in AASHTO. It is based on the yield line theory of concrete slabs and uses the work-energy method to establish the formula of a members strength. The barrier strength is confirmed by crash testing as outlined in AASHTO [A13.7.2], The design method of concrete barriers is described in the AASHTO manual. By solving the work-energy equation provided by the AASHTO Specification, the value for the critical length of the yield line pattern can be determined. 3.3 About SAP2000 SAP2000 is a 3-dimensional finite element analysis software. It can be applied to steel, concrete, timber, plates, shells, etc., as well as geo-technical engineering problem. SAP2000 is the latest and most powerful version of the well-known SAP series of structural analysis programs. It offers the following features: -Static and time-history analysis -Linear analysis; and nonlinear analysis (newer version) -A wide variety of loading option 16 -Frame and shell structural elements, including beam-column, truss, membrane, and plane behavior -Dynamic/seismic analysis and static pushover analysis SAP2000 automatically converts the users object-based model into an element- based model that is used for analysis. The element-based model is called the analysis model, and it consists of traditional finite elements and joints (nodes). Results of the analysis are reported back to the user on the object-based model. SAP2000 can be used to analyze structural member systems, and thin plate members such as shear-wall systems, and slabs. The newer version of SAP2000 is able to simulate a solid mass, such as soil or liquid material. 3.4 Establishment of the Research Model Reinforced soil, concrete panels, concrete barriers, and concrete moment slabs are modeled as solid elements in SAP2000. The solid elements are comprised of eight- node elements, based on an isopara-metric formulation that includes nine optional incompatible bending modes. Incompatible bending modes significantly improve the bending behavior of the element if the element geometry is of a rectangular form. Improved behavior is exhibited even with non-rectangular geometry. Each solid element has six quadrilateral faces with a joint located at each of the eight comers. 17 The solid element acts upon the three translational degrees of freedom at each of its nodes. Rotational degrees of freedom are not activated. These elements contribute stiffness to all of the translational degree of freedom. The connection of solid faces has the same condition as the solid element. The solid element models a general state of stress or strain in the three-dimensional solid. All six stress or strain components are active for solid element. The material properties of solid elements include: 1. Mass density 2. Weight density 3. Modulus of elasticity 4. Poisson ratio 5. Shear modulus 6. Coefficient of thermal expansion 3.4.1 Research Model Details The computerized model consists of reinforced soil and concrete barrier: Reinforced Soil The dimensions of the reinforced soil zone are approximately 120 feet in length (X- direction, longitudinal), 24 feet in height (H) (Z-direction, vertical) and 17 feet deep 18 (0.7H) (Y-direction, transversal). The retained soils extend 30 feet back from the reinforced zone (Y-direction). The base soils below the reinforced zone and backfill soils extend 20 feet deep (Z-direction) and are modeled as Colorado Class I backfill. The concrete wall facing panels are 6 in thickness. a. The concrete panels are modeled as solid elements with a mesh measuring 3(X-direction) x 3(Z-direction) x 0.5(Y-direction). b. The reinforced soil is modeled as a solid element with a mesh measuring 3(X) x 3(Z) x 17(Y). c. The backfill soils and base soils are modeled as solid elements as well. However, we meshed those elements adjacent to the concrete barrier into smaller elements so that change of displacement and stress distributions can be accurately determined. The typical cross section of this model is in Figure. 3.1. Figure 3.2 shows the research model (transverse section) and dimensions; Figure 3.3 shows the model in a 3D view. Concrete barrier a. The barrier (CDOT type 7) is located on top of the concrete panel wall facing. There is no direct connection between the barrier and the concrete panels or the reinforced soil. An expansion joint is established between 19 Figure 3.1 Typical Section of the Research Model Figure 3.2 Finite Element Modeling of Retaining Wall System 20 Vertical Z-direction Outside Barrier Inside Barrier / Transversal Figure 3.3 3-D View of the Research Model 21 the concrete bridge rail and concrete panels, b. The thickness of the concrete moment slab is approximately 8 and the length of the concrete slab is eight feet in our model. The concrete moment slab is meshed into a grid measuring 1 (X) x 4(Y). We are able to consider the barrier and concrete moment slab as a single structural element when they are connected by steel reinforcing bars, as specified in CDOTs standard details. Figure 3.4 shows a detail of the barrier on the research model. The elimination of horizontal load transfer from the concrete barrier to the concrete panels is established