Effects Of Bedding Void On Internal Moment Increase In Concrete Pipes

Transcription

1 University of Central Florida Electronic Theses and Dissertations Masters Thesis (Open Access) Effects Of Bedding Void On Internal Moment Increase In Concrete Pipes 2005 Jad Kazma University of Central Florida Find similar works at: University of Central Florida Libraries Part of the Civil Engineering Commons STARS Citation Kazma, Jad, "Effects Of Bedding Void On Internal Moment Increase In Concrete Pipes" (2005). Electronic Theses and Dissertations. Paper 342. This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of STARS. For more information, please contact

2 EFFECTS OF BEDDING VOID ON INTERNAL MOMENT INCREASE IN CONCRETE PIPES by JAD SAMIR KAZMA B.S. University of Florida, 2001 A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Civil and Environmental Engineering in the College of Engineering and Computer Science at the University of Central Florida Orlando, Florida Spring Term 2005

3 2004 Jad Samir Kazma ii

4 ABSTRACT Large diameter concrete pipes have been used in many areas of central Florida to carry pressured sewage flow. These pipes have been typically located at six feet below finished roadway elevation, and ranges in diameter from thirty six to sixty inches. The water table is typically located at shallow depth below finished roadway elevation, and generally fluctuates between five to ten feet depending on the relative roadway elevation to mean sea level. These pipes are under pressure when carrying the sewage flow, but return to normal atmospheric pressures when the flow stops. Since the water table encases most of the pipe circumference, no leaks is developed from the water table to the pipe when the pipe is under pressure. Once the pressure in the pipes returns to zero, the water starts seeping into the pipe while washing the subgrade with it into the pipe s interior. The subgrade washes into the pipe at the joint inverts between adjacent pieces of the pipe, since the invert is where the most tension exists in the joint under the weight of the soil and traffic loading above the pipe, making it the most probable location where a gap in the joint would form. This would cause the origination of a small void under the pipe, which creates pressure redistribution in the subgrade reaction under the pipe. As the void develops in the middle third of the bedding under the invert, pressure redistribution occurs to the outer two thirds of the bedding. As the stress increases in the outer portions of the bedding, more subgrade material is washed into the pipe when it is not under pressure, making the void larger. As the void becomes large, the moment in the pipe is greatly increased, and therefore the gap in the joint is increased due to the tension increase at the bottom of the pipe. More material is allowed into the pipe, and the void becomes deeper as fewer restrictions are encountered between the water table and the empty pipe. As the pipe becomes pressurized, more iii

5 subgrade material is disturbed by the leak from the inside of the pipe to the outside, and void is constantly generated. The void then leads to the continuous settlement of the roadway. It is intended by this study to model the stresses in the subgrade around the pipe using a finite element software to determine the effects of void in the pipe s bedding on the stress around the pipe s outer perimeter. The stresses calculated as a result of the void will then be used in determining the increase in internal moment created in the pipe as the void is generated and became larger and deeper. Average stresses on the top and bottom of the pipe were calculated due to the soil profile dead load and live load caused by loading the soil profile with one and two HS-20 trucks. The average stresses were recalculated after the addition of void in the pipe bedding. The void width and depth were varied to come up with the case that would generate the highest unbalanced load on the pipe. The average bottom stress was subtracted from the average top stress to determine the unbalanced load on the pipe that would cause an internal moment in the pipe. At the most critical case, a forty kilo pounds per foot moment was caused by the existence of the void under the sixty inch diameter pipe used in the model. Such a moment is large to be resisted by either the pipe alone or the pipe reinforced by an additional structural support, unless such support is accompanied by void decrease and a mean to stop the subgrade from eroding into the pipe. iv

6 TABLE OF CONTENTS LIST OF FIGURES... vi LIST OF TABLES...xiii LIST OF ACRONYMS/ABBREVIATIONS... xvii CHAPTER ONE: INTRODUCTION... 1 CHAPTER TWO: LITERATURE REVIEW... 5 CHAPTER THREE: METHODOLOGY... 9 CHAPTER FOUR: FINDINGS CHAPTER FIVE: MODELING FOR EXPERIMENT CHAPTER SIX: CONCLUSION APPENDIX A: FIGURES APPENDIX B: OUTPUT OF VERTICAL STRESS DISTRIBUTION LIST OF REFERENCES v

7 LIST OF FIGURES Figure 1: Soil Cross Section (No Live Load, No Pipe) Figure 2: Soil Cross Section Stress Contour in psi (No Live Load, No Pipe) Figure 3: Soil Cross Section with water table at five feet (No Live Load, No Pipe) Figure 4: Soil Cross Section with water table at five feet Stress Contour in psi (No Live Load, No Pipe) Figure 5: Soil and Pipe Cross Section (Dead Load, No Void) Figure 6: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, No Void) Figure 7: Vertical Stress above pipe in psi, Dead Load only without Void in pipe s bedding Figure 8: Vertical Stress below pipe in psi, Dead Load only without Void in pipe s bedding Figure 9: Beam / Pipe model Figure 10: Soil and Pipe Cross Section (Dead Load, Small Void in pipe s bedding) Figure 11: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Small Void in pipe s bedding) Figure 12: Vertical Stress above pipe in psi, Dead Load only with Small Void in pipe s bedding Figure 13: Vertical Stress below pipe in psi, Dead Load only with Small Void in pipe s bedding Figure 14: Soil and Pipe Cross Section (Dead Load, Small and Deep Void in pipe s bedding).. 65 Figure 15: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Small and Deep Void in pipe s bedding) vi

8 Figure 16: Vertical Stress above pipe in psi, Dead Load only with Small and Deep Void in pipe s bedding Figure 17: Vertical Stress below pipe in psi, Dead Load only with Small and Deep Void in pipe s bedding Figure 18: Soil and Pipe Cross Section (Dead Load, Large Void in pipe s bedding) Figure 19: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Large Void in pipe s bedding) Figure 20: Vertical Stress above pipe in psi, Dead Load only with Large Void in pipe s bedding Figure 21: Vertical Stress below pipe in psi, Dead Load only with Large Void in pipe s bedding Figure 22: Soil and Pipe Cross Section (Dead Load, Large and Deep Void in pipe s bedding).. 73 Figure 23: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Large and Deep Void in pipe s bedding) Figure 24: Vertical Stress above pipe in psi, Dead Load only with Large and Deep Void in pipe s bedding Figure 25: Vertical Stress below pipe in psi, Dead Load only with Large and Deep Void in pipe s bedding Figure 26: Soil and Pipe Cross Section with water table at five feet (Dead Load, Large and Deep Void in pipe s bedding) Figure 27: Soil and Pipe Cross Section with water table at five feet Stress Contour in psi (Dead Load, Large and Deep Void in pipe s bedding) vii

9 Figure 28: Vertical Stress above pipe under water in psi, Dead Load only with Large and Deep Void in pipe s bedding Figure 29: Vertical Stress below pipe under water in psi, Dead Load only with Large and Deep Void in pipe s bedding Figure 30: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, No Void) Figure 31: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck,, Dead Load excluded No Void) Figure 32: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) without Void in pipe s bedding Figure 33: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) without Void in pipe s bedding Figure 34: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Small Void in pipe s bedding) Figure 35: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Small Void in pipe s bedding) Figure 36: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Small Void in pipe s bedding Figure 37: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Small Void in pipe s bedding Figure 38: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Small and Deep Void in pipe s bedding) Figure 39: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Small and Deep Void in pipe s bedding) viii

10 Figure 40: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Small and Deep Void in pipe s bedding Figure 41: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Small and Deep Void in pipe s bedding Figure 42: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Large Void in pipe s bedding) Figure 43: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Large Void in pipe s bedding) Figure 44: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Large Void in pipe s bedding Figure 45: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Large Void in pipe s bedding Figure 46: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Large and Deep Void in pipe s bedding) Figure 47: Soil and Pipe Cross Section _ Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Large and Deep Void in pipe s bedding) Figure 48: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Large and Deep Void in pipe s bedding Figure 49: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Large and Deep Void in pipe s bedding Figure 50: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, No Void in pipe s bedding) ix

11 Figure 51: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, No Void in pipe s bedding) Figure 52: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) without Void in pipe s bedding Figure 53: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) without Void in pipe s bedding Figure 54: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Small Void in pipe s bedding) Figure 55: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Small Void in pipe s bedding) Figure 56: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Small Void in pipe s bedding Figure 57: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Small Void in pipe s bedding Figure 58: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Small and Deep Void in pipe s bedding) Figure 59: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Small and Deep Void in pipe s bedding) Figure 60: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Small and Deep Void in pipe s bedding Figure 61: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Small and Deep Void in pipe s bedding x

12 Figure 62: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Large Void in pipe s bedding) Figure 63: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Large Void in pipe s bedding) Figure 64: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Large Void in pipe s bedding Figure 65: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Large Void in pipe s bedding Figure 66: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) Figure 67: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) Figure 68: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding Figure 69: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding Figure 70: Soil and Pipe Cross Section with water table at five feet (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) Figure 71: Soil and Pipe Cross Section with water table at five feet Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) Figure 72: Vertical Stress above pipe under water in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding xi

13 Figure 73: Vertical Stress below pipe under water in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding Figure 74: STAAD Model properties of FRP wrapped Pipe with Hydrostone collar Figure 75: STAAD Model Loads on FRP wrapped Pipe with Hydrostone Collar Figure 76: STAAD Model Maximum Moments in FRP wrapped Pipe with Hydrostone collar Figure 77: STAAD Model Shear Forces -and Bending Stresses 1 of 4 - in FRP wrapped Pipe with Hydrostone Collar Figure 78: STAAD Model Bending Stresses 2 of 4 in FRP wrapped Pipe with Hydrostone Collar Figure 79: STAAD Model Bending Stresses 3 of 4 in FRP wrapped Pipe with Hydrostone Collar Figure 80: STAAD Model Bending Stresses 4 of 4 in FRP wrapped Pipe with Hydrostone Collar Figure 81: STAAD Model Summary of Bending Stresses in FRP wrapped Pipe with Hydrostone Collar xii

