USE OF PILE DRIVING ANALYSIS FOR ASSESSMENT OF AXIAL LOAD CAPACITY OF PILES

Transcription

1 JOINT TRANSPORTATION RESEARCH PROGRAM INDIANA DEPARTMENT OF TRANSPORTATION AND PURDUE UNIVERSITY USE OF PILE DRIVING ANALYSIS FOR ASSESSMENT OF AXIAL LOAD CAPACITY OF PILES Rodrigo Salgado Profeor of Civil Engineering School of Civil Engineering Purdue Univerity Correponding Author Yanbei Zhang Graduate Reearch Aitant School of Civil Engineering Purdue Univerity SPR-3378 Report Number: FHWA/IN/JTRP-2012/11 DOI: /

2 RECOMMENDED CITATION Salgado, R., and Y. Zhang. Ue of Pile Driving Analyi for Aement of Axial Load Capacity of Pile. Publication FHWA/ IN/JTRP-2012/11. Joint Tranportation Reearch Program, Indiana Department of Tranportation and Purdue Univerity, Wet Lafayette, Indiana, doi: / CORRESPONDING AUTHOR Profeor Rodrigo Salgado School of Civil Engineering Purdue Univerity (765) JOINT TRANSPORTATION RESEARCH PROGRAM The Joint Tranportation Reearch Program erve a a vehicle for INDOT collaboration with higher education intitution and indutry in Indiana to facilitate innovation that reult in continuou improvement in the planning, deign, contruction, operation, management and economic efficiency of the Indiana tranportation infratructure. Publihed report of the Joint Tranportation Reearch Program are available at: NOTICE The content of thi report reflect the view of the author, who are reponible for the fact and the accuracy of the data preented herein. The content do not necearily reflect the official view and policie of the Indiana Department of Tranportation or the Federal Highway Adminitration. The report doe not contitute a tandard, pecification or regulation.

3 1. Report No. FHWA/IN/JTRP 2012/11 TECHNICAL REPORT STANDARD TITLE PAGE 2. Government Acceion No. 3. Recipient' Catalog No. 4. Title and Subtitle Ue of Pile Driving Analyi for Aement of Axial Load Capacity of Pile 5. Report Date May Performing Organization Code 7. Author() Rodrigo Salgado and Yanbei Zhang 9. Performing Organization Name and Addre Joint Tranportation Reearch Program Purdue Univerity 550 Stadium Mall Drive Wet Lafayette, IN Sponoring Agency Name and Addre Indiana Department of Tranportation State Office Building 100 North Senate Avenue Indianapoli, IN Performing Organization Report No. FHWA/IN/JTRP 2012/ Work Unit No. 11. Contract or Grant No. SPR Type of Report and Period Covered Final Report 14. Sponoring Agency Code 15. Supplementary Note Prepared in cooperation with the Indiana Department of Tranportation and Federal Highway Adminitration. 16. Abtract Driven pile are commonly ued in foundation engineering. Pile driving formulae, which directly relate the pile et per blow to the capacity of the pile, are commonly ued to decide whether an intalled pile will have the deigned capacity. However, exiting formulae have been propoed baed on empirical obervation and have not been validated cientifically, o ome might over predict pile capacity, while other may be too conervative. In thi report, a more advanced and realitic model developed at Purdue Univerity for dynamic pile driving analyi wa ued to develop more accurate pile driving formulae. Thee formulae are derived for pile intalled in typical oil profile: a floating pile in and, an end bearing pile in and, a floating pile in clay, an end bearing pile in clay and a pile croing a normally conolidated clay layer and reting on a dene and layer. The propoed driving formulae are validated through well documented cae hitorie of driven pile. Comparion of the prediction from the propoed formulae with the reult from tatic load tet, dynamic load tet and conventional formulae how that they produce reaonably accurate prediction of pile capacity baed on pile et obervation. 17. Key Word pile deign, numerical modeling, pile dynamic, dynamic analyi, pile driving formula, pile analyi, pile bearing capacity 19. Security Claif. (of thi report) 20. Security Claif. (of thi page) 18. Ditribution Statement No retriction. Thi document i available to the public through the National Technical Information Service Springfield, VA No. of Page 22. Price Unclaified Unclaified 34 Form DOT F (8 69)