by an expansion joint between the concrete barrier and the concrete panels. By using an expansion joint, the deflection, shear force, and moment of the barrier/slab do not transfer directly to the concrete panels. In the event a vehicle impact damages the concrete barrier, the repairs will be limited to the concrete barrier and potentially the anchor slab. This is a key benefit to the isolated system of barrier and anchor slab. 22 Figure 3.4 Research Model Detail 23 A limited version of the SAP2000 8 Plus was used in this research. It lacks a friction function that would model the actual friction interface between slab and soil on any two different materials. To compensate for this in our research, a layer of alternative material between the anchor slab and top of soil is added to simulate a frictional interface. It essentially acts like a sort of material that keeps a continuity of deflection between the anchor slab and reinforced soil. The expansion joint was modeled as a layer of 3 thickness alternative material between the concrete panel and the concrete barrier. Appendix A shows the calculation of Youngs Modular of alternative material. The calculation is based on mechanics of materials theory and previous research. 3.4.2 Loading Details The calculation of the lateral earth pressure uses Rankine theory. Rankine (1856) theory is applicable to conditions where the wall friction angle is equal to the slope of backfill surface. It is a simple method for calculating the active and passive earth pressures exerted on the retaining structure. It can be used for regular configurations and is widely used by practicing engineers. The AASHTO design method utilizes Rankine earth pressure theory, for vertical or near-vertical walls constructed with discrete modular pre-cast concrete facing. This 24 method dictates the same design requirements for internal stability as for steel reinforcement. The selection of material properties is based on polymer science and performance data for each particular product or standard values when product information is unavailable. This method does not include the Segmental Retaining Wall (SRW) or any facing unit in the overall MSE analysis. Although not specifically stated by AASHTO (1994), the connection design between geo- synthetic reinforcement and SRW facing unit is usually based upon the maximum applied tension (AASHTO TF 27, 1990). The design life is 75 to 100 years for permanent structures. AASHTO LRFD specifies in section 3.7.2 Test Level Selection Criteria: TL-4 Test Load Four taken to be generally acceptable for the majority of applications on high-speed highways, freeways, expressways, and interstate highways with a mixture of trucks and heavy vehicles; TL-5 and TL-6 Test Level Five and Six taken to be generally acceptable for applications on freeways with high-speed, high-traffic volume and a higher ratio of heavy vehicles and a highway with unfavorable site conditions; The impact load in this research was adopted from AASHTO Table A13.2-1 (p. A13-5). Test levels TL-4, TL-5, and TL-6 design forces are used in the analysis. The impact loads for TL-4, TL-5, and TL-6, respectively, are 55 kip, 124 kip, and 175 kip (Transverse direction); 18 kip, 80 kip, and 80 kip (Vertical, Down); 18 kip, 41 25 kip, and 58 kip (Longitudinal) per AASHTO 2000, Section A13-2. The impact load TL-6 is used in the most cases when we investigate the yield line. The AASHTO test loads include loads on the three directions: transverse, vertical, and longitudinal. Due to the model was meshed into a 12 width (x-direction), we have converted the specified uniform loads to point loads at each of joints, 12 inch apart, vertically, horizontally, and longitudinally. A linear time-history analysis is used to the established model. Results of the National Cooperative Highway Research Program Report 350 show that the X acceleration, Y acceleration, and Z acceleration decreased sharply around 0.5 sec, and back to normal around 0.1 sec. (Appendix B). The loads in our model were assumed to have the same acceleration rate, with a decay time of 0.05 second as shown in Figure 3.5. 26 tN O Figure 3.5 Impact Load Factor vs. Time (Chang and Fatih, CDOT-DTD-R-2003-2) 27 Time (sec) 3.5 Assumptions of the Research Model The assumptions used in the research model are as follows: 1. Due to limitations of SAP2000, a thin layer (3) of material between the anchor slab solid element and reinforced soil was used to simulate the friction between two solid elements. 2. The concrete panels are assumed to have a strong and rigid connection with the reinforced soil. No separation between concrete panel and soil will occur. 3. The soil pressure is calculated using the Rankine method. 4. The model is fixed on its soil exterior boundaries, i.e. the three boundaries of the base soil and the back boundary of the backfill. 3.6 Design Data The parameters of design: /c = 4,000 psi (concrete compressive strength) /y = 60,000 psi (steel yield strength) The splitting tensile strength of concrete is an important parameter in determining when the first flexural crack may develop. The tensile strength, /t, was set as /t=7.5*( /c)Vt= 474 psi (/c=4000 psi). When the principal stress in the concrete member has exceeded the tensile strength, the concrete member is assumed to have failed. 