14 LIST OF TABLES Table 1: Average Y stress calculations on top half of pipe. (No additional load No void in bedding) Table 2: Average Y stress calculations on bottom half of pipe. (No additional load No void in bedding) Table 3: Average Y stress calculations on top half of pipe. (No additional load Small void in bedding) Table 4: Average Y stress calculations on bottom half of pipe. (No additional load Small void in bedding) Table 5: Average Y stress calculations on top half of pipe (No additional load Small deeper void in bedding) Table 6: Average Y stress calculations on bottom half of pipe (No additional load Small deeper void in bedding) Table 7: Average Y stress calculations on top half of pipe (No additional load Large void in bedding) Table 8: Average Y stress calculations on bottom half of pipe (No additional load Large void in bedding) Table 9: Average Y stress calculations on top half of pipe (No additional load Large deep void in bedding) Table 10: Average Y stress calculations on bottom half of pipe (No additional load Large deep void in bedding) xiii

15 Table 11: Average Y stress calculations on top half of pipe (No additional load Large deep void in bedding with water) Table 12: Average Y stress calculations on bottom half of pipe (No additional load Large deep void in bedding with water) Table 13: Average Y stress calculations on top half of pipe (1 truck No Void in bedding) Table 14: Average Y stress calculations on bottom half of pipe (1 truck No Void in bedding) Table 15: Average Y stress calculations on top half of pipe (1 truck Small Void in bedding) Table 16: Average Y stress calculations on bottom half of pipe (1 truck Small Void in bedding) Table 17: Average Y stress calculations on top half of pipe (1 truck Small and deep Void in bedding) Table 18: Average Y stress calculations on bottom half of pipe (1 truck Small and deep Void in bedding) Table 19: Average Y stress calculations on top half of pipe (1 truck Large Void in bedding) Table 20: Average Y stress calculations on bottom half of pipe (1 truck Large Void in bedding) Table 21: Average Y stress calculations on top half of pipe (1 truck Large and deep Void in bedding) Table 22: Average Y stress calculations on bottom half of pipe (1 truck Large and deep Void in bedding) xiv

16 Table 23: Average Y stress calculations on top half of pipe (2 trucks No Void in bedding) Table 24: Average Y stress calculations on bottom half of pipe (2 trucks No Void in bedding) Table 25: Average Y stress calculations on top half of pipe (2 trucks Small Void in bedding) Table 26: Average Y stress calculations on bottom half of pipe (2 trucks Small Void in bedding) Table 27: Average Y stress calculations on top half of pipe (2 trucks Small deeper Void in bedding) Table 28: Average Y stress calculations on bottom half of pipe (2 trucks Small deeper Void in bedding) Table 29: Average Y stress calculations on top half of pipe (2 trucks Large Void in bedding) Table 30: Average Y stress calculations on bottom half of pipe (2 trucks Large Void in bedding) Table 31: Average Y stress calculations on top half of pipe (2 trucks Large deeper Void in bedding) Table 32: Average Y stress calculations on bottom half of pipe (2 trucks Large deeper Void in bedding) Table 33: Average Y stress calculations on top half of pipe (2 trucks Large deeper Void in bedding with water) Table 34: Average Y stress calculations on bottom half of pipe (2 trucks Large deeper Void in bedding with water) xv

17 Table 35: Summary of Vertical Stresses xvi

18 LIST OF ACRONYMS/ABBREVIATIONS AASHTO American Association of State Highway and Transportation Officials ACI ACPA A LL American Concrete Institute American Concrete Pipe Association Distributed live load area on subsoil plane at outside top of pipe, square inches D o FRP FT H HS-20 Kips L e L L L T P PL Outside diameter of pipe, inches Fiber Reinforced Polymer Feet Height of backfill or fill material above top of pipe, inches Highway Semi trailer, twenty tons total weight Kilo Pounds Effective supporting length of pipe, feet Length of A LL parallel to longitudinal axis of pipe, feet Length of A LL perpendicular to longitudinal axis of pipe, feet Wheel load, pounds Prism load, weight of the column of earth cover over the pipe outside diameter, pounds per linear foot PSI VAF W Pounds per Square Inches Vertical Arching Factor, dimensionless Distributed live load pressure on A LL, pounds per square foot xvii

19 W T W L w Total live load on pipe, pounds Linearly distributed live load on pipe, pounds per linear foot Unit weight of backfill or fill material, pounds per cubic foot xviii

20 CHAPTER ONE: INTRODUCTION The American Concrete Pipe Association developed the concept of bedding to relate the supporting strength of buried pipe to strength obtained in a three edge bearing test. The bedding factors are dependent on the quality and width of contact between the pipe and the bedding. Bedding factors have been developed for four types of installation from finite element modeling to correlate between field and laboratory tests. It is possible to relate the moment increase analytically from one bedding condition to the other. However, the four standard installations range from good bedding material and good bedding compaction in type one installation to little control over compaction and quality of material in type four installation, but none deal with void under the pipe. The standard four types of installations also assumes that the pipe act as a continuous beam and defines the effective length between the supports as a constant. When the voids develop in the pipe, the length between the supports is redefined and the ACPA method is no longer valid. Therefore, no direct method is provided to determine the effects of void creation under the pipe, and finite element modeling is required to determine the additional unbalanced load in the field. A finite element model would be created using Sigma/W (a geotechnical finite element software). The model would consist of a cross section of the roadway and the underlying soil with a sixty inch diameter pipe located at a depth of sixty seven inches from roadway surface to its top. Three loading configurations would be analyzed to determine their effects on vertical stresses at the perimeter of the pipe. The first loading configuration considered is the dead load on the pipe. The dead load is due to the self weights of the asphalt layer, the base layer, the soil subgrade and embankment, and the pipe concrete material. The second loading case is to 1

21 consider the live load present due to one HS-20 truck separate from the dead load. This is achieved by considering all materials as an elastic medium that carries no weight. The truck would have one wheel superimposed to the top of the pipe to generate the largest vertical stresses on the pipe. The third and final loading case is to consider two trucks present simultaneously, one in each loading lane as defined by AASHTO. The live load is again considered separate from the dead load. The truck wheels of the two adjacent trucks are located at an equidistance from the pipe centerline in a way that does not violate the AASHTO truck transverse clear spacing. The finite element model would then be ran for each loading case in steps. In each step changes are made in two ways. First, the pipe s bedding condition are varied by creating a void under the pipe and changing the size of the void to generate maximum vertical stresses on the pipe, and secondly by adding a water table to the controlling case of dead load and live load. Only one live load case would be considered for the addition of the water table. The two live load cases would be compared, and the water table would be added to the controlling case at the step where the void creates the ultimate effects on increasing the vertical stress and therefore the unbalanced load on the pipe. In loading case number one (Dead Load), the first step consists of modeling the cross section without any void. In the Second step, a small and shallow void is created in the bedding under the pipe. The Third step is to make the small void from the previous step deeper. The Fourth step is to generate a large void under the pipe. The Fifth step is to make the large void deeper. Step Six consists of evaluating all the steps in loading case number one and selecting the controlling one and adding the water table to it. Step Six concludes loading case number one, 2

22 and loading case number one concludes the first stage in this study where the dead load in considered. Loading case number two (one HS-20 truck) is initiated in step number Seven. Step Seven consists of evaluating vertical stresses generated by the live load alone, and that is the case for all the subsequent steps in this study. No void is created under the pipe in step Seven. Step Eight is different from step Seven by the addition of a small and shallow void in the pipe s bedding. Step Nine consists of deepening the void created in the previous step. In step Ten, the void is recreated in a wider but shallow form. In step Eleven, the void from the previous step is made deeper. Step Eleven concludes loading case number two. The initial step in loading case number three (two HS-20 trucks) is step number Twelve. In this stage the live load is once more used to determine its effects alone on the vertical stresses around the pipe s perimeter. Step Twelve consists of a soil profile loaded with the two trucks without void in the pipe s bedding. The following step is step number Thirteen, in which a small and shallow void is created under the pipe. In step number Fourteen, the void from the previous step is made deeper. In step number Fifteen, the void is reshaped and made larger but shallower than the previous step. The final step of this loading case is step number Sixteen, where the void in the pipe s bedding from the previous step is made deeper. An evaluation of the steps in both loading case number two and three are compared at the same corresponding void levels, and the controlling case (proved later to be step Sixteen of loading case number three) is selected. The selected controlling case is then analyzed after the addition of a water table to the soil cross section. The previously mentioned step is step Seventeen. Loading case two and three are the constituents of the second stage of this study. 3

23 Step Seventeen concludes stage two of this study that deals with the effects of live load alone on the pipe. The unbalanced load from stage one (dead load) is added to the corresponding unbalanced load from stage two (live load) for case two and case three, and the controlling case selected to determine the ultimate internal moment generated in the pipe. 4

24 CHAPTER TWO: LITERATURE REVIEW The American Concrete Pipe Association has rigorously studied concrete pipes. A manual has been developed that deals with concrete pipe design. The Concrete Pipe Design Manual incorporates between the design and construction installation methods for any commercially available concrete size pipe. A comprehensive review of the concrete pipe design manual would be required in order to arrive at what has been done to understand the behavior of concrete pipes under live load and dead load imposed stresses. The concrete pipe design manual presents data on the design of concrete pipe systems in a readily usable form (American Concrete Pipe Association, 2001). The chapter dealing with loads and supporting strength will be highly beneficial in all of its content to this study. The theoretical equations presented in the loads and supporting strength chapter will be used to verify the results reached by finite element modeling in the initial steps of the modeling before the void initiation for the reasons mentioned previously in chapter one of this document. The first part of the loads and supporting strength chapter to be used in this research is the determination of the earth load on the pipe. The Prism Load of soil weight above the pipe and the Vertical Arching Factor are two concepts developed by ACPA in order to assess the dead load vertical stresses on the pipe. The second part of the loads and supporting strength chapter to be used is the part dealing with the determination of live load. The average stress resulting from live load stress distribution with depth over the pipe along with impact is presented. The bedding factor concept of relating supporting strength to the bedding quality of the pipe installation used is the basic concept of this study. As presented by ACPA, the bedding factor increases the better the quality of bedding is. The better the bedding is, the less is the 5

