THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

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1 THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING LATERAL LOADING OF BATTERED PILES WITH RESPECT TO FOOTING SIZE VINCENT JOHN DEROSA Spring 2010 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Civil Engineering with honors in Civil Engineering Reviewed and approved* by the following: Jeffrey Laman Associate Professor of Civil Engineering Thesis Supervisor Patrick Reed Associate Professor of Civil Engineering Honors Adviser *Signatures are on file in the Schreyer Honors College.

2 i Abstract The Pennsylvania Department of Transportation s current policy restricts the lateral loading of battered piles to a 3.5 to 1 vertical to horizontal load ratio. Accompanying this is the assumption that all lateral force is resisted by battered piles and conversely, none of the lateral force is resisted by vertical piles. These two decisions result in the need for additional piles and increased footing sizes, creating large total foundations. The purpose of this study is to analyze these two specifications in an attempt to reduce the required foundation size. Traditional Euler beam theory is studied to determine the behavior of battered and plumb piles, but is complicated due to nonlinear soil-pile interaction. As a result, the p-y method for relating pile deflection to soil resistance was used to predict pile behavior under the influence of varying load ratios in three different types of soils. Because the p-y method is an iterative process, the computer program Lpile was utilized to create the different curves based on individual soil and pile properties. The curves were then used to develop multi-linear spring constants that can effectively represent the soil in a structural analysis model. Piles at three different batters in three types of soil were analyzed under varying load ratios to determine the effects on pile deflection and bending moment. The results indicate that pile behavior is governed by the beam-column interaction equation and suggests that the actual lateral loads acting on the pile play a much more significant role in pile behavior than load ratios. In addition, results indicate that PennDOT s assumption that all lateral force is resisted by battered piles is extremely conservative and plumb piles are shown to have significant lateral resistance.

3 ii Table of Contents Chapter 1: Introduction Background Problem Statement Objectives Scope 2 Chapter 2: Literature Review General Equation p-y Method Battered Pile Effects Group Effects Characteristic Load Method Characteristic Load Method Group Modification Factors. 11 Chapter 3: Study Design Lpile SAP CLM Soil Types...15 Chapter 4: Study Procedure... 16

4 iii 4.1 Soil Properties Pile Properties Limit States 17 Chapter 5: Study Results Representative P-Y Curves Horizontal Resistance and Deflections Predicted by SAP2000 and Lpile Comparison of SAP and Lpile Results...29 Chapter 6: Discussion Plumb Piles Load Ratio Pile Deflection Soil Response SAP2000 and Lpile Comparison Characteristic Load Method Chapter 7: Conclusion 40 References..42

5 1 CHAPTER 1 Introduction 1.0 Background Foundations supporting large bridge structures must withstand both vertical gravity loads and lateral loads from a number of sources. These foundations are normally supported by steel H- piles that in turn must resist the vertical and lateral forces. While vertical pile forces present a challenge, most often the design for horizontal pile forces is more complex. Lateral loads from wind, earth, thermal, and hydraulic forces on a sub-structure as well as centripetal forces from trucks increase the need for horizontal resistance. Most often, battered piles as part of a pile group with plumb piles are used to resist these horizontal forces. 1.1 Problem Statement Initially, the Pennsylvania Department of Transportation s (PennDOT) policy for lateral loading on battered piles was to calculate the lateral capacity of the pile based on the actual loads resisted by the pile. However, with the incorporation of the load and resistance factor design (LRFD) method, PennDOT has since changed their policy to determine lateral pile capacity based on an assumed vertical to horizontal load ratio of 3.5:1. Accompanying this PennDOT policy is the assumption that all lateral force is resisted by battered piles (Kelly, et al., 1995) and conversely, none of the lateral force is resisted by vertical piles. While this makes the design of pile groups much simpler, it results in an overly conservative determination of pile group lateral force resisting capacity. In order to meet all PennDOT requirements, specifically the 3.5:1 ratio, it is often necessary to construct larger footings than may be required based on the results of a more complete analysis.