4 Introduction EXECUTIVE SUMMARY USE OF PILE DRIVING ANALYSIS FOR ASSESSMENT OF AXIAL LOAD CAPACITY OF PILES The dynamic repone of a pile during driving i very complex, involving the interaction of the hammer, cuhion, pile and oil during application of an impact load. The firt analyi aimed at imulating a hammer blow on a pile wa publihed in A revied, more realitic pile driving analyi wa recently developed at Purdue Univerity. Proper modeling of pile driving i important both for planning and inpecting pile driving operation. Reliable etimation of the load capacity of a driven pile baed on the eae or difficulty with which the pile i driven allow an inpector to decide when pile driving can be dicontinued. One of the tool ued to decide whether an intalled pile will have the predicted capacity i the pile driving formula. Pile driving formula directly relate the pile et per blow to the capacity of the pile, and, due to their implicity, thee formula have been ued often. However, exiting formula have been propoed baed on empirical obervation and have not been validated cientifically, o ome formula might over-predict pile capacity, while other may be too conervative. In thi tudy we ued the more advanced and realitic model developed at Purdue Univerity for dynamic pile driving analyi to develop more accurate pile driving formula, which conider both oil and pile variability. A review of the Purdue pile driving analyi method and a dicuion on election of model parameter to ue in the analyi precede the application of the analyi to typical oil profile. Pile driving formula are developed baed on the reult of thee analye for five ideal oil profile: floating pile in and and clay, end-bearing pile in and and clay, and pile croing clay reting on and. Well documented cae hitorie of driven pile in Lagrange and Japer Countie in Indiana are ued to validate the propoed pile driving formula. Comparion of the prediction of propoed formula with the reult of tatic load tet, dynamic load tet and conventional formula how that the propoed model i capable of producing more reaonable and accurate prediction of pile capacity baed on pile et obervation. Finding We have developed pile driving formula by fitting reult of a realitic pile driving analyi performed for cloed-ended teel pipe pile for five typical cae: 1. Floating pile in and. The pile driving formula i expreed in thi cae in term of five variable: the hammer efficiency, the normalized hammer weight, the normalized hammer drop height, the relative denity of the and and the pile et. 2. End-bearing pile in and. The pile driving formula in thi cae i expreed in term of five variable: the hammer efficiency, the normalized hammer weight, the normalized hammer drop height, the ratio of haft to bae relative denity and the pile et. 3. Floating pile in normally conolidated clay. The pile driving formula in thi cae i expreed in term of four variable: the hammer efficiency, the normalized hammer weight, the normalized hammer drop height and the normalized pile et. 4. Pile croing a normally conolidated clay layer and reting on an over-conolidated clay layer. The pile driving formula in thi cae i expreed in term of four variable: the hammer efficiency, the normalized hammer weight, the normalized hammer drop height and the normalized pile et. 5. Pile croing a clay layer and reting on a dene and layer. The propoed pile driving formula in thi cae i expreed in term of five variable: the hammer efficiency, the normalized hammer weight, the normalized hammer drop height, the ratio of haft relative denity to bae relative denity and the pile et. Implementation Up to 80% of Indiana Department of Tranportation (INDOT) project lack the budget to allow dynamic load teting a a mean to check the acceptability of driven pile, and therefore pile driving formula are ued. Similar number apply to other agencie and, indeed, private companie. Implementation of the reult of thi reearch will enable INDOT and other owner or contractor to take advantage of updated and improved pile driving formula in maller project, leading to more economical piling. Engineer can ue the pile driving formula propoed in thi report in their work by following the following tep: 1. baed on the oil profile information, decide which of the typical cae applie; 2. baed on hammer information, etimate the hammer efficiency, the hammer weight and the hammer drop height; 3. etimate the oil propertie to be ued baed on knowledge of the oil profile; 4. meaure the pile et per blow at the end of pile driving; 5. take the value of the oberved pile et into the correponding pile driving formula to calculate the etimated capacity of the pile.