25 moment generated in the pipe. Therefore, the bedding factor concept is taken a step further in this study so as to show the effects of poor bedding with void on the moment increase in the pipe. The supplemental data chapter provides technical information needed as the weight of the pipe per linear foot, as well as the wall thickness for various classes of pipes. The supplemental data chapter also represents a fundamental approach to understanding the mechanism of the joint between pipes. Conclusion about the origin of the bedding void creation in the pipe joints under the pipe has been drawn from material discussed in this chapter of the concrete pipe design manual. Another essential resource for the configuration of live loads is the Standard Specifications for Highway Bridges (American Association of State Highway and Transportation Officials, 1996). The approximate area of tire to roadway contact as presented in the specification is adopted by ACPA in the concrete pipe design manual and used in this paper. The truck wheel configurations is also presented by AASHTO and adopted by ACPA. The wheel configuration used is that wheels from the same truck are spaced six feet on centers in the transverse direction, and the allowed transverse distance between the centerlines of two adjacent trucks is four feet. Previous studies of interest to the subject of this study have been conducted and deals with reinforcing the joint with Fiber Reinforced Polymers to prevent the joint separation and erosion of the subgrade into the pipe. One of the studies was conducted at the University of Central Florida and deals with detecting void in pipe s bedding by the use of Ground Penetrating Radar (Suarez, 2004). The study also deals with using a Hydrostone Collar wrapped with an FRP material to prevent the joint support from collapsing under applied load that simulates the 6

26 worst bedding condition in the field. The experimental test from this study would be modeled by the use of a structural analysis software (STAAD) using the same material properties used in the experiment. The model would help in verifying the validity of the experiment, and help access the structural integrity of the FRP wrapping technique in providing the needed structural support to the joint. In understanding the properties of FRP and its potential applications, a technical letter published by the U.S. Army Corps of Engineers was consulted. The reasons to consider the application of FRP Composites for structural considerations were numerous (Composite Materials, 1997). Their Tensile Strength can range from about the strength of mild reinforcing steel to stronger than that of prestressing steel (Composite Materials). Other reasons included their good fatigue and corrosion resistance, and Low Mass (Composite Materials). Structural repairs of conventional materials using FRP composites can be made advantageous from the standpoint of ease of installation and reduced maintenance costs (Composite Materials). Examples of FRP Composite applications are given in Appendix B of the previously mentioned technical letter, and joint repair was one of the possible applications stated but no detailed study was provided. Similar Studies were conducted by the ACPA in the 1970 dealing with the interaction of buried concrete pipe and soil (American Concrete Pipe Association). The research resulted in the comprehensive finite element computer program SPIDA, Soil-Pipe Interaction Design and Analysis, for the direct design of buried pipe (American Concrete Pipe Association). Since then, the SPID parameter studies were used in the development of four new Standard Installations that take into account modern installation techniques to replace the Martson/Spangler beddings (American Concrete Pipe Association). However, the Four Standard 7

27 installations deals with pipe in full contact with bedding, while the bedding properties range from high quality and high compaction effort in type I to little or no control over materials or compaction (American Concrete Pipe Association). No studies where found that deals with void creation in the bedding under malfunctioning joints. This Study would then perform as an extension to the previous studies performed by ACPA, but with the use of a different finite element software (Sigma/W) and it will consider the creation and the worsening effects of void in the bedding. At later studies, result from this study could be used to determine bedding factors for different shape of voids under FRP reinforced joints. 8

28 CHAPTER THREE: METHODOLOGY The methodology used in researching the effects of void in pipes bedding is finite element modeling. Throughout the research, a model of the subject pipe would be created with the finite element software, the conditions will then be varied and the effects of the varied parameters compared and studied in order to determine the ultimate effect. First a simple model that does not encompass a concrete pipe would be generated and then its stresses calculated by the finite element software. The model stresses are then calculated by theoretical closed form geotechnical equations and the results compared to the software results. Upon verifications by the closed form solutions, the validity of the model is determined, and more complicated parameters are incorporated. Once the pipe is included, and before the void introduction, it is possible to determine the stresses by the finite element program and still check the results by more straightforward closed form equations that have been developed by the American Concrete Pipe Association and are derived from scrupulous finite element modeling also. The vertical stresses can be checked for the stage where the dead load is considered and also for the stage that only deals with the live loads. Once more a conclusion can be drawn to the relative proximity between the model results generated by the finite element software and the results from the American Concrete Pipe Association equations. The model soundness is once more determined. Modeling and theoretical comparisons have been the main research methodologies employed when the void under the pipe was not present. However, only model-based evaluations would be used in the post void introduction steps for each of the two stages. Modeling the pipe soil and void configuration in a computer would help us understand the void 9

29 effects on the pipe, and remediation techniques are proposed based on the magnitude of the vertical stress increase on the pipe circumference that in turn induces an internal moment in the pipe. 10

30 CHAPTER FOUR: FINDINGS The first progress taken toward modeling consisted of plotting a soil cross section and calculating the insitu stresses (See Figure 1). No pipe was included at this phase. The ground profile consisted of three layers. The top being the asphalt layer, with a thickness of four inches. A linear-elastic material behavior was selected to model the asphalt layer because the main required output from the model is the stress distribution with depth below the surface, and therefore a linear-elastic behavior is adequate. The asphalt layer required input parameters are Young s modulus and Poisson s ratio, and where estimated as psi and 0.35 respectively. The second layer is the base, and was selected to be ten inches in thickness. A linear-elastic material behavior was also selected. The base layer required input parameters are Young s modulus and Poisson s ratio, and where estimated as psi and 0.35 respectively. The third layer is the subgrade, and it consists of existing sandy material. A linear-elastic material behavior was also selected for the third layer. The subgrade layer input parameters are Young s modulus and Poisson s ratio, and where estimated as psi and 0.40 respectively. The depth of the third layer extends indefinitely downward, but was selected to be 23.8 ft which is adequate for modeling purpose and convenient for the drawing scale. The width of the cross section was taken as two twelve foot lanes since it would be necessary later on to simulate the multiple truck presence to determine its effects of stress increase on the pipe. The element thickness was chosen based on the area of contact between the wheel and asphalt as specified by AASHTO, which assumes the area of contact to be rectangular. The element thickness is the depth of the cross section of soil that the finite element program (Sigma/W) 11

31 would analyze. The element thickness was chosen at this step to allow compatibility with the load placement at the stage where the live load would be applied. For the live load application, an HS-20 truck which carries a load of 32 Kips per heaviest axle was used. The axle load was divided by two to calculate the dual wheel load. The truck tire pressure was then calculated by dividing the 16 Kips wheel load by the rectangular area of contact specified by AASHTO. The rectangular area of contact between the tire and the asphalt is specified as 20 inches in the transverse direction and 10 inches in the longitudinal direction. The 10 inches was used as the element thickness of the finite element problem for the reason mentioned before. The contact area generated consists of 200 square inches. When 16 Kips are divided by 200 square inches, the pressure applied on the rectangular contact area is found to be 80 psi. A body load was then added to the three material types. This step is required in order to be able to obtain insitu stresses in the soil. The asphalt unit weight was taken to be 145 pounds per cubic ft. The base layer unit weight was taken to be 120 pounds per cubic ft. And the natural subgrade unit weight was taken to be 105 pounds per cubic ft. A load deformation analysis was then performed on the cross section without adding any external loads to the soil surface. This load deformation analysis is only performed to get the insitu stresses in the soil due to its own weight only (See Figure 2). In the second draft, a water table was added at a depth of five feet below the surface (See Figure 3). A load deformation analysis was also performed (See Figure 4), and a hand calculation was done to confirm that stresses generated by the model are the same stresses determined by closed form solutions. The two results where identical. 12

32 In the first step of modeling, the cross section of the soil was then redrawn with the addition of a concrete pipe having a 60 inches inside diameter, with its top located at a depth of 67 inches below the roadway surface to simulate actual conditions (See Figure 5). The centerline of the pipe was set to coincide with the centerline of the roadway. Concrete material was added to the material list of the software. The two required input of the concrete material where the modulus of Elasticity and Poison s Ratio. The Modulus of Elasticity was calculated for a concrete compressive strength of 3000 psi by the ACI formula (as shown in equation 1 below), and was calculated to be 3,120,000 psi. E c = f' c psi (Equation 1) On the other hand, poison s ratio was taken to be 0.01 since concrete is assumed to be very rigid, and does not expand laterally by more than 1 % of the compressive strain. A body load or unit weight of concrete material of 150 pounds per cubic feet was also added in order to be able to model the stress increase in the bedding under the pipe due to the prism load and the pipe self weight. The walls of the concrete pipe was selected to be 5 inches as required for Wall A type by the American Concrete Pipe Association from the Concrete Pipe Design Manual Illustration 5.2. Still no additional external load was added, only the self weight of the soil and concrete pipe. The total vertical stresses where then calculated by the software (See Figure 6). The vertical stresses on the pipe circumference where then plotted against their horizontal X coordinates. The stress distribution at the top of the pipe was found to be 5.37 psi in the middle and increased as we moved away from the centerline of the pipe to 6.28 psi before dropping back to

33 toward the sides of the pipe (See Figure 7). This stress distribution is due to the arching of the pipe. The American Concrete Pipe Association, referred to by ACPA from here on, accounts for it by a Vertical Arching Factor that is multiplied by the prism load, which is the dead load of the column of earth that is over the pipe. The VAF is a function of the type of pipe installation, which is dictated by the quality of bedding under the pipe. Four types of installations are specified by the ACPA, type I being the best installation and type IV being the worst. A VAF of 1.35, 1.40, 1.40, and 1.45 are indicated for installation type I, II, III, and IV respectively. The Prism Load was calculated by equation 2 as following. PL := w H + D o ( 4 π ) D 8 o (Equation 2) Where Do is the pipe outer diameter in inches. H is the height of Soil over top of the pipe. And w is the unit weight of the soil over the pipe in Pounds per cubic inches. Since three materials are located above the pipe in our model, the Prism Load equation becomes as shown in Equation 3 below. PL := w 1 H 1 D 0 4 π + + w 3 H ( ) ( w 2 H 2 ) ( ) D o (Equation 3) 14

34 Where w1, w2, and w3 are the unit weights of the Asphalt Layer, Base Layer, and Subgrade Layer respectively. And H1, H2 are the thickness of the Asphalt Layer and Base Layer respectively. While H3 is the thickness of the Subgrade on top of the pipe. When plugging in the following values, the prism load can be calculated as following: D o := 70in w 1 = lb in 3 H 1 := 4in w 2 = lb in 3 H 2 := 10in w 3 = lb in 3 H 3 := 53in PL := w 1 H 1 PL = D o 4 π + + w 3 H ( ) ( w 2 H 2 ) lb in ( ) D o The prism load in pounds per foot is 3953, as given by the solution of the closed form equation provided by ACPA. Assuming a type I installation, the prism load after applying the 1.35 Vertical Arching Factor becomes 5340 pounds per foot. The Average Stress is then calculated from the original stress distribution on the top half and the bottom half of the pipe. The Average stress is calculated by summing the areas under the stress curve distribution and dividing the total by the horizontal span of the curve which is the same as the pipe outside diameter. The curve shape is assumed to vary linearly between the stresses calculated by the software at the nodes on the pipe perimeter. 15