6 2 1.2 Objectives The objective of this study is to determine if the vertical to horizontal load ratio of 3.5:1 can be relaxed to 3:1 or less, thus decreasing footing sizes. The study will also describe the capacity of both plumb and battered piles under different loading ratios. This behavior is a factor of pile stiffness, surrounding soil characteristics such as shear strength and effective unit weight, connection conditions, and type of loading. These factors will be addressed to determine if the ratio can be decreased still further in ideal conditions. 1.3 Scope There are many factors that govern the behavior of piles as well as limit states that determine how piles will fail. This study will analyze the weak axis behavior of an HP12x53 steel pile under static vertical and lateral loads. It will assume that piles are spaced at least seven diameters apart so grouping effects are negligible. As a consequence, data from this study can be applied to a pile group containing any number of piles by simply adding the results from the individual test pile. Finally, piles will be analyzed for the limit states of displacement, bending moment for laterally loaded piles, and combined beam-column behavior using the interaction equation for piles with both vertical and lateral forces. Previous PennDOT studies have indicated that most often the maximum allowed horizontal displacement of one inch will control analysis, and therefore this limit has been enforced here as well.

7 3 This study can be used as a baseline for further analysis. It provides the warrant for possible full scale testing and further assessment in order to bring about potential change in the Department s load ratio specifications.

8 4 CHAPTER 2 Literature Review The following is a review of the literature needed to analyze pile behavior. This parametric study uses the general Euler beam equation with a modification for the nonlinear soil-pile interaction term. As a result of this term, p-y curves are developed and implemented in computer models to accurately create multi-linear springs. In addition, p-y curves were modified to account for battered and group effects. Finally, the remainder of this chapter will describe the Characteristic Load Method, a tool designers use in order to simplify pile behavior. 2.1 General Equation The response of a laterally loaded pile depends on the interaction between soil and structure. Analysis must include both the interdependent deformation of the pile and of the soil. A pile can be analyzed using traditional Euler beam theory with a slight modification for the soil-structure interaction. The general equation for such behavior is given as: (Equation 1) where corresponds to the resultant soil resistance per unit length along the pile when the pile is caused to displace a lateral distance, y (Reese, et al., 2006). If soil reaction has a linear relationship with lateral pile deflection, the equation has a closed solution and is easily solved. However, as the load transferred from the pile to the soil increases by a percentage of its value, the deflection increases by a greater percentage. Therefore, while the pile itself may continue to behave linearly, the behavior of the pile/soil system is nonlinear (Duncan, et al., 1994). As a result, the solution to this equation often involves an iterative procedure that uses the p-y method to account for the nonlinear term.

9 5 2.2 p-y Method The present study uses the p-y method to model the nonlinear soil-pile interaction. The soil resistance per unit length, p, around a pile is a function of the lateral pile displacement, y. Figure 1 presents a uniform distribution of soil stresses normal to a plumb pile. If the pile is caused to deflect a distance y due to some lateral force, the soil stress distribution will change in response. Greater stress will develop on the front face of the pile while stresses in the rear decrease. Figure 1: Soil Stresses Around a Pile (Pando, et al., 2006), no restrictions

10 6 Reese (1994) proposed a series of equations that attempts to graph the soil-pile interaction, called the p-y method. The equations and corresponding constants are empirically based and the multiple steps involved can be cumbersome, especially when several curves for different soils must be developed. Prior to routine computer use, Reese s equations were one of the only ways in which pile deflection could be related to soil resistance, which led to the creation of various simplified procedures for determining pile behavior. However, the computer has made the formation of p-y curves much easier and more accurate with its ability to iterate numerous times per second. This study uses the software Lpile to create p-y curves for the three different soils. While the resulting output curve may be similar, the program iterates instead of using the empirical equations and thus the curves may be considered more accurate. Figure 2 was developed using Reese s equations and shows a characteristic p-y curve for a plumb pile in clay at a depth of 12 inches using the properties listed in Tables 1 and 2. In comparison to Figure 10c, the Lpile generated p-y curve of the same properties, the Reese equation curve is more conservative and a pile designed using this data would not be utilizing the full soil resistance capacity. Figure 2: P-Y Curve for Plumb Pile at 12 Inch Depth in Clay