5 CONTENTS 1.INTRODUCTION ProblemStatement ObjectiveandOrganization PARAMETERSELECTION Introduction AdvancedModelforPileDrivingAnalyi Determination of Small-Strain Shear Modulu Determination of Soil Vicoity Parameter Determination of Static Unit Shaft Reitance Determination of Static Unit Bae Reitance Determination of Other Parameter PILEDRIVINGFORMULAS Introduction FloatingPileinSand End-BearingPileinSand FloatingPileinClay End-Bearing Pile in Clay ClayoverSand EffectofHammerWeightandDropHeight CASESTUDY Lagrange County JaperCounty SUMMARYANDCONCLUSION REFERENCES... 23

6 LIST OF TABLES Table Page Table 1.1 Summary of Pile Driving Formula 1 Table 2.1 Exponent k for (2-9) 3 Table 3.1 Specification of ICE-42S Hammer 5 Table 3.2 Simulation Cae for Floating Pile in Sand 5 Table 3.3 Value of A and B in Pile Driving Formula for Floating Pile in Sand 5 Table 3.4 Simulation Cae for End-Bearing Pile in Sand 8 Table 3.5 Parameter for Power Function for End-Bearing Pile in Sand 8 Table 3.6 Simulation Cae for Floating Pile in Clay 10 Table 3.7 Simulation Cae for End-Bearing Pile in Clay 11 Table 3.8 Simulation Cae for End-Bearing Pile Penetrated through Clay and Reted on Sand 12 Table 3.9 Parameter of Power Function for Pile in Clay over Sand 13 Table 3.10 Hammer Parameter 13 Table 3.11 Summary of Solution to Equation (3-21) for Typical Soil Profile 14 Table 4.1 Parameter for a and b in Gate Formula for SI and Englih Unit Sytem 22 Table 4.2 Meaured and Predicted Pile Capacity in Lagrange County 22 Table 4.3 Meaured and Predicted Pile Capacity in Japer County 22 Table 5.1 Summary of Pile Driving Formula for Floating and End-Bearing Pile in Typical Soil Depoit 23

7 LIST OF FIGURES Figure Page Figure 2.1 Soil model along pile haft 2 Figure 2.2 Propoed oil model at pile bae 3 Figure 2.3 Lumped mae ytem of 1D dynamic analyi 3 Figure 3.1 Floating pile in and 5 Figure 3.2 Multiplier A veru relative denity for floating pile in and 6 Figure 3.3 Exponent B veru relative denity for a floating pile in and 6 Figure 3.4 Simulated data (point) and propoed pile driving formula (line) for floating pile in and 6 Figure 3.5 Pile driving formula with imulated data for D R 5 10% 6 Figure 3.6 Pile driving formula with imulated data for D R 5 20% 6 Figure 3.7 Pile driving formula with imulated data for D R 5 30% 7 Figure 3.8 Pile driving formula with imulated data for D R 5 40% 7 Figure 3.9 Pile driving formula with imulated data for D R 5 50% 7 Figure 3.10 Pile driving formula with imulated data for D R 5 60% 7 Figure 3.11 Pile driving formula with imulated data for D R 5 70% 7 Figure 3.12 Pile driving formula with imulated data for D R 5 80% 7 Figure 3.13 Pile driving formula with imulated data for D R 5 90% 8 Figure 3.14 End-bearing pile in and 8 Figure 3.15 Multiplier A veru relative denity ratio for end-bearing pile in and 8 Figure 3.16 Exponent B veru relative denity ratio for end-bearing pile in and 8 Figure 3.17 Simulated data (point) and propoed pile driving formula (line) for end-bearing pile in and 9 Figure 3.18 Propoed pile driving formula for end-bearing pile in and: D Rb 5 40% 9 Figure 3.19 Propoed pile driving formula for end-bearing pile in and: D Rb 5 50% 9 Figure 3.20 Propoed pile driving formula for end-bearing pile in and: D Rb 5 60% 9 Figure 3.21 Propoed pile driving formula for end-bearing pile in and: D Rb 5 70% 10 Figure 3.22 Propoed pile driving formula for end-bearing pile in and: D Rb 5 80% 10 Figure 3.23 Propoed pile driving formula for end-bearing pile in and: D Rb 5 90% 10 Figure 3.24 Floating pile in clay 10 Figure 3.25 Simulated data (point) and propoed pile driving formula (line) for floating pile in clay 11 Figure 3.26 Pile driving formula for floating pile in clay 11 Figure 3.27 End-bearing pile in clay 11 Figure 3.28 Simulated data (point) and propoed pile driving formula (line) of all OCR value for end-bearing pile in clay 12 Figure 3.29 End-bearing pile penetrated through clay and reted on and 12 Figure 3.30 Multiplier A veru relative denity for pile in clay over and 13 Figure 3.31 Exponent B veru relative denity for pile in clay over and 13 Figure 3.32 Simulated data (point) and propoed pile driving formula (line) of end-bearing pile through clay on and 13 Figure 3.33 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for floating pile in and Figure 3.34 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 1 (W/W R and H/L R 5 2.5) 14 14