35 The average Stress on the top half of the pipe was calculated to be 5.79 psi (See Table 1). If the average stress is multiplied by the pipe outside diameter, it should yield the field prism load which would also includes the Vertical Arching Factor. The field prism load is then calculated as following: Average_stress := 5.79 lb in 2 PL := Average_stress D o PL = lb ft The field prism load of 4864 pounds per foot is very close to the more theoretically calculated prism load of 5340 pounds per foot given by the ACPA formula. The percentage difference being 9 percent higher theoretically than in the field. This is indicating the accuracy of the Vertical Arching Factor introduced by ACPA in estimating the field arching effects that a pipe produces. The total vertical stress is calculated by the software at the bottom half of the pipe at the nodes that are located along the circumference of the pipe (See Figure 8). The stress peaks at the bottom in the middle at 9.10 psi, and drops in a parabolic manner as we move toward the sides of the pipe to 3.64 psi. The stress distribution under the pipe shows that most of the support comes from the middle third of the bedding. The average stress distribution at the bottom of the pipe was calculated by summing the areas under the pressure distribution curve and dividing the result by the horizontal span of the curve. 16

36 The average stress at the bottom of the pipe was calculated to be 7.95 psi (See Table 2). The support to the pipe provided by the bedding soil pressure is converted to a linear load on the pipe centerline (Bedding Reaction) by multiplying the average stress by the pipe outer diameter, which yields the following: Average_bottom_vertical_stress:= 7.95 psi Bedding_reaction:= Average_bottom_vertical_stress D o Bedding_reaction= lbf ft Assuming that the no void exists yet in the bedding, and that the pipe is not going to settle more than 0.2 inches (which was calculated by the software at the node along the centerline of the pipe at the bottom, and considered negligible) under the stresses caused by the weight of the earth cover over the pipe. A simply supported beam model can be formed such that the middle of the beam is the joint in two adjoining pipes, and the simple supports are the middle of the two adjoining pipes (See Figure 9). If the settlement is negligible, the beam center is not deflecting downward, and the stresses in the beam are null (the pipe carries no moment). For this condition to exist in our model, being that the settlement is negligible, static equilibrium has to be maintained at the joint. First, the distributed linear load that is acting on the element thickness of 10 inches has to be converted to a point load acting on the joint. Static equilibrium is satisfied by setting the sum of the vertical forces equal to zero at the joint. By doing so, the bedding reaction should equal the sum of the prism load and the pipe self weight. The beam supports are a 17

37 mathematical representation of the bedding reaction outside the 10 inches element thickness which would carry the prism load and the pipe self weight in that same region. The weight of the pipe per linear foot is then found by subtracting the prism load of 4864 pounds per foot from the bedding reaction of 6678 pounds per foot. The pipe self weight is found to be 1814 pounds per foot. In the concrete design manual, the weight of the pipe is 1473 pounds per foot. When multiplied by the 1.35 Vertical Arching Factor would result in 1989 pounds per foot, which is also an increase of 9 percent over the pipe self weight as estimated by the finite element software. Again, the accuracy of the Vertical Arching Factor checked to the same 9 percent difference that was proven earlier for the prism load. The Vertical Arching Factor that is most appropriate for use with our model is therefore (1-.09) x 1.35 = What have been proven so far is that the finite elements model results are to within 9 percent of the closed hand solutions presented by the ACPA concrete design manual. Also was proven that the pipe carries no moment, and the entire stresses from the prism load and the pipe self weight are balanced by the stresses provided by the soil bedding reaction. At the second step, the soil profile is copied to a new file and a void is created in the bedding below the pipe. In order to create the void, a void material had to be created (See Figure 10). The void material was selected as linear elastic material with two required input parameters, the Modulus of Elasticity and Poison s ratio which were estimated to be psi and 0.01 respectively. The low modulus of elasticity is required to have a linear elastic material behave as void, and the low poison s ratio is to indicate that the void when compressed by x amount axially would be distorted and expand by one percent of the same amount in the radial direction. No body load was added to the weightless void material. The vertical stress was then calculated by the software and plotted in contours (See Figure 10). 18

38 The stress distribution at the top of the pipe was found to be 5.40 psi (an increase of 0.03 psi from the file without void in bedding, See Figure 12) in the middle and increased to 6.22 psi (a decrease of.06 psi) before dropping back to 3.60 psi (a decrease of.04 psi) toward the sides of the pipe. The Average stress distribution on the top of the pipe was calculated from the previous earth pressure curve by assuming that stresses calculated by the software at the nodes along the pipe perimeter vary linearly. The Average stress distribution was found to be 5.75 psi (See Table 3). The stress distribution curve over the top of the pipe does not vary considerably before and after the void creation. The stress distribution along the bottom half of the pipe varies by a considerable amount in shape as a result of the void creation (See Figure 13). The void is now located in the middle third of the bedding under the pipe, where most of the stress was previously distributed. As a result, the stress is redistributed from the middle third to the outer two thirds which are now providing most of the support to the pipe. The Stress peaks at psi (a considerably higher number than the previously calculated 9.10psi) before the middle third, and then drops linearly to 9.79 psi before starting to drop again in a parabolic shape to a minimum of 3.60 psi at the sides of the pipe. Although the stress distribution in the soil under the pipe has significantly changed in shape and individual stress magnitudes, but the average stress distribution remained within proximity. The new bottom average vertical stress was calculated as 7.68 psi (not much different than the previous 7.95 psi before the initial void creation, See Table 4). The bedding reaction can be determined by the following: 19

39 Average_bottom_vertical_stress:= 7.68 psi Bedding_reaction:= Average_bottom_vertical_stress D o lbf Bedding_reaction= ft When subtracting the self weight of the pipe as determined in the previous step to be 1814 pounds per foot from the new bedding reaction of 6451 pounds per foot, we get 4637 pounds per foot. In order for the pipe not to have any internal moment, the average stress on its top should not exceed the 4637 pounds per foot. But the average stress on its top is 5.75 psi which translates to 4830 pounds per foot, leaving the difference with 4637 pounds per foot to create an unbalanced load of 193 pounds per foot to the top of the pipe. The unbalanced load of 193 pounds per foot contributes to the creation of a small moment in the pipe (See Table 35). The third step is to increase the depth of the small void in the bedding under the pipe keeping the width of initial void created between the pipe and the bedding unchanged (See Figure 14). The effects of the void depth increase on the vertical stress distribution would then be analyzed (See Figure 15). The vertical stress distribution at the top of the pipe as generated by the finite element model was found to be 5.42 psi at the node located at the top of the pipe (an increase of 0.05 psi from the stress at the same location when no void in the bedding existed, See Figure 16) in the middle and increased to 6.09 psi (a decrease of 0.19 psi) before dropping back to 3.58 psi (a decrease of 0.06 psi) toward the sides of the pipe. 20

40 The average stress distribution on the top of the pipe was found to be 5.67 psi (See Table 5). Also the stress distribution curve over the top of the pipe does not vary considerably before the void creation and after the void is created and deepened. The stress distribution along the bottom half of the pipe varies by a considerable amount in shape and magnitude of individual stresses as a result of the void deepening (See Figure 17). In the previous step where the small void was initiated, the stress managed to redistribute at the outer two thirds outside of the middle third occupied by the void by almost doubling in magnitude at the edges of the void and only loosing some of it average stress (0.27 psi) over the entire pipe diameter. The shape linearly decreased to a stress slightly higher in magnitude than the peak magnitude value before the creation of the void, and then decreased in a parabolic shape. After the void deepens, the magnitude of the stress at the nodes at the edges of the void decreased to a magnitude 7.63 psi, even less than the peak value before the creation of the void. The stress curve then increases linearly to a stress peak magnitude of psi that is slightly larger than the peak value before the creation of the void, before dropping in a parabolic shape to 3.58 psi at the sides of the pipe. The Average vertical stress at the bottom of the pipe was also greatly affected by the deepening of the void. The Average stress was calculated as 5.26 psi (See Table 6). The bedding reaction can be calculated as following: Average_bottom_vertical_stress:= 5.26 psi Bedding_reaction:= Average_bottom_vertical_stress Do lbf Bedding_reaction= ft 21

41 When subtracting the self weight of the pipe as determined earlier to be 1814 pounds per foot from the new bedding reaction of 4418 pounds per foot, we get 2604 pounds per foot. In order for the pipe not to have any internal moment, the average stress on its top should not exceed the 2604 pounds per foot. But the average stress on its top is 5.67 psi which equals 4763 pounds per foot, making the unbalance load the difference between 4763 and The unbalanced load of 2159 pounds per foot contributes to the creation of a larger moment than the one from the previous step (See Table 35). In the fourth step, the void previously created will be filled, and a larger void in the bedding under the pipe will be created keeping its depth minimal (See Figure 18). The program is run and the vertical stresses calculated along the pipe circumference (See Figure 19). We have noticed no great variation in the magnitude of the average top stress or the stress distribution curve shape when the void under the pipe was small or small and deep. The previous stress curves on the top of the pipe circumference consisted of two concave downward parabolas at the outside two thirds of the pipe diameter and a concave upward parabola at the middle third. When the void gets larger, the entire stress distribution curve shape on top of the pipe changes however. The curve in this case consists of a single parabola concave downward and peaking in magnitude at the middle with a stress value of 5.32 psi and drops to 2.46 psi at the sides before re-increasing linearly to 3.21 psi (See Figure 20). Most of the stress being applied by the soil to the top of the pipe is applied toward the middle. The Average stress distribution on the top of the pipe was then computed to be 4.60 psi (See Table 7). When multiplying this stress by the outer diameter of the pipe, the uniform linear load that is exerted by the soil on the top of the pipe is found to be 3864 pounds per foot. 22