28 Table 3.1 Properties of Material Concrete Reinforced Soil Backfill/Base Soil Expansion Joint Mass(lb/ft3) 145/m3 109 109 62 Unit Weight (lb/ft3) 145 125 130 17.28 Elastic Modulus (psi) 3,262x103 42x103 8xl03 /15.9x103 0.07x103 Poissons Ratio 0.1 0.4 0.35 0.4 The load factors used in load combinations: Dead load: 1.50 (earth pressure) Impact load: 1.75 (when using impact load as a static load) Design factors for traffic railings (AASHTO 2000 Section A13-2, Table A13.2-1): Table 3.2 Test Load Magnitude TL-4 TL-5 TL-6 Load Transverse (kip) 54 124 175 Load Longitudinal (kip) 18 41 58 Load Vertical (kip) 18 80 80 29 Table 3.3 Test Load Length TL-4 TL-5 TL-6 Length (Transverse) (ft) 3.5 8 8 Length (Longitudinal) (ft) 3.5 8 8 Length (Vertical) (ft) 18 40 40 Figure 3.6 Directions of Three Load Components 30 4. Analysis Results and Discussions 4.1 Yield Zone Pattern of the Concrete Barrier under Impact Load Included in Appendix A, is the calculation of the critical length of yield line for the CDOT Type 7 barrier by using the AASHTO Specifications. In the calculation of strength (Appendix A), the concrete barrier was divided into three segments. The analysis was done for each of the three components individually. The total moment strengths about the vertical axis and horizontal axis were obtained by summing the moment strengths of three components vertically and horizontally. Table 4.1 Critical Length of the Yield Line TL-4 TL-5 TL-6 Length of Yield Line (AASHTO) 10.5 13.5 13.5 The design method of yield line is based on the location of maximum moment, i. e. location of maximum principal stress. The approach of research is observing stress contour to determine a potential max stress zone, i.e. potential maximum moment zone. Through the observation, the principal stress on the barrier and slab on the central of retaining system is the stress in the X-direction, i.e. the stress (X- 31 direction) is a principal stress at most of interested locations. In the thesis, the major stress contour that we observed are the stress contours on X-direction. Two additional models of the concrete barrier were established. The Model A is a concrete barrier that has fixed support on the bottom, similar to most full-scale test models. The Model B is a concrete barrier on 8 concrete deck, which is the case defined in AASHTO and most common application. By investigating these models along with our research model and comparing the research model, we are able to evaluate and compare results of the yield line method defined in AASHTO. 4.1.1 Model A Concrete Barrier (Bottom Fixed) This model simulates a simplified classic structural analysis model. The barrier is a cantilevered element, fixed on the bottom. The length of the Model A is 80 feet. The cross section of the barrier is shown in Figure 4.1. The lateral load is a lateral impact concentrate load that acts on the top of barrier. The magnitude of lateral load is 175 kip, the transverse load of TL-6. Due to the fixed support condition at the bottom of the barrier, the only possible location for deformations is the top of the barrier. Therefore, the concept of yield line is assumed to have a wider opening deformation at the top, tapering to zero at 32 Cross Section at the Center of Barrier 3-D View of Model A Figure 4.1 Model ABarrier Fixed at the Bottom 33 the bottom, essentially in the shape of a V. Therefore, the stress contours should have the maximum stress (X-direction) on top of outside face of barrier and maximum stress (X-direction) on the top of inside face of barrier in certain distance from the center of retaining wall. Figure 4.2 shows the tensile stress contours in the X-direction on the outside of barrier. We can see the change of tensile stresses. The range of tensile stresses changes sharply in the adjacent 1.5-foot zones each side of the location of the load. It is clearly that the maximum stress (X-direction) is on top of barrier. Figure 4.3 shows the stress contour (X-direction) on the inside face of the barrier. The locations of the maximum tensile stresses (X-direction) on the top of the barrier are about 8 feet from each side of the center of lateral load. We can consider that the yield zone pattern of model A under later load matches the assumption of pattern and concept of the yield line in AASFITO. It has a character of the yield line of plate. The total length of the yield line calculated by the AASHTO method is 13.5 feet (Table 4.1). This calculated length is slightly longer than the length calculated in the 34 Figure 4.2 Stress Contours (X-Direction) on the Outside Face of the Barrier under Transverse Load of TL-6 (Model A) 35 Figure 4.3 Stress Contours (X-Direction) on the Inside Face of the Barrier under Transverse Load of TL-6 (Model A) 36 research model. The calculations of the length of the yield line in Appendix A. 4.3.2 Model B Concrete Barrier on Bridge Deck This model simulates a practical case that is commonly encountered by bridge