11 7 The data from p-y curves allows the soil to be modeled as a series of independent, multi-linear springs. The springs effectively replace the soil in a numerical structural analysis model that can then be used to determine the behavior of the laterally loaded piles (Pando, et al., 2006). As Figure 3 shows, the springs must be included along the entire depth of the pile to accurately represent the soil. The closer the springs are spaced, the more precise the model. There are a number of different curves depending on certain soil properties including effective unit weight and shear strength as well as pile properties such as pile diameter and length. The soil and pile properties used in this study to construct the nine p-y curves are presented in Tables 1 and 2. Figure 3: Soil Modeled as Multilinear Springs (Pando, et al., 2006), no restrictions

12 8 2.3 Battered Pile Effects The p-y curves created from the Reese equations are solely for vertical piles. However, piles are battered when analysis indicates the presence of high lateral loads. In this way, a component of the force is resisted through axial compression and therefore, the load resisted by pile bending is decreased. In order to account for batter effects, Zhang Limin (1999) proposed a factor to modify the two most important properties of the Reese p-y curves, the initial subgrade modulus, K sb, and the ultimate soil resistance, P ult (Limin, et al., 1999). Limin states that the overall shape of the curve remains constant from the vertical case, but the K sb and P ult change according to pile batter governed by the equations: K sb =ΨK s Equation 2 P ub = ΨP u. Equation 3 The factor where K pb and K p are the passive earth pressure coefficients for inclined and vertical walls respectively. λ is the coefficient that accounts for the size of the clay passive soil wedge through its relative density. The same Ψ factor is used to modify both the initial subgrade modulus and the ultimate soil resistance for battered piles. Figure 4 shows that for a constant lateral pile deflection, the battered pile will activate a larger soil resistance than a plumb pile.

13 9 Figure 4: Battered Effects to p-y Curve (Pando, et al., 2006), no restrictions 2.4 Group Effects In addition to batter modification, p-y curves must also be altered due to grouping effects. Tests have indicated that the average load for a pile in a closely spaced group will be substantially less than that of a single, isolated pile at the same deflection (Rollins, et al., 2006). Group effects are magnified on leading piles that carry significantly higher loads compared to trailing piles in the same direction. These interactions are thought to be caused by interference with the failure surfaces of the piles in front of them. The response of one pile to a lateral load will cause displacement of the soil between adjacent piles, causing adding deflections to these trailing piles. Since group deflections are larger, maximum moments will also be greater. Figure 5 illustrates the overlapping soil stress zones caused by group effects. While not drawn to scale, the figure indicates that the active soil region for a single pile will overlap the active soil region for an adjacent pile, causing greater deflections and thus decreasing group efficiency. Rollins proposes that as pile spacing becomes approximately seven pile diameters or greater, there will be less

14 10 overlap of adjacent failure planes and thus group effects can be ignored (Rollins, et al., 2006). This study assumes that piles are spaced at least this distance so the results of the single isolated pile can be added linearly to account for any additional piles as part of a pile group. Figure 5: Active Soil Overlap (Smith, 2005), by permission 2.5 Characteristic Load Method Evans and Duncan developed a procedure termed the Characteristic Load Method in order to simplify the above p-y analysis (Duncan, et al., 1994). p-y analyses were performed for a variety of free head and fixed head loading conditions and the results were represented as dimensionless relationships by dividing loads, moments, and deflections by a characteristic load, moment, and

15 11 deflection respectively. The expressions for the characteristic equations were developed through repeated trials and are functions of pile and soil properties. Larger values of the characteristic load and characteristic moment indicate greater capacity of the pile to resist lateral loads and deflections. Using the characteristic properties, graphs were constructed that relate the dimensionless variables of load, moment and deflection. This method can be used to determine: 1. Ground-line deflections due to lateral loads for free and fixed head conditions. 2. Ground-line deflections due to moments applied at the ground-line. 3. Maximum moments for free and fixed head conditions. 4. The location of the maximum moment in the pile. 2.6 Characteristic Load Method Group Modification Factors As previously discussed, closely spaced piles (spacing < 7 pile diameters) will exhibit less resistance to lateral loads and thus experience more deflection due to group effects. Ooi and Duncan (1994) proposed that CLM equations can be altered by a factor to account for closely spaced piles (Ooi, et al., 1994). The two main limitations of this method include the use of an average pile spacing so only rectangular pile groups can be analyzed and the fact that individual pile loads within the group cannot be determined. The latter weakness is in conflict with the Rollins theory that leading piles will carry more load than trailing piles. However, the CLM is the only method that allows the behavior of laterally loaded piles to be analyzed without the help of complex computer processes.