42 The stress distribution under the pipe becomes largely insignificant in magnitude except toward the sides of the pipe under the haunches where some soil remains. The stress shape is linear and increases from 3.21 psi at the sides as we move a short distance toward the middle, and peaks at a value of psi and drops back to psi and jumps immediately to 0 psi at the same point as the void is encountered (See Figure 21). The average vertical stress under the pipe was then calculated as 2.46 psi (See Table 8). The bedding reaction can be determined by multiplying the average stress by the outer diameter of the pipe. The bedding reaction is calculated as 2066 pounds per foot. When subtracting the self weight of the pipe (1814 pounds per foot) from the bedding reaction, we get 252 pounds per foot. In order for the pipe not to have any internal moment, the average stress on its top should not exceed the 252 pounds per foot. But the soil load on top of the pipe was calculated as 3864 pounds per foot, making the unbalance load the difference between 3864 and 252. The unbalanced load of 3612 pounds per foot contributes to the creation of a larger moment than the one from the previous step when the void was small and deep (See Table 35). In the fifth step, the void width would remain the same, but the depth is increased (See Figure 22). No noticeable difference at this stage in the stress distribution shape at the top or the bottom of the pipe (See Figure 23 for stress contour). The individual vertical stress magnitudes at the nodes are similar to the ones calculated when the void was shallow. The stress at the top peaks at a value of 5.33 psi at the middle and decrease in a parabolic shape and reaches 2.38 psi at the sides of the pipe before re-increasing linearly to a value of 3.28 psi at the outside edges of the pipe (See Figure 24). 23

43 The average vertical stress on top of the pipe was then computed to be 4.51 psi (See Table 9). When multiplying this stress by the outer diameter of the pipe, the uniform linear load that is exerted by the soil on the top of the pipe is found to be 3788 pounds per foot. The stress distribution under the pipe is linear and increases from 3.28 psi at the sides as we move a short distance toward the middle, and peaks at a value of psi and drops back to psi and jumps immediately to 0 psi at the same point as the void is encountered (See Figure 25). The average vertical stress under the pipe was then calculated as 2.37 psi (See Table 10). The bedding reaction can be determined by multiplying the average stress by the outer diameter of the pipe. The bedding reaction is calculated as 1990 pounds per foot. When subtracting the self weight of the pipe (1814 pounds per foot) from the bedding reaction, we get 176 pounds per foot. In order for the pipe not to have any internal moment, the average stress on its top should not exceed the 176 pounds per foot. But the soil load on top of the pipe was calculated as 3788 pounds per foot, making the unbalance load the difference between 3788 and 176. The unbalanced load of 3612 pounds per foot contributes to the creation of the same large moment as the one from the previous step when the void was large but not deep (See Table 35). Also noticed was that the unbalanced load reached a peak value of 3612 pounds per foot, and was unchanged in the last two steps. It was also observed that as the void widens and deepens, the average vertical stress on top of the pipe decreased slightly. This phenomenon is due to the increase in the shear stress in the soil s vertical planes above the sides of the pipe, which provides some resistance and alleviates the vertical stress on top of the pipe as the void increases. The final step (step 6) in determining the soil dead load effects on a pipe underlined by void is to add a water table at a depth of five feet below the roadway surface to simulate field 24

44 conditions (See Figure 26). This step required the creation of a material similar to subgrade with the difference being a higher body load to simulate the saturated unit weight of subgrade material. This material was used instead of the previous subgrade material below the water table. A body load of 120 pounds per cubic feet was selected. The Modulus of Elasticity and poison s ratio remained unchanged at psi and 0.40 respectively. The void was kept large and deep as it was the case in the last step. The vertical stress was then calculated by the software and plotted in contours (See Figure 27). The vertical stress curve on top of the pipe maintained the same shape as in the previous step with the exception of slight changes in the magnitude of individual stresses at the nodes. The vertical stresses at the nodes along the top circumference of the pipe in this case are slightly higher than the previous step, with a peak value in the middle of 6.13 psi and diminishing to 2.76 psi toward the edges of the pipe before increasing linearly to 3.76 psi at the sides (See Figure 28). The average stress on top of the pipe was calculated as 5.21 psi (See Table 11), which translated to a distributed load on top of the pipe of 4376 pounds per foot. The shape of the stress curve on the bottom of the pipe did not change as well. Slight changes in the magnitude of individual stresses at the nodes were only observed. The stresses increased linearly from 3.76 psi at the sides of the pipe to a peak value of psi at a distance inward approx imately equal to the wall thickness of the pipe, before dropping to psi at the start of the void, and immediately to 0 psi afterward at that same point (See Figure 29). The average vertical stress at the bottom was calculated as 2.68 psi (See Table 12), which translates to a bedding reaction of 2251 pounds per foot. When subtracting the self weight of the pipe (1814 pounds per foot) from the bedding reaction, we get 437 pounds per foot. In order for the pipe not to have any internal moment, the average stress on its top should not exceed the 437 pounds per 25

45 foot. But the soil load on top of the pipe was calculated as 4376 pounds per foot, making the unbalance load the difference between 4376 and 437. The unbalanced load of 3939 pounds per foot contributes to the creation of a larger moment than the one from the previous step when no water table existed in the subgrade (See Table 35). The previous stage created the largest unbalanced load, and therefore would be used as the controlling case in determining the dead load effects on the pipe underlined by void. At the point where the peak unbalanced load due to dead load is reached, the internal moment in pipe reaches a maximum and does not increase if the void deepens as long as the material remains the same. The pipe now acts as a beam, and the entire support of the unbalanced load is now in the form of flexural stresses in the pipe. The joints between adjacent pipes are critical and are susceptible to opening at the bottom. The joint opening would allow more material to erode into the pipe, creating voids extending to great depth and causing the road continuous settlement. At the previous stage, the dead load effects on a pipe underlined by void were studied. In the next stage, the live load effects from one HS-20 truck would be studied on the same pipe with the same proportions of underlined void. The first live load step (step 7) to be looked at is the live loading case with one HS-20 truck without void in the pipe s bedding. The truck s heaviest axle will be loaded to the soil profile with one of its wheel on top of the pipe and the other wheel centered approximately six feet away (See Figure 30). All the material body loads were turned off in order to get the separate effects of the live load on the pipe. 26

46 The ACPA assumes the wheel load stress to spread with depth. The area that the load would spread to is equal to 20 + (1.75 x H) inches in the transverse direction and 10 + (1.75 x H) inches in the longitudinal direction. H being the height of material at the top of the pipe. We will use the wheel longitudinal distribution provided by ACPA, but will rely on the modeling software to calculate the exact wheel distribution in the transverse direction. Theoretically, before any void is created, the distributed live load on top of the pipe is calculated by the following procedure suggested by ACPA: H := 67in L t := 20in H L l := 10in H A LL := L t L l A LL = in 2 P := lbf Impact := 0 Since H is greater than 3 ft, as per AASHTO in the Standard Specification for Highway Bridges W := P ( 1 Impact) ALL W = psi W T := WL l D o W T = lbf L e := L l D o L e = ft ( ) WT lbf W L := W L L = e ft 27

47 The vertical pressure on top of the pipe is concentrated in the element thickness of the section and should be redistributed over the longitudinal distance provided by the previous formula. In order to do so, the average stress distribution on top of the pipe should be multiplied by 10 inches than divided by the longitudinal wheel distribution distance of inches. The vertical stresses were then calculated by the software, and stress contours plot generated (See Figure 31). The vertical stress curve on top of the pipe peaks at psi under the edge of the superimposed wheel that is closest to the second wheel. The stress then drops to a minimum value of 1.55 psi at the side of the pipe that is closest to the wheel, while remaining at a slightly higher value at the other side of the pipe at 2.53 psi (See Figure 32). The average stress on top of the pipe was calculated as 17 psi (See Table 13). It is observed that the vertical stress diminishes with depth as suggested by the formula provided by ACPA presented above, which consider the stress as linearly decreasing with depth. The magnitude of the vertical stress calculated by the software at the nodes locates at the bottom circumference of the pipe are less in value from their counterparts at the top. The peak value was psi and decreased gradually to 1.55 psi on one side of the pipe and 2.53 psi under the other (See Figure 33). The average stress at the bottom of the pipe was calculated as psi (See Table 14). If we multiply the average top stress of psi by 10 inches and divide by inches, a pressure on top of the pipe of psi is reached. When compared to the pressure of psi previously calculated by the ACPA formula for one wheel, a conclusion is made that the second wheel located six feet away from the center of the first wheel, only contributes psi (or 31 28

48 pe rcent) of the total pressure; while the first wheel being closer to the on top of the pipe contributes with the majority of the pressure (69 percent). The unbalanced distributed load on the pipe is found by subtracting the pressure below from the pressure above and redistributing it along the suggested longitudinal distance and multiplying the result by the pipe diameter as following: Average_top_pressure := 17psi Average_bottom_pressure := 13.88psi element_thickness := 10in Ll := in element_thickness Unbalanced_load := ( Average_top_pressure Average_bottom_pressure ) D L o l Unbalanced_load = lbf ft The unbalanced load on the pipe was calculated to be pounds per foot (as shown in Table 35). Step eight is to create a small void in the pipe bedding (See Figure 34). The profile is loaded with one truck at the same location of the previous step. The vertical stresses are then calculated by the software, and the contour of vertical stresses are plotted (See Figure 35). The stress peaks on top of the pipe at psi under the edge of the wheel superimposed on the pipe. The stress drops to a minimum of 2.54 psi and 1.44 psi at the sides of the pipe (See Figure 36). The average stress above the pipe was calculated to be psi (See Table 15). The stress peaks under the pipe at psi near the edge of the void to the other side of the superimposed 29

49 wheel, the stress then decrease to 2.54 psi and 1.44 psi at the sides of the pipe (See Figure 37). The average stress below the pipe was calculated at psi (See Table 16). The unbalanced load on the pipe is the found by subtracting the average stress on the bottom of the pipe from the average stress on its top, and then redistributing the pressure along the ACPA suggested longitudinal distance and multiplying the result by the pipe diameter. The unbalanced load on the pipe was calculated to be pounds per foot (as shown in Table 35). Average_top_pressure := 16.95psi Average_bottom_pressure := 13.31psi element_thickness := 10in Ll := in element_thickness Unbalanced_load := ( Average_top_pressure Average_bottom_pressure ) D L o l Unbalanced_load = lbf ft Step nine consists of making the small void deeper under the pipe (See Figure 38). The vertical stresses are then calculated by the software, and the contour of vertical stresses are plotted (See Figure 39). The stress peaks on top of the pipe at psi under the edge of the wheel superimposed on the pipe. The stress drops to a minimum of 2.56 psi and 1.24 psi at the sides of the pipe (See Figure 40). The average stress above the pipe was calculated to be psi (See Table 17). The stress peaks under the pipe at psi near the edge of the void to the same side of the superimposed wheel, the stress then decrease to 2.56 psi and 1.24 psi at the sides of the pipe (See Figure 41). The average stress below the pipe was calculated at psi 30