8 Figure 3.35 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 2 (W/W R and H/L R 5 5) Figure 3.36 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 3 (W/W R and H/L R 5 7.5) Figure 3.37 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 4 (W/W R and H/L R 5 10) Figure 3.38 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 5 (W/W R and H/L R 5 5) Figure 3.39 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 6 (W/W R and H/L R 5 5) Figure 3.40 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 7 (W/W R and H/L R 5 5) Figure 3.41 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile in and Figure 3.42 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in and: Hammer 1 (W/W R and H/L R 5 2.5) Figure 3.43 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in and: Hammer 2 (W/W R and H/L R 5 5) Figure 3.44 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in and: Hammer 3 (W/W R and H/L R 5 7.5) Figure 3.45 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in and: Hammer 4 (W/W R and H/L R 5 10) Figure 3.46 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in and: Hammer 5 (W/W R and H/L R 5 5) Figure 3.47 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in and: Hammer 6 (W/W R and H/L R 5 5) Figure 3.48 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in and: Hammer 7 (W/W R and H/L R 5 5) Figure 3.49 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for floating pile in clay Figure 3.50 Comparion between imulated data and predicted value by propoed formula for floating pile in clay: Hammer 1 (W/W R and H/L R 5 2.5) Figure 3.51 Comparion between imulated data and predicted value by propoed formula for floating pile in clay: Hammer 2 (W/W R and H/L R 5 5) Figure 3.52 Comparion between imulated data and predicted value by propoed formula for floating pile in clay: Hammer 3 (W/W R and H/L R 5 7.5) Figure 3.53 Comparion between imulated data and predicted value by propoed formula for floating pile in clay: Hammer 4 (W/W R and H/L R 5 10) Figure 3.54 Comparion between imulated data and predicted value by propoed formula for floating pile in clay: Hammer 5 (W/W R and H/L R 5 5) Figure 3.55 Comparion between imulated data and predicted value by propoed formula for floating pile in clay: Hammer 6 (W/W R and H/L R 5 5) Figure 3.56 Comparion between imulated data and predicted value by propoed formula for floating pile in clay: Hammer 7 (W/W R and H/L R 5 5) Figure 3.57 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile in clay Figure 3.58 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in clay: Hammer 1 (W/W R and H/L R 5 2.5) Figure 3.59 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in clay: Hammer 2 (W/W R and H/L R 5 5)

9 Figure 3.60 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in clay: Hammer 3 (W/W R and H/L R 5 7.5) Figure 3.61 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in clay: Hammer 4 (W/W R and H/L R 5 10) Figure 3.62 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in clay: Hammer 5 (W/W R and H/L R 5 5) Figure 3.63 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in clay: Hammer 6 (W/W R and H/L R 5 5) Figure 3.64 Comparion between imulated data and predicted value by propoed formula for end-bearing pile in clay: Hammer 7 (W/W R and H/L R 5 5) Figure 3.65 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and Figure 3.66 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and: Hammer 1 (W/W R and H/L R 5 2.5) Figure 3.67 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and: Hammer 2 (W/W R and H/L R 5 5) Figure 3.68 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and: Hammer 3 (W/W R and H/L R 5 7.5) Figure 3.69 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and: Hammer 4 (W/W R and H/L R 5 10) Figure 3.70 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and: Hammer 5 (W/W R and H/L R 5 5) Figure 3.71 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and: Hammer 6 (W/W R and H/L R 5 5) Figure 3.72 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for end-bearing pile through clay on and: Hammer 7 (W/W R and H/L R 5 5)