engineers and discussed in AASHTO. The model includes a concrete barrier seated on the edge of an 8 thick concrete deck with 7 overhang (Figure 4.4). The dimension of barrier is same as the model of the barrier with a fixed base. The span of model is 8.5, which is modeled as a space of exterior girder and interior girder. The length of Model B is 80 feet in longitudinal direction. The lateral load is an impact concentrate load that acts on the top of barrier. The magnitude of lateral load is 175 kip, the transverse load of TL-6. The movement of the Model B is restricted by concrete deck. The deflection of barrier is based on the rigidity of the deck such as span of deck, thickness of deck, and length of cantilever. When rotation (about X-axis) of the barrier occurs under a later load, concrete barrier and deck will rotate together. The assumption of joint rigidity will reflect the movement of the joint of barrier and end of deck. The classical structural analysis is able to apply on this structure. 37 Figure 4.4 Model BBarrier on Concrete Deck 38 Figure 4.5 shows tensile stress (X-direction) contours on the outside of the barrier. The zone of tensile stresses increase from the top of the barrier to the bottom of the barrier. The possible location of the maximum tensile stress extends to the bottom barrier. This pattern is the opposite of that assumed by AASHTO that we discussed in the section of Model A. Figure 4.6 shows the stress (X-direction) contour on the inside face of the barrier. It appears that the yield zone pattern is an opposite one that assumed by AASHTO. Figure 4.7 show that the tensile stresses (X-direction) spreads continuously from the bottom of the barrier to the first support of the deck. The stresses decrease specifically after passing the first support. Figure 4.8 shows stress contours (X-direction) on a cross section at the center of concrete barrier and deck. It appears that the outside face of barrier presents a tensile stress and maximum stress is above the joint of barrier and deck. The top of concrete cantilever appears on tensile stress. Figure 4.9 shows stress contours (Z-direction) on a cross section at the center of concrete barrier and deck. Under lateral load, it appears tensile stress (Z-direction) is 39 Figure 4.5 Stress Contours (X-Direction) on the Outside Face of the Barrier under Transverse Load of TL-6 (Model B) 40 Figure 4.6 Stress Contours (X-Direction) on the Inside Face of Barrier under Transverse Load of TL-6 (Model B) 41 Figure 4.7 Stress Contours (X-Direction) on the Top of Deck under Transverse Load of TL-6 (Model B) 42 42a ' 4M6S3&&! Figure 4.8 Stress Contours (X-Direction) |a 375. 450 Figure 4.9 Stress Contours (Z-Direction) 43 on inside of face of barrier and extend to top of the concrete cantilever, which meets the assumption of joint rigidity in the classical structural analysis. The above results show that the barrier and deck act together as an integral structure. Their displacements and stress distributions match each other closely as the impact load affects the entire structure. This matches the theory of the classic structural analysis. The yield zone pattern of the barrier does not match the assumed failure pattern of the yield line as shown by AASHTO. It does not have a character of the yield line of plate. 4.1.3 Research Model In this model, the support condition for the barrier is an interface between the anchor slab and reinforced soil. It is considered a semi-fixed boundary condition, compared to the fixed conditions in Model A and Model B. The friction surface allows limited movement and rotation at the bottom of the barrier and the anchor slab. Figure 4.10 shows the maximum stresses (X-direction) and minimum stresses (X- direction) on the top of the outside face of the barrier under TL-6 impact loading. The majority of the stress influences are contained within 30 feet from each side of the center of loading. By analyzing the time-history model with longitudinal load, 44 Figure 4.10 Maximum and Minimum Stresses (X-Direction) on the Outside Top of Barrier under TL-6 45 Stress (X-Direction) (ksi) the location of the maximum stress can be found within zones approximately 8 feet from each side of the center of loading, instead of at the center of the point of application of the load. Since the test loading is not a symmetric loading system, the stress distribution will not symmetrically distribute. The maximum stress in the X- direction is 0.40 ksi, which is slightly less than the splitting tensile strength of concrete /t=0.474 ksi. Figure 4.11 shows the stress distributions of barrier when the barrier is under TL-6. The directions of stress are longitudinal (X-direction), transverse (Y-direction), and vertical (Z-direction). The periods of loading are 0.10 second and 0.15 second. Sequential changes of stress (X-direction) distribution on the barrier and slab are shown in Figure 4.12. During 0.0 second to 0.2 second, the barrier is under longitudinal tensile stress, especial on the bottom of barrier. During 0.25 second to 0.30 second, portion of anchor slab is under longitudinal tensile stress. After 030 second, the barrier is under minor stress condition. 