50 (See Table 18). The unbalanced load on the pipe is the found by subtracting the average stress on the bottom of the pipe from the average stress on its top, and then redistributing the pressure along the ACPA suggested longitudinal distance and multiplying the result by the pipe diameter. The unbalanced load on the pipe was calculated to be pounds per foot (as shown in Table 35). Average_top_pressure := 16.78psi Average_bottom_pressure:= 11.51psi element_thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l Unbalanced_load= lbf ft Step ten consists of creating a large void under the pipe (See Figure 42). The vertical stresses are then calculated by the software, and the contour of vertical stresses are plotted (See Figure 43). The stress peaks on top of the pipe at psi under the edge of the wheel superimposed on the pipe. The stress drops to a minimum of 2.65 psi and negative 0.24 psi at the sides of the pipe (See Figure 44). The average stress above the pipe was calculated to be psi (See Table 19). The stress peaks under the pipe at psi near the edge of the void, the stress then decrease to 2.65 psi and negative 0.24 psi at the sides of the pipe (See Figure 45). The average stress below the pipe was calculated at 4.94 psi (See Table 20). The unbalanced load on the pipe is the found by subtracting the average stress on the bottom of the pipe from the 31

51 average stress on its top, and then redistributing the pressure along the ACPA suggested longitudinal distance and multiplying the result by the pipe diameter. The unbalanced load on the pipe was calculated to be pounds per foot (as shown in Table 35). Average_top_pressure := 14.99psi Average_bottom_pressure:= 4.94psi element_thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l lbf Unbalanced_load= ft Step eleven consists of making the large void deeper under the pipe (See Figure 46). The vertical stresses are then calculated by the software, and the contour of vertical stresses are plotted (See Figure 47). The stress peaks on top of the pipe at psi under the edge of the wheel superimposed on the pipe. The stress drops to a minimum of 2.74 psi and negative 0.33 psi at the sides of the pipe (See Figure 48). The average stress above the pipe was calculated to be psi (See Table 21). The stress peaks under the pipe at psi near the edge of the void, the stress then decrease to 2.74 psi and negative 0.33 psi at the sides of the pipe (See Figure 49). The average stress below the pipe was calculated at 4.50 psi (See Table 22). The unbalanced load on the pipe is the found by subtracting the average stress on the bottom of the pipe from the average stress on its top, and then redistributing the pressure along the ACPA 32

52 suggested longitudinal distance and multiplying the result by the pipe diameter. The unbalanced load on the pipe was calculated to be pounds per foot (as shown in Table 35). Average_top_pressure := 14.74psi Average_bottom_pressure:= 4.50psi element_thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l lbf Unbalanced_load= ft The next Stage is to load the profile with two trucks. In step twelve, the two trucks are placed symmetrically to the roadway centerline keeping four feet approximately between the wheels of the two different trucks in order to satisfy the AASHTO requirement of clear distance between two adjacent trucks (See Figure 50). The program is run and vertical stresses are calculated at the nodes around the pipe and plotted in contours (See Figure 51). The stress curves on the top of the pipe circumference consisted of two concave downward parabolas at the outside two thirds of the pipe diameter and a concave upward parabola at the middle third (See Figure 52). The maximum stress magnitude is located at the vertex of the concave downward parabolas and is psi, while the vertex of the concave upward parabola is psi and located at the centerline of the pipe. The average vertical stress on top was calculated as psi (See Table 23). The stress curve at the bottom of the pipe follows the same shape as the one on top (See Figure 53). The maximum stress magnitude at a node at the bottom of the pipe is located at the 33

53 vertex of the concave downward parabolas and is psi, while the vertex of the concave upward parabola is psi and located at the centerline of the pipe. The average stress at the bottom of the pipe circumference was calculated as psi (See Table 24). The unbalanced distributed load on the pipe is: Average_top_pressure := 26.94psi Average_bottom_pressure:= 24.03psi element_thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l Unbalanced_load= lbf ft The previous results show that the unbalanced load from one truck generates more unbalanced load than two trucks. This is possible since the one truck will have a wheel sitting right at the centerline of the pipe, while the wheels of the two opposite trucks are both at approximately two feet away from the centerline of the pipe. The unbalanced load generated by one truck was only seven percent higher than the one generated by the two trucks. Step thirteen is to initiate a void under the pipe and calculate vertical stress at the pipe circumference. The void generated would be minimal in depth and width (See Figure 54). The vertical stresses were calculated by the software and plotted in contours (See Figure 55). As in the previous step, minimal changes occurred in the shape and magnitude of the stress curve on top of the pipe. The stress curves on the top of the pipe circumference consisted of two 34

54 concave downward parabolas at the outside two thirds of the pipe diameter and a concave upward parabola at the middle third. The maximum stress magnitude is located at the vertex of the concave downward parabolas and is psi, while the vertex of the concave upward parabola is psi and located at the centerline of the pipe (See Figure 56). The average vertical stress on top of the pipe was calculated as psi (See Table 25). The bottom stress curve has gained magnitude at the nodes adjacent to the void, and stress redistribution occurred. The maximum stress was psi and dropped linearly to psi before dropping along a parabolic shape to 4.49 psi (See Figure 57). The average vertical bottom stress at the bottom of the pipe was calculated to be psi (See Table 26). The unbalanced load was then calculated as following: Average_top_pressure := 26.85psi Average_bottom_pressure:= 23.04psi element_thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l Unbalanced_load= lbf ft The unbalanced load generated by one truck still controls over the two trucks unbalanced load when the void is small void, but this would be the last step at which one tuck would generates more unbalanced load as we will see. 35

55 Step fourteen is to deepen the narrow void in the middle third of the pipe bedding (See Figure 58). The vertical stresses were calculated by the software and contours plotted (See Figure 59). The stress curve on top of the pipe remains unchanged to a large extent in shape and magnitude of individual stresses from the similar curves in the last two steps. The stress curves on the top of the pipe circumference consisted of two concave downward parabolas at the outside two thirds of the pipe diameter and a concave upward parabola at the middle third. The maximum stress magnitude is located at the vertex of the concave downward parabolas and is psi, while the vertex of the concave upward parabola is psi and located at the centerline of the pipe. The stress dropped to 4.34 psi at the sides of the pipe (See Figure 60). The average vertical stress was calculated as psi (See Table 27). The stress at the bottom of the pipe peaks at the outer two middle thirds of the bedding to a value of psi (See Figure 61). The average stress was calculated to be psi at the bottom of the pipe (See Table 28). The unbalanced load was calculated as before by: Average_top_pressure := 26.56psi Average_bottom_pressure:= 20.97psi element_thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l Unbalanced_load= lbf ft 36

56 In step fifteen, the void is made larger but kept at a minimal depth (See Figure 62). The vertical stresses were then calculated by the software and plotted in contours (See Figure 63). The vertical stress curve at the top of the pipe approaches a single concave downward parabola, but the maximum stress is not at the centerline of the pipe. The stress at the centerline of the pipe is psi and reaches a maximum not far from the centerline location at a value of psi. The stress then drops to 0.81 psi close to the edges and bounces linearly upward to a value of 3.13 psi at the sides of the pipe (See Figure 64). The average vertical pressure at the top was calculated to be psi (See Table 29). The stress at the bottom becomes linear and highly concentrated in magnitude toward the gap openings. The maximum value of stress is psi and drops linearly to 3.13 psi at the sides of the pipe (See Figure 65). The average vertical bottom stress was calculated to be 7.26 psi (See Table30). The unbalanced distributed load was found to be as following: Average_top_pressure := psi Average_bottom_pressure := 7.26 psi element_thickness := 10in L l := in element_thickness Unbalanced_load := ( Average_top_pressure Average_bottom_pressure ) L l lbf Unbalanced_load = ft D o Step sixteen is to deepen the existing wide void (See Figure 66). The vertical stresses were then calculated by the software and plotted in contours (See Figure 67). The stress curve 37

57 on top of the pipe remains greatly unchanged from the last step in shape and in magnitude of stress at individual nodes. The stress starts at the centerline of the pipe with a value of psi then reaches a maximum of psi at a near distance to the centerline before dropping along the parabola to a minimum of 0.41 psi near the edges before increasing linearly to 3.15 psi at the sides of the pipe (See Figure 68). The vertical average stress at the top of the pipe was calculated to be psi (See Table 31). The stress curve at the bottom also remained unchanged in shape and to a degree in individual stress magnitudes at the nodes. The stress starts increasing linearly from the sides of the pipe where the stress value is 3.15 psi to a peak value of psi at the edges of the void (See Figure 32). The average vertical stress at the bottom of the pipe was calculated to be 3.56 psi. The unbalanced distributed load on the pipe was calculated as previously by the following: Average_top_pressure := 22.99psi Average_bottom_pressure:= 6.80psi element_thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l Unbalanced_load= lbf ft The unbalanced load reached a maximum value and remained unchanged in the last two steps. The average vertical stress on the top of the pipe decreased slightly as the void deepened. The difference was made up by the shear in the vertical planes above the sides of the pipe. 38

58 Step seventeen is to add a water table at a depth of five feet to the previous step to simulate actual conditions (See Figure 70). The water table was added to the previous step since it was determined that it was controlling in generating the maximum unbalanced load on the pipe. Vertical Stresses were then computed by the software and stress contours generated (See Figure 71). No changes is necessary to the body load of material below the water because we are only analyzing the stresses generated by the live load and considering it separate from dead load, which was considered in the first stage. The vertical stresses were calculated by the software along the circumference of the pipe. The vertical stress curve on top of the pipe remained unchanged to a great extent in shape and in magnitude from the last two steps. The stress magnitude at the centerline of the pipe was found to be psi, and then increased to a maximum value of psi at a short distance from the centerline. The stress value then reached a minimum of 0.29 psi near the edges of the pipe before increasing linearly to a value equal to 2.99 psi at the sides of the pipe (See Figure 72). The average vertical stress on top of the pipe was calculated to be psi (See Table 33). The stress at the bottom of the pipe starts by a minimum values of 2.99 psi at the edges of the pipe before increasing along a linear slope to reach a maximum of psi shortly before reaching the edges of the void. The stress then decrease linearly to psi at the edges of the void, and at the same point jumps back to zero due to the void (See Figure 73). The average vertical stress on the bottom of the pipe was found to be 6.66 psi (See Table 34). The unbalanced distributed load is found by the following: 39