16 12 CHAPTER 3 STUDY DESIGN A parametric study was used to analyze the behavior of both plumb and battered piles under vertical and lateral loads. Due to the nonlinear soil-pile interaction, computer methods must be used that can iterate many times to develop a solution to Equation 1. Based on the limit states of deflection and beam-column behavior, loads in various ratios were applied to the pile until failure. This data was used to determine if the vertical to horizontal load ratio of 3.5:1 can be relaxed. 3.1 Lpile There is no readily available, reasonably applied, manual method for solving the nonlinear, fourth order differential equation. This leads to the need for computer codes which are able to iterate many times to find a solution to the equation. This study will use the student version of Ensoft s Lpile computer program that accompanies the Reese (2006) text. Lpile solves the nonlinear differential equation presented earlier by arbitrarily selecting values for. The deflections are calculated along the length of the pile and used to construct p-y curves which give a new value for computed values of. This process continues until convergence occurs between the assumed and. Lpile is then able to use these p-y curves to predict pile head deflection and bending moments versus depth along the entire length of the pile. 3.2 SAP2000 The structural analysis software SAP2000 was used to compare the results obtained using Lpile. Piles were modeled as line elements with the necessary characteristics (dimensions, moment of inertia, Young s modulus) to correctly represent a Grade 50, HP12x53 steel member with weak

17 13 axis bending. The study analyzed the behavior of the representative pile in Figure 6 solely along the x-axis. As a result, the connection indicated at the bottom of the pile, node 31, only prohibits displacement in the vertical direction. The soil elements were modeled by multi-linear springs placed every foot along the depth of the pile as discussed earlier using the data from p-y curves created from Lpile. In order to calculate the multi-linear spring constants, it is necessary to multiply the soil resistance given by the p-y curves times the depth being analyzed to convert the values into forces of pounds. While Figure 6 shows that the springs are on only one side of the pile, the constants were entered such that the soil has the same reactive force for pile deflections in both the positive and negative x-axis. Using this model, piles were loaded in the positive x-axis direction for lateral loads and vertically downward (negative z-axis) for vertical loads at node 1 under various load ratios. SAP2000 output the results of pile deflection and bending moment at every node along the depth of the pile. These values were then used to compare against the results predicted from Lpile to check for accuracy between the two models.

18 Figure 6: Representative Pile Modeled in SAP

19 Characteristic Load Method Further comparison will be performed using Duncan s Characteristic Load Method. While this analysis is limited to plumb piles in the sand and clay cases with no axial loads, it will provide additional comparison data. The CLM is a widely available program with a relatively simple interface that caters well toward initial analysis. A comparison to the other more rigorous methods will indicate whether the CLM has merit as a useful preliminary tool. 3.4 Soil Types This study analyzes the behavior of piles in three different soil types commonly found throughout Pennsylvania. Duiker indicates there are three main soil types that make up the majority of the Commonwealth s subsurface; regions he names the Alleghany High Plateau, Pittsburgh Plateau, and the Ridge and Valley Province (Duiker, 2010). The Alleghany High Plateau (north central Pennsylvania) and the Ridge and Valley Province (south central into eastern Pennsylvania) are characterized by sandy loam and will be assumed as sand in this study. The Pittsburgh Plateau (southwestern Pennsylvania) is made up of clay and silt soils and thus both of these types of soil will be examined.