46 Stress distribution at 0.10 second X-direction Y-direction Z-direction Stress distribution at 0.15 second X-direction Y-direction Z-direction [ n ; m ~w -23. -8. 1 21.. W; 51. g) - Figure 4.11 Sequential Stress Distributions (Three Directions) at 0.10 s, and 0.15s under TL-6 47 Time=0.05s Time=0.10s Time=0.15s Time=0.20s Time=0.25s Time=0.30s Time=0.35s Time=0.40s Time=0.45s Time=0.50s C .-g, _aL'-agfrsz* * w El Figure 4.12 Sequential Changes of Stress Distribution under TL-6 48 Figure 4.13 shows the stress contours in the X-direction on the outside of the barrier. The shape of the contours indicates that a potential maximum tensile stress is located at the bottom of barrier. The distribution of stress contours in this model is essentially the opposite of the distribution in AASHTO, which shows that a potential maximum tensile stress is located on the top of barrier. The tensile stress spreads out within an 8-foot zone from each side of the center of load on the bottom of barrier. Because AASHTO test loads are applied in three directions, the X-direction tensile stresses alone might not present a clear distribution of actual stress contours. Figure 4.14 shows the stress (X-direction) contour distribution on the outside of barrier when we increased the lateral load (three times of TL-6). In this figure, stresses contour is more visible, but matches the assumption of yield line theory in AASHTO. Figure 4.15 shows the stress (Z-direction) contour distribution on the barrier when we simulate TL-6 loads. The moment about longitudinal axis is presented by the stress (Z-direction). By observing the figure, the maximum moment about longitudinal axis is on the lower stem of barrier, but at the bottom of barrier. This phenomenon meets the rigidity assumption of the classical structural analysis on the joint of the barrier and the slab. 49 Figure 4.13 Stress Contours (X-Direction) of the Outside Face of the Barrier under TL-6 50 Figure 4.14 Stress Contours (X-Direction) of the Outside Face of the Barrier under Increased Lateral Load ksw 21s immmmmmmmmmmmM Figure 4.15 Stress Contours (Z Direction) on the Barrier and Anchor Slab 51 Figure 4.16 shows a stress (X-direction) contour on the top of anchor slab when the system is under TL-6. The edge of anchor slab (away from barrier) is under compress stress, the joint of barrier and slab is under a tensile stress, and Maximum tensile stress is at the center of load. It is a typical stress pattern of beam that is under bending condition. As previously discussed, the assembly of barrier and the moment slab was modeled as a concrete member using SAP2000. When a lateral load acts on the barrier, the concrete barrier acts in cooperation with the anchor slab, as an L-shaped concrete member. The lateral load produces a moment at the bottom of the barrier. The moment is distributed to the concrete slab, per the assumption of joint rigidity. When the structure is under a lateral load, two major deformations occur: rotation and sliding. When the structure has sufficient capacity to resist the lateral load, the structures deformed shape indicates that it is resisting loads primarily by bending deformation. When the structure has insufficient capacity to resist the lateral load, the structures deformed shape indicates that is undergoing sliding deformation, and little bending deformation. 52 Figure 4.16 Stress Contours (X-Direction) on the Top Face of the Anchor Slab under TL-6 53 When the structure exhibits bending deformation, the concrete barrier and the moment slab rotate about the point of load application, and the moment slab has an upward displacement if the joint at the base of the barrier is rigid. When an upward displacement of the moment slab occurs, the moment slab relies primarily upon gravity and its own dead load to resist this movement. Further research into this phenomenon could help practicing engineers refine the design method of the reinforcement in the moment slab. The barrier and the moment slab elements act as an element when a lateral load acts on the barrier. The load produces a moment at the bottom of the barrier. If the joint between the barrier and slab has enough strength, the moment produced by the impulse load will re-distribute at the joint. The concrete panels act as a simple support under the joint. The moment distributed to the slab produces an upward displacement and a negative moment on the anchor slab. In Figure 4.17, under TL-6, the screen capture shows the concrete assembly exhibits a specific sliding deformation, and only a minor bending deformation. When the concrete assembly is under a sliding deformation, the anchor slab acts like a deep beam and the barrier acts like a flange of the deep beam to resist a lateral 54 Figure 4.17 Sliding Deformation of the Research Model load. The moment of inertia of the composite barrier/slab assembly is very large horizontally when consider it laid on the top of retaining wall system. The tensile strength of concrete is a limiting factor in concrete design. For concrete materials, the allowable compression strength is at least 12 times the allowable tensile strength. Utilizing concretes compressive strength and neglecting its tensile strength has always been a major principle of structural engineering. The assembly of concrete barrier w/anchor slab is calculated as a deep beam. It can resist more lateral load and more efficiently use the properties of concrete material. 