59 Average_top_pressure := 22.54psi Average_bottom_pressure:= 6.66psi element_ thickness := 10in L l := in element_thickness Unbalanced_load:= ( Average_top_pressure Average_bottom_pressure) D L o l lbf Unbalanced_load= ft The results of the entire seventeen steps were summarized in Table 35 (listed in Appendix B). The controlling case that would create the biggest moment in the pipe can now be selected from Table 35 by adding the unbalanced load created by the dead load step to each corresponding live load step. The maximum unbalanced load was found when step six was added to step seventeen, and was calculated to be 4990 pounds per foot. Conservatively assuming that the void extends from the middle of one pipe to the middle of the adjacent pipe, the unsupported length would become the standard 8 feet length of concrete pipe ((1/2)x(8ft)+(1/2)x(8ft)). The maximum moment generated in the pipe would then be calculated at the joint midway between the two supports to be: w := L := 8ft 4990 lbf ft wl 2 M max := M 8 max = 39920lbf ft 40

60 CHAPTER FIVE: MODELING FOR EXPERIMENT The moment calculated in the previous chapter would be generated in the pipe at the joint between two adjacent pipe pieces. The joint is in itself incapable of resisting any moment, and would be generally considered as a pin support in structural analysis. The pin support failure under moment would be similar to a plastic hinge developed in the middle of a simply supported beam under an ultimate moment that exceeds the structural capacity of the beam itself, therefore resulting in the catastrophic failure of the beam. The catastrophic failure of the pipe would then lead to the collapse of the pipe, the excessive settlement of the roadway pavement on top of it, and eventually the failure of the pavement. A possible solution to resisting the generated moment in the pipe would be to wrap the pipe joint with material capable of providing the structural support needed to this deficient joint, in order to restore the pipe load carrying capacity and make it again act as a continuous beam -instead of the simply supported section that was created by the gap opening- as specified by the American Concrete Pipe Association. The material would have to provide the structural capacity along with a way to stop the erosion of the soil into the pipe. A non-reinforced concrete collar around the joint would generally be a quick solution, but the soil erosion trend is expected to continue after the collar placement -even if it is in smaller amounts- as water seeps between the pipe and the collar, and the concrete collar is again susceptible to cracking and opening like the joint in the previous stage. Therefore, it is recommended that the material used to provide a fix structural support to the pipe be stronger than the pipe itself. Such material characteristics are found in Fiber Reinforced Polymers as described in the paper published by the United States Army Corp of Engineers (Composite Materials, 1997). 41

61 A published Thesis at the University of Central Florida support the fact that FRP material are capable of providing a greater resistance to the moment than the pipe itself (Suarez, 2004). The joint wrapped with FRP would be capable of providing a stronger resistance to the moment than the pipe material, and would not crack until after the pipe has failed at a location that is close to the pipe joint where the moment is high (Suarez, 2004). This capacity would make the joint efficient, and with the use of a proven sealing material on the inside of the joint, the soil erosion problem would be minimized and the repair system would never fail afterward. A small moment would always remain due to the underlying small void, but the joint would not open allowing more soil material to penetrate the pipe while generating a greater void that would lead to the catastrophic failure of the pipe and pavement. To determine the efficiency of using FRP material in the support of the joint, an experiment was performed by Suarez at the structural laboratory of the University of Central Florida, in which two eight feet pipe pieces with a fifteen inch inside diameter were joined together at the joint. A collar formed from Hydrostone material was poured around the joint, and Fiber Reinforced Polymers where then wrapped around the collar. The two concrete pipe pieces, Hydrostone collar, and FRP system were labeled specimen 3F-0/90 to indicate the angles at which the FRP was applied to the joint (Suarez). The two pieces where supported by three wooden block supports, one at each side and one toward the middle close to the joint. The load was applied by a hydraulic actuator at a distance of inches from the left support. The specimen was tested for determine the joint shear efficiency according to ASTM C497-03a. The joint was determined to be efficient in resisting shear. In the next stage, the middle support was removed and only the two outer supports remained. The distance between the two outer supports was chosen to be fifteen feet. Keeping 42

62 the load location the same as before, the system was then loaded to failure to simulate the worst bedding condition under a pipe joint. The failure load was measured to be 3.5 kilo pounds. The void in this case spans between the two supports. This test would generate a moment at the joint between the two pipes and in the pipe itself, and the outcome of the test results would help us in realizing the structural soundness of the FRP wrapped joint. The results from the test show that the failure occurs in the pipe close to the wrapped joint and not in the joint itself. For the previous experiment to be clearly interpreted, a structural model would be created using the same material properties used in the experiment and the same pipe, Hydrostone collar, and FRP wrapping dimensions. Also, the supports and the applied load location would be maintained at their equivalent experiment locations. The modeling would be done using STAAD, the structural analysis and design software. At the start of the modeling, four nodes are defined. Node one is at the origin and has a zero coordinates in the x, y, and z coordinates. Node two has zero coordinates in the y and z directions, but has an x coordinate of ft. Node three has zero coordinates in the y and z coordinates, but has an x coordinate of ft. Node four also has zero coordinates in the y and z coordinates, and a ft x coordinate. Next, three beam members are define between the four nodes. The first member represents the first concrete pipe piece and is located between nodes one and two with a total length of ft. The second member represents also the second concrete pipe piece and is located between nodes three and four with a total length of ft. The third member represents the FRP wrapping and spans between nodes two and three with a length of 2.25 ft. The fourth member represents the Hydrostone collar and also spans between the second and third nodes with a length of 2.25 ft. The next step is to define the members section properties. The concrete pipe is defined as a hollow pipe with an inside 43

63 diameter of 15 inches and a pipe thickness of 2.25 inches. The FRP material is defined as an octagonal hollow tube with an outer diameter of ft and a thickness of 0.15 inches. The Hydrostone collar is defined as a hollow octagonal tube also, with an outer diameter of ft and a thickness of ft. After defining the section properties, material properties were defined to assign them to their corresponding sections. Material number three was selected to be the concrete material with an Elasticity Modulus of 3,150,000 psi and a Poison s Ratio of A normal concrete with a pounds per cubic feet was assigned. The second material was used to assign the Hydrostone properties. The Modulus of Elasticity of the Hydrostone material was calculated by equation 1 (See Chapter 4) by using the one-hour compressive strength provided in Table 11 in Suarez. To be on the conservative side, the Poison s Ratio was assumed to be similar to the concrete Poison s Ration even though it is expected to be higher due to the Hydrostone high dry compressive strength. The Hydrostone density of 108 pounds per cubic feet was also taken from Table 11 in Suarez. The FRP material was assigned to material number one with a Modulus of Elasticity of 6,440,000 psi as given in Table 12 in Suarez. Conservatively, a Poison Ratio of 0.2, which represents a slightly higher Poison Ratio than that of concrete was used. The previous assumption was granted given into consideration the high strength of FRP material. To complete the model parameters, two pin supports were added to node one and node four. Refer to figure 74 to view all the model parameters as previously described. The next step was to define the loads into the model (See Figure 75). Two basic load cases were defined. The first load case consisted of the dead load of the material, and was automatically calculated by the software given the material and section properties. The self load was defined to act in the negative y direction, as is the case for all gravity weights. The second 44

64 load case was the failure load of 3500 pounds as determined by Suarez s experiment, and was acting at a point on the first member at a distance ft right of the first node at the same location where the load was acting in the experiment. A service load combination of dead and applied loads was assigned to load case number three to represent the total load service load on the model system. Also present in Figure 75 was a three-dimensional photo taken in STAAD of member four and three that represents the Hydrostone collar and its FRP cover respectively. The model was then ran and the results were presented in Figure 76 through 81. The maximum service moments were presented in Figure 76. In the first member (first concrete pipe), the maximum moment was at the second node at a distance of ft from the first node, the moment was calculated to be Kip-ft. The maximum moment in the second member (second concrete pipe) was at the third node and measured at Kip-ft. The maximum moment in the third member (FRP wrap) was measured at node two and measured as Kipft. The maximum moment in the fourth member (Hydrostone collar) was also measured at node two to be Kip-ft. The maximum shear forces were calculated and presented in Figure 77. The maximum p ositive shear in member one (first concrete pipe) was calculated at node one and measured as Kips, while the negative shear in the same member was calculated at node two to be Kips. The maximum negative shear in the second member (second concrete pipe) was calculated at node number four to be Kips. Only negative shear exists in member two, three, and four. The maximum negative shear in member three (FRP wrap) was measured at node three to be Kips. The maximum negative shear in member four (Hydrostone collar) was measured at node three to be Kips. 45

65 The combined axial and bending stresses were presented in Figure 77 through 80, and then summarized in Figure 81. The maximum stress that was measured in member one (first concrete pipe) was psi measured at the location of the maximum moment close to the point of load application. The maximum stress that was measured in member two (second concrete pipe) was found to be psi. The maximum stress in the third member (FRP wrap) was measured at psi, while the stress in the Hydrostone collar was measured at psi. The analysis of these results proves the validity of the experiment performed by Suarez at the University of Central Florida. The moment was higher in the concrete pipe due to the application point of the load. The failure stress in the concrete pipe was very close to the Modulus of Rupture of the concrete material calculated by the ACI equation represented in equation 15 below: f r := 7.5 f' c (Equation 15) The modulus of rupture was calculated for a compressive strength of concrete of 2500 psi by equation 15, and found to be 375 psi. The stress at which the concrete pipe failed at according to the model was 296 psi; compared to the Modulus of Rupture, there is a 21 percent variation. The difference could be attributed to material and workmanship, and is usually accounted for in design by the use of a strength reduction factor. The shear was greatly carried by the Hydrostone collar at the joint, while the FRP provided the resistance to bending, as it was determined by observing that the bending stresses where higher in the FRP than in the Hydrostone. The FRP acted to confine the Hydrostone and 46

66 prevent its failure in tension, and reduced the Hydrostone stresses to third of the stresses present in the pipe. The stress measured in the FRP (236 psi) was less than 0.5 percent of its ultimate tensile strength of psi. The previous analysis shows how effective the joint structural support provided by the Hydrostone-FRP system. The moment resisted in the pipe can be as large as the pipe capacity and support provided to the joint by the Hydrostone-FRP system would not be at risk. The only problem that remained to be addressed was the leak at the joint, which also existed before the system was loaded (Suarez). 47