20 16 CHAPTER 4 - Study Procedure In order to determine if the load ratio can be relaxed, this parametric study used SAP2000 and Lpile to solve the nonlinear soil-pile equation. Piles at three different batters (plumb, 4:1, and 3:1) will be modeled in three soil types commonly found in Pennsylvania (sand, silt, and soft clay). Through computer iteration, piles were loaded in the appropriate ratio until failure of one of the limit states, deflection or beam-column behavior. This data was then correlated to the behavior of pile under the 3.5:1 load ratio. 4.1 Soil Properties The following table indicates the soil properties of the three different types of soil used in this study. Lpile utilized these values when constructing respective p-y curves. Sand Effective Unit Weight Internal Friction Angle p-y Modulus, k pci 35 degrees 90 pci Soft Clay Effective Unit Weight pci Undrained Cohesion 8.5 psi Strain Factor Silt Effective Unit Weight pci Undrained Cohesion psi Intern Friction Angle 34 degrees p-y Modulus 500 pci Strain Factor Table 1: Soil Properties

21 Pile Properties The following table is a list of the geometric properties for an HP12x53 steel pile: HP 12x53 Length Distance from Pile Top to Ground Surface Diameter Cross Sectional Area Moment of Inertia, Iy Modulus of Elasticity, E Plastic Section Modulus, Zy Available Flexural Strength, ΦMy Available Compressive Strength, ΦPn 360 in 0 in 12 in 15.5 in^2 127 in^4 29,000 ksi 32.2 in^ k-in kip Table 2: Pile Properties 4.3 Limit States In order to evaluate the behavior under the various load ratios, piles will be governed by the two limiting factors of deflection and beam-column action. Because piles will be loaded vertically in axial compression as well as laterally inducing bending moments, they will be subject to the interaction equation presented in Equation 4 which relates beam-column behavior. This behavior is governed by the equations, when Equation 4a when Equation 4b where P r = required compressive strength, lbs P c = available compressive strength, lbs M ry = required flexural strength based on weak axis bending, in-lbs M cy = available flexural strength based on weak axis bending, in-lbs

22 18 In addition to beam-column interaction, pile behavior will be governed by a maximum horizontal displacement of one inch, the highest lateral movement allowed by PennDOT at any strength or extreme limit state. PennDOT however, limits the design horizontal deflection to ½ inch at the Service Limit State (Pennsylvania Department of Transportation, 2007). Using SAP2000 and Lpile computer models, piles at three different batter angles will be loaded in the desired ratio until one of the above limit states is reached. SAP2000 models will output the deflections and moments at one foot increments while Lpile can graph behavior at every point along the depth of the pile. 4.4 Study Procedure Figure 7 presents a flowchart of the study procedure describing in brief the steps involved in this study. This procedure will be used to analyze the behavior of piles under various vertical to horizontal load ratios to determine if the PennDOT specification of a 3.5:1 ratio can be altered.

23 Figure 7: Study Procedure Flowchart 19

24 20 CHAPTER 5 - Study Results This section describes the results of the parametric study. It includes the p-y curves used to develop the multi-linear springs in the SAP computer models. In addition, the analysis of the piles under the various load ratios will be displayed through two sets of graphs. Figures 11 and 12 show the load ratio versus the actual horizontal loads resisted by the pile for both SAP and Lpile computer models. Figures 13 and 14 contain a series of graphs indicating the load ratio versus pile deflection based upon the computer models. In addition, the predicted capacity from the CLM that can only be applied to plumb piles in sand and clay are presented on Figures 11(a), 11(c), 12(a), and 12(c). Finally, Figures compares the results predicted by SAP2000 and Lpile to explore the precision between the different approaches. 5.1 Representative P-Y Curves Figures 8-11 are representative p-y curves for the three different soil types. The curves were created using Ensoft s Lpile software and indicate soil resistance in pounds per inch depth versus pile deflection in inches. The curves below show only the p-y data for depths of 12, 36, and 60 inches while in the study, curves were created at every foot of depth along the length of the pile.