55 4.1.4 Summary of the Yield Zone Pattern There is no boundary condition in the calculation of the yield line in AASHTO. When we compare Model A, Model B, and the Research Model, we consider that the boundary condition is a key factor in determining the failure pattern of the concrete barrier. Based on the above discussion, the theory of the yield line in AASHTO is applicable if the barrier rests on the ground. However, the barrier works together with adjacent structural elements when the boundary condition changed, such as the concrete bridge deck like the case of Model B. In Model B, the concrete bridge deck will deflect and rotate when a lateral load acts on the barrier. The work by exterior force will transfer to the entire structure instead of the barrier itself. The calculations of the yield line in AASHTO will not apply on the Model B properly. Figure 4.18-23 show stress contours (longitudinal) under an exaggerated horizontal concentrated load (three times of the transverse load of TL-6) on the barrier of Model A, Model B, and the research model separately by linear time-historic analysis method. 56 Figure 4.18 and 4.19 show the inside face and outside faces of barrier. The stress contours (longitudinal) on the Model A has a character of the yield line of a plate as discussed in section 4.1.1. It is an ideal design model. Figure 4.20 and 4.21 show the stress contours (longitudinal) on the both faces of the barrier. When the barrier has less restriction like the research model, the yield zone extends into the anchor slab from the bottom of barrier to the top of anchor slab. The face of the barrier still remains a sort of character of the yield zones of plate, such as V-shape of the yield zone even if it wider on the top of the barrier and breaks on the bottom at the center of load. Figure 4.22 and 4.23 show the outside face of barrier and top of anchor slab. When the barrier has lesser restriction, in model B case, the character of the yield zone of plate disappears on the outside and inside faces of barrier. However, the character of the yield line of plate appears on the top of the anchor slab. From above observations of three models, the character of the yield zone of plate could move from the barrier to the anchor slab when the restriction of boundary of supporter is released gradually. 57 mtm&mn..- *5-^1 Figure 4.18 Yield Zone on Outside Face of Model A EHfcr.T:$rr 0.92 t oe >! Figure 4.19 Yield Zone on Inside Face of Model A 58 wmn& ' Figure 4.20 Yield Zone on Outside Face of the Research Model . 0.92 Figure 4.21 Yield Zone on Inside Face of the Research Model 59 Figure 4.22 Yield Zone on Outside Face of Model B Figure 4.23 Yield Zone on Top Face of Anchor Slab of Model B 60 4.2 Displacement of the Research Model The displacement of the retaining structure is very complicated if the structure is under a combination of impact load and earth pressure. Further complication arises when the retaining structure is reinforced by having a relatively rigid moment slab placed on the top of the retaining structure. The maximum displacement of the retaining system is shown in Figure 4.24 when the structure modeled under AASHTO test loads. The majority of the impact damage will be observed at the top of the barrier. The calculated displacement of the concrete panels under the barrier/slab decreases from top to bottom. The following table lists the maximum horizontal displacement at the top of barrier under the different testing levels load and earth pressure. Table 4.2 Displacement at the Top of Barrier TL-4 TL-5 TL-6 Displacement (Top of Barrier) 0.155 in 0.256 in 0.322 in 61 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 Maximum Displacement at Front of Barrier and Retaining Wall (in) Figure 4.24 Displacement of Retaining System under TL-4, TL-5, and TL-6 62 The following table lists the maximum horizontal displacement of the concrete panels at the top of reinforced soil under the different testing level load and earth pressure (Figure 4.25). Table 4.3 Displacement at the Top of Wall TL-4 TL-5 TL-6 Max. Displacement (Concrete Panels) 0.078 in 0.078 in 0.082 in The displacements in the longitudinal direction extend horizontally on both sides of the central point of the lateral load. Previous research shows that the transverse displacement of a Type 7 barrier is observed over more than 70 feet on both sides from the center of AASHTO TL-5a impact load. Figure 4.26 presents the longitudinal displacements of the barrier under a TL-4, TL- 5, and TL-6 impact loads, and shows that the length of 120 feet in this model is not sufficient to study the displacement in the longitudinal direction. 