67 CHAPTER SIX: CONCLUSION It was determined from this study that with void initi ation, stress redistribution occurs in the bedding under the pipe. As the void gets larger, the moment in the pipe gets larger. The vertical stress on the pipe circumference due to the dead load of the soil and the live load gene rated by loading the roadway with one and two HS-20 t rucks were calculated in separate stages for multiple void shapes. The Dead load and Live load average stresses were converted to unbalanced loads on the pipe. The Dead unbalanced loads were then added to their corresponding Live unbalanced loads resulting from the sam e void configuratio n for the one and two truck load cases. The controlling total unbalance d load situati on was then selected by comparing th e sum of the Dead and Live unbalanced load due to o ne HS-20 truck with the sum o f the Dead and Live unbalanced load due to two HS-20 trucks. T he controlling unbalanced load was then used to determine the maximum moment in the pipe. Table 35 (listed in Appendix B, and reproduced below) show the average stresses on the top a nd bottom half of the pipe summarized for different void configuration steps and for each one of the Dead load and Live load stages, along with the resulting corresponding unbalanced load for each step on top of the pipe. The controlling unbalanced load was found from the sum of step six and step seventeen (See Table 35 below), and the maximum unbalanced load was determined to be 4990 pounds per foot, which corresponds to a moment approximately equal to 40 Kilo pounds per foot. 48

68 Table 35 Summary of Vertical Stresses Top Bottom Unbalanced Step Case (psi) (psi) Load (lb/ft) 1 No additional load - No void in bedding No additional load - Small void in bedding No additional load - small deep void in bedding No additional load - Large void in bedding No additional load - Large deep void in bedding No additional load - Large deep void in bedding under water One truck loaded - No void in bedding One truck loaded - Small void in bedding One truck loaded - Small deep void in bedding One truck loaded - Large void in bedding One truck loaded - Large deep void in bedding Two trucks loaded - No void in bedding Two trucks loaded -Small void in bedding Two trucks loaded -Small deep void in bedding Two trucks loaded -Large void in bedding Two trucks loaded -Large deep void in bedding Two trucks loaded - Large deep void in bedding under water The largest moment calculated would need to be resisted by a structural mean in order to prevent the pipe from separating at the invert, where the maximum moment is generated. However, the moment is too large to be resisted by a structural support in a feasible manner. It would then be ideal to backfill the large void and control the washing of the subgrade into the pipe so as to be able to lower the moment to a controllable value. It would also be hard to backfill the entire void under the pipe without removing it, and it will be assumed that a small void would remain in the bedding. 49

69 It is then advisable to use a structural mean that would also provide the pipe joints with water tightness to control the subgrade material seepage into the pipe with water infiltration. The structural capacity of the medium would only be required to provide support against the moment generated by step 2 in addition to step 8 (See Table 35) as small void remains in the bedding as previously stated. The best mean to achieve water tightness and structural resistance to bottom joint tension separation would be to wrap the pipe joint with fiber reinforced polymers. The joint would then become resistant to the erosion of the subgrade material (with the help of a sealing material applied from inside the pipe at the joint location) and would be provided the additional strength required to resist the unbalanced load on top of the pipe due to the remaining small void in the bedding. 50

70 APPENDIX A: FIGURES 51

71 Figure 1: Soil Cross Section (No Live Load, No Pipe) 52

72 Figure 2: Soil Cross Section Stress Contour in psi (No Live Load, No Pipe) 53

73 Figure 3: Soil Cross Section with water table at five feet (No Live Load, No Pipe) 54

74 Figure 4: Soil Cross Section with water table at five feet Stress Contour in psi (No Live Load, No Pipe) 55

75 Figure 5: Soil and Pipe Cross Section (Dead Load, No Void) 56

76 Figure 6: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, No Void) 57

77 Figure 7: Vertical Stress above pipe in psi, Dead Load only without Void in pipe s bedding 58

78 Figure 8: Vertical Stress below pipe in psi, Dead Load only without Void in pipe s bedding 59

79 Figure 9: Beam / Pipe model 60

80 Figure 10: Soil and Pipe Cross Section (Dead Load, Small Void in pipe s bedding) 61

81 Figure 11: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Small Void in pipe s bedding) 62

82 Figure 12: Vertical Stress above pipe in psi, Dead Load only with Small Void in pipe s bedding 63

83 Figure 13: Vertical Stress below pipe in psi, Dead Load only with Small Void in pipe s bedding 64

84 Figure 14: Soil and Pipe Cross Section (Dead Load, Small and Deep Void in pipe s bedding) 65

85 Figure 15: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Small and Deep Void in pipe s bedding) 66

86 Figure 16: Vertical Stress above pipe in psi, Dead Load only with Small and Deep Void in pipe s bedding 67

87 Figure 17: Vertical Stress below pipe in psi, Dead Load only with Small and Deep Void in pipe s bedding 68

88 Figure 18: Soil and Pipe Cross Section (Dead Load, Large Void in pipe s bedding) 69

89 Figure 19: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Large Void in pipe s bedding) 70

90 Figure 20: Vertical Stress above pipe in psi, Dead Load only with Large Void in pipe s bedding 71

91 Figure 21: Vertical Stress below pipe in psi, Dead Load only with Large Void in pipe s bedding 72

92 Figure 22: Soil and Pipe Cross Section (Dead Load, Large and Deep Void in pipe s bedding) 73

93 Figure 23: Soil and Pipe Cross Section Stress Contour in psi (Dead Load, Large and Deep Void in pipe s bedding) 74

94 Figure 24: Vertical Stress above pipe in psi, Dead Load only with Large and Deep Void in pipe s bedding 75

95 Figure 25: Vertical Stress below pipe in psi, Dead Load only with Large and Deep Void in pipe s bedding 76

96 Figure 26: Soil and Pipe Cross Section with water table at five feet (Dead Load, Large and Deep Void in pipe s bedding) 77

97 Figure 27: Soil and Pipe Cross Section with water table at five feet Stress Contour in psi (Dead Load, Large and Deep Void in pipe s bedding) 78

98 Figure 28: Vertical Stress above pipe under water in psi, Dead Load only with Large and Deep Void in pipe s bedding 79

99 Figure 29: Vertical Stress below pipe under water in psi, Dead Load only with Large and Deep Void in pipe s bedding 80

100 Figure 30: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, No Void) 81

101 Figure 31: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck,, Dead Load excluded No Void) 82

102 Figure 32: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) without Void in pipe s bedding 83

103 Figure 33: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) without Void in pipe s bedding 84

104 Figure 34: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Small Void in pipe s bedding) 85

105 Figure 35: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Small Void in pipe s bedding) 86

106 Figure 36: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Small Void in pipe s bedding 87

107 Figure 37: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Small Void in pipe s bedding 88

108 Figure 38: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Small and Deep Void in pipe s bedding) 89

109 Figure 39: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Small and Deep Void in pipe s bedding) 90

110 Figure 40: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Small and Deep Void in pipe s bedding 91

111 Figure 41: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Small and Deep Void in pipe s bedding 92

112 Figure 42: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Large Void in pipe s bedding) 93

113 Figure 43: Soil and Pipe Cross Section Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Large Void in pipe s bedding) 94

114 Figure 44: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Large Void in pipe s bedding 95

115 Figure 45: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Large Void in pipe s bedding 96

116 Figure 46: Soil and Pipe Cross Section (1 HS-20 Truck, Dead Load excluded, Large and Deep Void in pipe s bedding) 97

117 Figure 47: Soil and Pipe Cross Section _ Stress Contour in psi (1 HS-20 Truck, Dead Load excluded, Large and Deep Void in pipe s bedding) 98

118 Figure 48: Vertical Stress above pipe in psi, Live Load only (1 HS-20 Truck) with Large and Deep Void in pipe s bedding 99

119 Figure 49: Vertical Stress below pipe in psi, Live Load only (1 HS-20 Truck) with Large and Deep Void in pipe s bedding 100

120 Figure 50: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, No Void in pipe s bedding) 101

121 Figure 51: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, No Void in pipe s bedding) 102

122 Figure 52: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) without Void in pipe s bedding 103

123 Figure 53: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) without Void in pipe s bedding 104

124 Figure 54: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Small Void in pipe s bedding) 105

125 Figure 55: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Small Void in pipe s bedding) 106

126 Figure 56: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Small Void in pipe s bedding 107

127 Figure 57: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Small Void in pipe s bedding 108

128 Figure 58: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Small and Deep Void in pipe s bedding) 109

129 Figure 59: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Small and Deep Void in pipe s bedding) 110

130 Figure 60: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Small and Deep Void in pipe s bedding 111

131 Figure 61: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Small and Deep Void in pipe s bedding 112

132 Figure 62: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Large Void in pipe s bedding) 113

133 Figure 63: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Large Void in pipe s bedding) 114

134 Figure 64: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Large Void in pipe s bedding 115

135 Figure 65: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Large Void in pipe s bedding 116

136 Figure 66: Soil and Pipe Cross Section (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) 117

137 Figure 67: Soil and Pipe Cross Section Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) 118

138 Figure 68: Vertical Stress above pipe in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding 119

139 Figure 69: Vertical Stress below pipe in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding 120

140 Figure 70: Soil and Pipe Cross Section with water table at five feet (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) 121

141 Figure 71: Soil and Pipe Cross Section with water table at five feet Stress Contour in psi (2 HS-20 Trucks, Dead Load excluded, Large and Deep Void in pipe s bedding) 122

142 Figure 72: Vertical Stress above pipe under water in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding 123

143 Figure 73: Vertical Stress below pipe under water in psi, Live Load only (2 HS-20 Trucks) with Large and Deep Void in pipe s bedding 124

144 Figure 74: STAAD Model properties of FRP wrapped Pipe with Hydrostone collar 125

145 Figure 75: STAAD Model Loads on FRP wrapped Pipe with Hydrostone Collar 126

146 Figure 76: STAAD Model Maximum Moments in FRP wrapped Pipe with Hydrostone collar 127

147 Figure 77: STAAD Model Shear Forces -and Bending Stresses 1 of 4 - in FRP wrapped Pipe with Hydrostone Collar 128

148 Figure 78: STAAD Model Bending Stresses 2 of 4 in FRP wrapped Pipe with Hydrostone Collar 129

149 Figure 79: STAAD Model Bending Stresses 3 of 4 in FRP wrapped Pipe with Hydrostone Collar 130