25 21 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 8: Representative P-Y Curves for Sand at Depths of 12, 36, and 60 Inches

26 22 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 9: Representative P-Y Curves for Silt at Depths of 12, 36, and 60 Inches

27 23 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 10: Representative P-Y Curves for Clay at Depths of 12, 36, and 60 Inches

28 Horizontal Resistance and Deflections Predicted by SAP2000 and Lpile Figures 11 and 12 present the actual horizontal loads resisted by the pile versus the vertical to horizontal load ratio. Figure 11Figure 11 shows the lateral resistance predicted by SAP models while Figure 12 presents Lpile predictions. The x on the sand and clay graphs shows the lateral resistance predicted by the Characteristic Load Method which can only be used to analyze plumb piles with no axial loads. Figures 13 and 14 present pile deflection in inches versus the vertical to horizontal load ratio predicted by SAP2000 and Lpile. The first set, Figure 13 displays deflections predicted by the SAP models while the second set, Figure 14, shows Lpile results.

29 25 (a) Sand (b) Silt (c) Clay Figure 11: Horizontal Resistance Predicted by SAP model

30 26 (a) Sand (b) Silt (c) Clay Figure 12: Horizontal Resistance Predicted by Lpile Model

31 27 (a) Sand (b) Silt (c) Clay Figure 13: Deflection Predicted by SAP Model

32 28 (a) Sand (b) Silt (c) Clay Figure 14: Deflection Predicted by Lpile Model

33 Comparison of SAP and Lpile Results Figures present a more detailed comparison of the results predicted by SAP and Lpile computer models. This data will be used to analyze the precision between the two different methods. The first three sets of graphs show the difference in horizontal resistances separated by pile batter and then by soil type between the two models. The following three sets of curves, figures 18 20, indicate the deflection comparisons.

34 30 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 15: Comparison of Horizontal Resistance Predicted by SAP and Lpile Models in Sand

35 31 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 16: Comparison of Horizontal Resistance Predicted by SAP and Lpile Models in Silt

36 32 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 17: Comparison of Horizontal Resistance Predicted by SAP and Lpile Models in Clay

37 33 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 18: Comparison of Deflection Predicted by SAP and Lpile Models in Sand

38 34 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 19: Comparison of Deflection Predicted by SAP and Lpile Models in Silt

39 35 (a) Plumb (b) 4:1 Batter (c) 3:1 Batter Figure 20: Comparison of Deflection Predicted by SAP and Lpile Models in Clay

40 36 CHAPTER 6 - Discussion The following is a discussion of the results of this study. First, PennDOT s assumption that all lateral load is resisted by battered piles and none by plumb piles is analyzed. Then, the load ratio will be compared to the bending moment and pile deflection to determine its merit. Finally, the computer models will be analyzed for precision of their respective results. 6.1 Plumb Piles The parametric study indicates that plumb piles in all three types of soil under both models have a significant level of lateral resistance. Even using the most conservative values predicted by the study, plumb piles in sand were shown to still have 71.7% of the lateral capacity that piles battered at 3:1 have. This percentage increases to 90.2% for soft clay and to 91.8% for silt. As a result, PennDOT s assumption that all lateral load is resisted by the lateral component of the battered piles and none by the bending moment in plumb piles is extremely conservative and ultimately unwarranted. This fact alone suggests the need for possible further investigation by PennDOT, including full scale studies, to reevaluate their current loading policy. A change of this particular assumption will go a long way in reducing foundation sizes. 6.2 Load Ratio Beyond preliminary design, the load ratio has little effect on the actual carrying capacities of piles. The results indicate that piles of all batters in each of the three different soils are able to withstand force ratios greater than or less than 3.5:1. Previous PennDOT studies suggested that the maximum allowable deflection of one inch was most often the limiting factor in pile loading. However, the current study indicates that pile loads were governed by the beam-column