63 Figure 4.25 Displacement of the Wall under TL-4, TL-5, and TL-6 64 Figure 4.26 Horizontal Displacement at the Top of Barrier under TL-4, TL-5, and TL-6 65 4.3 Displacement on the Concrete Barrier and Anchor Slab Since the AASHTO test loads are a combination of loads in three directions: X- direction (longitudinal), Y-direction (horizontal or transversal), and Z-direction (vertical), the deflection and stress distribution on the barrier will not be symmetric. According the assumption of yield line theory of barrier in the AASHTO Specification, the maximum moment of about Z-axis is on outside face of barrier at location of center of load; and the maximum moment of Z-axis is on inside face of barrier at a certain distance away from the center of load. The stress in the X- direction reflects the moment about Z-axis. Meanwhile, the stress contour reflects the stress changes along the barrier in the X direction. 66 5. Design Comparison 5.1 Current Design Approach for Concrete Barrier As previously discussed, the current design method for concrete barriers is based on the AASHTO Design Specifications. The AASHTO design method is appropriate for concrete barriers mounted at the bottom only. This method only considers the internal energy and work of the exterior load on the barrier itself, and does not consider the adjacent structures. The usage of this specification for barrier design will be limited if boundary conditions of the barrier do not match the assumptions inherent in the AASHTO method. In chapter 4, we analyzed several barriers supported on several different boundary support conditions. Since the stress patterns in the research results do not match the assumptions of the yield line specified in AASHTO, it appears that the AASHTO method is neither applicable to our research model, nor to the case of the barrier on a concrete deck (Model B). It may mean that the work by an exterior load at certain locations on the barrier will decrease since displacements of adjacent structures occur. Therefore, the AASHTO specifications may not be an accurate design method for concrete barriers in cases other than that of a fixed base condition. 67 5.2 Strength Calculation of Barrier Using Research Results To compare our research to the design method of a concrete barrier specified in the AASHTO Specifications, the strength of the concrete barrier is computed using the AASHTO Specifications (Appendix B, Conventional Calculation), using the results of the research model under TL-6 impact loading. These results include moments and shears on the bottom of concrete barrier, as well as the maximum moments on concrete anchor slab. Since the research model was established using solid elements, the following assumptions have been made: 1. The critical cross section that an impulse load acts on will be used as a typical section for the investigation of strength. The maximum moment on the anchor slab (moment about X-axis) and the maximum moment (moment about X-axis) on the inside surface of barrier will occur on the critical cross section, it is in the center of retaining wall. 2. The maximum shear stress (perpendicular to the vertical surface of concrete barrier) in the solid element on the bottom of concrete barrier will be used as ultimate shear strength design. 68 3. The maximum compress stress (Z-direction) on the outside surface of barrier combines with the maximum tensile stress at the backside of barrier as a maximum moment at the critical cross section. The bending moment and shear strengths of the concrete barrier and anchor slab are calculated using American Concrete Institute, Building Code Requirement for Structural Concrete (ACI 319-99). The calculations can be found Appendix B. 5.3 Design Results Comparison Table 5.1 Comparison of Concrete Barrier Designs Design Moment (kp-ft) Provided Rebar Shear(kip) Concrete Shear Strength (kip) CDOT Standard Detail N/A #5@8 N/A N/A Research Results 22.74 #5@8 10.96 21.56 Table 5.2 Comparison of Anchor Slab Design Max. Moment (kp-ft) Provided Rebar Reqd Rebar (sq.in.) Provided Rebar (sq. in.) CDOT Standard Detail N/A #5@8 N/A 0.47 Research | Results 11.27 #5@8 0.31 0.47 69 6. Conclusions and Recommendations 6.1 Conclusions 6.1.1 Yield Zone Pattern The research shows that the theory of the yield line and failure pattern in the AASHTO Specifications could not be applied to the research model properly. It could apply to the barrier with a fixed bottom, especially for moment-restricted and movement-restricted conditions. Such conditions may include cases where the barrier has fixed supports, or is mounted on the ground, or on top of a mass whose moment of inertia is much greater than barriers, etc. For a structure with varied boundary conditions, the yield line theory may not be applicable properly. For the research model, the design of barrier can still adopt the design method of AASHTO since a calculation formula of concrete barrier has not been established. The design method of anchor slab can be established by using the transverse load of AASHTO test load acts at the long side direction of anchor slab, that is a laid on the reinforced soil and as a deep beam to resist the transverse load. For Model B, barrier should be designed to associate to adjacent structural 70 components as an entire structure, but as an individual member like adopted in AASHTO Specifications. 