41 37 interaction equation given by Equation 4. As a result of restricting loads to one kip increments, some of the interaction equations did not reach 100%. However, all interactions that did not reach 100% because of the unit kip rounding came within 3% or less of the maximum ratio of axial plus bending forces allowed by the interaction equation. In this way, lateral pile capacity is primarily influenced by the bending moment due to the applied horizontal load, given by M ry in Equation 4. Additional factors of the interaction equation, such as available flexural strength (M cy ) and available compressive strength (P c ), are based on pile geometry and do not depend on the loads; they are constant properties of the steel shape and will not fluctuate. The last term of the interaction equation, the applied axial load (P r ), is dependent upon the applied horizontal load and only changes after the desired horizontal load has been established. In this way, the factors of the beam-column interaction equation, which this study has shown to govern pile behavior, are dependent on either pile geometry or the applied horizontal load. Therefore, the load ratio is a much less significant factor to determine pile capacity when compared to the applied horizontal load and resulting bending moment. 6.3 Pile Deflection Unlike previous PennDOT studies suggested, pile deflections did not govern behavior. Instead, pile deflections were significantly less than one inch for all three types of soil and each pile batter. In fact, pile displacements in silt and battered piles in sand were less than the design criteria of one half inch specified by PennDOT. As a result, the practical design of piles using PennDOT specifications will not require significant reduction in the maximum lateral loads found in this study. In this way, pile design can be considered efficient because practical design

42 38 will be based on pile moment capacity as opposed to serviceability conditions. Piles will develop nearly their full lateral capacity before reaching the one-half inch deflection limit. 6.4 Soil Response As indicated by the p-y curves, silt has the stiffest response to a unit pile deflection. Therefore, piles in silt are able to withstand larger lateral loads correlating to the behavior predicted by both models. Plumb piles in silt have stiffer lateral capacities than battered piles in the other two soils. This high lateral carrying capacity may eliminate the need for battered piles altogether, especially since SAP2000 predicted an increase in horizontal load resistance of only about 9% from plumb to piles battered at 3 vertical to 1 horizontal. Therefore, this study suggests that sites with stiff soils such as silts be analyzed fully before the determination to use battered piles. There may be occurrences where this option is unnecessary, especially for low lateral loads. 6.5 SAP2000 and Lpile Comparison Overall, the lateral capacities obtained from SAP2000 and Lpile computer models had great agreement, especially for piles in sand and clay. However, most results generally indicate that Lpile analysis predicted slightly larger capacities when compared to SAP200, most notably for the silt trials. Still, even the greatest difference in results predicted an increase of only about 12% in lateral capacity from SAP2000 to Lpile. Conversely, the deflections from each model were not as consistent. There was no general pattern of one model predicting certain deflections based on the results from all soil types. Individually however, it is clear that SAP2000 consistently predicted larger deflections in silt

43 39 while Lpile produced larger deflections in clay. Even still, the maximum difference from all three soil cases was only 0.12 inches in clay, a divergence of about 20%. In the end, even with the differences in deflections from each model, all predicted results were less than the one inch limit state. 6.6 Characteristic Load Method The CLM was used as a final comparison against the results of SAP2000 and Lpile models. This analysis predicted lower lateral resistance for plumb piles in sand and clay with no axial loads, the only two cases this simplified method can be used for. However, the CLM did calculate lateral capacities that were within 25% of the resistance predicted by SAP models. While this method is extremely limited in its use, plumb piles with no axial loads, a preliminarily technique that calculates conservative lateral resistances may have some merit as an initial tool.

44 40 CHAPTER 7 - Conclusion The purpose of this study was to determine if the PennDOT specification of a 3.5:1 vertical to horizontal pile load ratio may be altered. While aspects of traditional Euler beam theory were used to determine pile behavior, the nonlinear soil-pile interaction prevented Equation 1 from having a closed solution. As a result, p-y curves relating pile displacement to soil resistance per unit depth were used as part of an iterative process in the computer programs SAP2000 and Lpile to calculate a solution. Piles at three different batters (plumb, 4:1, and 3:1) were loaded at specified ratios in three different soils commonly found throughout Pennsylvania. Piles were loaded until failure of one of two limit states: deflection greater than one inch or failure of the beam-column interaction equation (Equation 4). From these models, plumb piles can be analyzed for lateral load carrying capacity and the 3.5:1 load ratio can be evaluated. The load ratio has merit as a tool in preliminary design. After soil properties are determined, the ratio can be used to establish initial pile capacities based on previous studies with similar soil profiles. In this way, the designer can use estimate pile capacities to establish a preliminary design. However, additional research must always be made to determine the true capacity of the steel H piles. In this way, the ratio will not prevent time spent with field studies but can be used as a starting point in design. The results of this parametric study indicate that piles are able to resist force ratios both greater and less than 3.5 vertical to 1 horizontal. In this way, the importance of the load ratio is much less significant than the actual applied lateral and vertical loads. Therefore, standards of pile loading may be more appropriately based on soil and pile properties than load ratios. In addition,