6.1.2 Displacement under Impact Load and Earth Pressure The combination of the concrete barrier and anchor slab is a good design concept for retaining wall system under traffic impact loads. It can efficiently distribute stresses and reduce horizontal displacements. When reinforced soil mass is a relatively stiff material, the horizontal displacement of the retaining wall system is relative small, comparing to the horizontal displacement of the concrete barrier and anchor slab. Based on our research, we conclude that the structural concept of the barrier and anchor slab over an MSE wall is safe and stable when subjected to test loads in AASHTO. 6.1.3 Stress Distributions on Concrete Barrier and Anchor Slab When a lateral test load specified in AASHTO, such as TL-6, acts on the barrier/anchor slab, there is not a specific failure pattern on the barrier. The assembly of barrier/anchor slab appears like a deep beam to resist the lateral load. When the friction between reinforced soil and anchor slab does not sufficiently resist the lateral load, i.e. the sliding movement occurs; this phenomenon will be 71 more obviously seen. The design method of concrete barrier could use the calculation method of AASHTO that is a more conservative calculation for Model B and the research model. For anchor slab for the case of research model, a calculation method of deep beam that is under horizontal load is recommended. To increasing the resistance between the assembly of barrier and anchor slab, I recommend adding a toe at the end of anchor slab (Figure 6.1). The toe will increase the sliding resistance of the anchor slab and reduce a horizontal movement. 6.2 Recommendations for Future Research This research presents the performance of a concrete barrier and anchor slab system under AASHTO test loads. Additional research in the future could address the following topics: 1. Using non-linear analysis method(s) to simulate the interface between concrete anchor slab and reinforced soil for more accurate results. 2. Deformation shape of the top of the concrete barrier. 3. Stress distribution on the top of concrete barrier in three directions. 72 Figure 6.1 Recommended Detail of Concrete Barrier with Anchor Slab 73 4. Re-establish the formula for strength of the concrete barrier with anchor slab according to the concept of work-energy under impact loads. 5. Establishing a range of boundary condition by a ratio of the rigidity of barrier and the rigidity of support of barrier. The range will be used to evaluate if the yield line design theory of AASHTO can apply to the structure. 74 APPENDIX 75 A. Conventional Calculations Calculation of Youngs Modulus of Alternative Material Calculation of Strength of the Barrier using the AASHTO Design Method Critical Length of Yield Line on Barrier under TL-4, TL-5, and TL-6 of AASHTO Calculation of the Concrete Strength of the Barrier, Anchor Slab using the Research Results 76 Calculation of Youngs Modular of Alternative Material The unit weight of the concrete slab (8 thickness) is 150 pcf* 8712-100.5 psf The coefficient of friction between the concrete slab and soil is 0.5 (TL-4, TL-5), and 0.8 (TL-6) for an 80 ft long concrete slab. 0 iQ 40 fcO JQ VQQ Length of J0.* ft Figure A.l Frictional Resistance versus Length of Jersey Barrier (Chang and Fatih, 2003,2004; CDOT-DTD-R-2003-2) For TL-4 and TL-5 (coefficient of friction =0.5) The maximum capacity of resistance force between soil and slab (consider the slab self-weight only): V=unit weight friction unit area (sqft) 77 =100.5pl*0.5 1ft* 1ft =50.3 psf Average shear on the bottom of slab x(average)=V/A..............................................(A-1) for unit area A=1 sqft x(average)=50.3 p/sqft The moduli of elasticity in tension and shear (E and G) are related by G=E/(2(l+v)).................................................(A-2) G=E/(2xl.5)=E/3 vPossions ratio=0.5 for rubber-like material x =G(p.........................................................(A-3) =E/3*(p=50.3 psf 9 Angle of object under shear force E=50.3*3/9=l 50.9/9 When 9 is small, tg9=9. From previous results of research, the displacement of barrier is 0.24 for 12 thickness slab. The 9 is equal 0.24/12=0.02. Therefore, E=150.9/9=150.9/0.02=7545 psft =52.3 psi=0.052 ksi 78 For TL-6 (coefficient of friction is 0.8) Using the same way, we calculate: V-30.4 E= 12060 psft=83.75 psi=0.087 ksi For simplified calculations in this research, the elastic modulus of the alternative material will be 0.07 ksi. 79 Calculation of Strength of the Barrier using the AASHTO Design Method 80 81 5>e^ >vi.e- JL = i #4j o.Z0*"1 \^"- 5^5"" ----- ! j. A ** As -f* /e>.&9 -fc ^ = g>,-z *!<Â£ /o,65 4'5 ^ "7 !_________;_ = e>,Â£K5" i = 1,0 xg>,~Z V (io = VV4-.5 | 32. at | *^ A-cvfC.. = h&"- ^\4'.l'? vc^As-j2 fc>.SF*-fc.'- b ....... = ,7.'-6=p//o.88*Â£.?5<4- * e>nfe I 3.z5" >z.z5 ^9^ Mnm = 14/4?-fij C^-^A ) 1 = Â£>l* U.^x^o Â£ >4-.T5 oTI^/'Z- ^ ; k ~ . ! : - 3> | : AxrbaJl 7V(ftn-e^C^ S&-e*-y4i^ a^turfj \J&*Jho Mm H = jep M*x + Â£p A'Ptir +
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