45 41 the data suggests that the PennDOT assumption that vertical piles do not resist lateral load is inefficient. The results predicted in this study indicate that this assumption may ignore as much as 91% of the lateral capacity of the plumb pile based on the silt soil profile. The study also indicates that pile capacities predicted from SAP2000 and Lpile computer models agreed quite well. Both models predicted similar forces for the sand and clay soil profiles, while Lpile calculated slightly larger capacities in the silt model. However, there was a larger difference between the two models when predicting deflections. Further full scale studies may be performed to determine the true accuracy of these programs. Lastly, the CLM predicted lower pile resistances than both the SAP and Lpile computer models. The predicted values were within 25% of the SAP results and thus, the CLM may still have merit has a preliminary design aide. In general, the results of this study indicate the warrant for potential further testing and analysis of PennDOT specifications. It shows that the load ratio may not play a significant role in pile behavior, and the assumption that none of the lateral load is resisted by plumb piles may be extremely inefficient. A change in either of these specifications would go a long way in reducing overall foundation sizes.

46 42 References Duiker, S. W The Soils of Pennsylvania. Crop and Soil Management [Online] [Cited: January 19, 2010.] Duncan, J Michael, Evans, Leonard T and Ooi, Phillip S Lateral Load Analysis of Single Piles and Drilled Shafts. Journal of Geotechnical Engineering, Vol 120, No. 6. s.l. : ASCE, 1994, pp Kelly, Brian, Withiam, Jim and Voytko, Ed Distribution of Lateral Load in Pile Groups Supporting Abutments and Retaining Walls. s.l. : Pennsylvania Department of Transportation, Modjeski and Masters, Final Summary. Limin, Zhang, McVay, C Michael and Lai, W Peter Centrifuge Modelling of Laterally Loaded Single Piles. s.l. : Canadian Geotechnical Journal, Ooi, Phillip S and Duncan, J Michael Lateral Load Analysis of Groups of Piles and Drilled Shafts. Journal of Geotechnical Engineering, Vol 120, No. 6. s.l. : ASCE, 1994, pp Pando, Miguel A, et al A Laboratory and Field Study of Composite Piles for Bridge Substructures. Charlottesville : Virginia Transportation Research Council, Final Report, FHWA-HRT Pennsylvania Department of Transportation Design Manual Part 4. s.l. : Commonwealth of Pennsylvania, Reese, Lymon C and Van Impe, William F Single Piles and Pile Groups Under Lateral Loading. Brookfield : A.A. Balkema Publishers, 1st Edition, Reese, Lymon, Isenhower, William and Wang, Shin-Tower Analysis and Design of Shallow and Deep Foundations. Hoboken : John Wiley and Sons, Rollins, Kyle M, et al Pile Spacing Effects on Lateral Pile Group Behavior: Analysis. Journal of Geotechnical and Geoenvironmental Engineering, Vol 132, No. 10. s.l. : ASCE, Smith, Ian Pile Foundation Design. Edinburgh, Scotland : Napier University, 2005.

47 Academic Vita of Vincent DeRosa PO BOX 358, Botsford, CT Education Bachelor of Science in Civil Engineering (structures focus), Expected May 2010 The Schreyer Honors College at The Pennsylvania State University Honors in Civil Engineering Thesis Title: Lateral Loading of Battered Piles with Respect to Footing Size Thesis Supervisor: Dr. Jeffrey Laman Honors and Awards Dean s List (3.50+), Spring 2007 through Fall 2010 Chi Epsilon Civil Engineering Honors Society Ean H. C. Hong Memorial Scholarship Schreyer Honors College Scholarship Triangle Fraternity Pennsylvania State Chapter Scholarship Teaching Experience Teaching Intern at the Pennsylvania State University for senior level steel design class Affiliations American Society of Civil Engineers Member Triangle Engineering and Science Fraternity Member Pennsylvania State University Steel Bridge Team Member