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11 1. INTRODUCTION 1.1 Problem Statement Driven pile are commonly ued in foundation olution. Becaue the pile driving proce i variable and impoe ignificant change to the tate of the oil around the pile that are difficult to model, both the deign and quality control of piling operation have been ubject to coniderable uncertainty and have been approached conervatively. It i deirable from a reearch point of view to develop reliable mean to evaluate pile capacity during the deign tage and then verify that that capacity i available during the intallation proce. One of the method to verify whether an intalled pile will have the predicted capacity i through the ue of pile driving formula, which directly relate the pile et per blow with the capacity of the pile. Due to it implicity, the Gate Formula (1) i commonly ued by INDOT engineer in mall- to medium-cale project. There are other pile driving formula available in the literature; a ummary i given in Table 1.1. Mot of thee formula are empirical in nature and may not be applicable to every oil depoit. Thee formula have not been validated cientifically, o ome might over-predict pile capacity, while other may be too conervative. Reearch at Purdue Univerity ha recently produced advance in dynamic analyi of pile driving. The preent tudy wa motivated by a deire to put thee analye to ue in pile driving verification. A number of project exit with budget that are too mall to jutify dynamic load tet. Thee project would benefit from the ue of pile driving formula developed baed on dynamic analyi. Thi report propoe a method by which uch formula can be developed and propoe formula for a number of typical oil profile. Thee formula hould be at the preent time conidered firt reult, requiring further validation. 1.2 Objective and Organization In Chapter 2, we briefly introduce the advanced oil reaction model and the olution cheme ued for the advanced pile driving imulation model; we then dicu the election of parameter for ue in. In Chapter 3, we preent the imulation reult for typical oil profile, and then develop pile driving formula baed on thoe reult. In Chapter 4, we validate the formula by comparion with field tet reult (from tatic load tet and dynamic load tet on intrumented pile in well characterized oil) a well a with conventional pile driving formula. Chapter 5 contain a ummary of the main finding of thi report. TABLE 1.1 Summary of Pile Driving Formula Name Equation Canadian National Building Code Q u ~ e he h C 1, C 1 ~C 4 ~ W rzn 2 0:5W p, C 2 ~ 3Q u zc 2 C 3 W r zw p 2A, C 3~ L E zc 4, C 4 ~3:7 10 {10 m 2 =kn Danih Formula (3) Q u ~ e rffiffiffiffiffiffiffiffiffiffiffi he h e heh L, C 1 ~ zc 1 2AE Eytelwein Formula (4) Q u ~ e heh, C~2:5mm C W p =W r p Gate Formula (1) Q u ~a ffiffiffiffiffiffiffiffiffi e h E h ðb{ logðþ Þ, a~104:5, b~2:4, in mm Janbu Formula (3) Modified ENR (5) AASHTO (1990) (6) Q u ~ e qffiffiffiffiffiffiffiffiffiffiffiffi he h k u, k u~c d 1z 1z l, C Cd d ~0:75z0:15 W p, l~ e he h L W r AE 2 Q u ~ 1:25e he h zc Wr zn 2 W p W r zw p Q u ~ 2hW ð rza r pþ, c~2:5mm zc, c~2:5mm Navy-McKay Formula Q u ~ e he h ð1z0:3c 1 Þ, C 1~ W p W r Pacific Coat Uniform Building Code Q u ~ e he h C 1, C 1 ~ W rzkw p, C 2 ~ Q ul, k~0:25 for teel pile, 0:10 for all other pile: zc 2 W r zw p AE Source: (2). Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11 1

12 2. PARAMETER SELECTION 2.1 Introduction For many year, the tate of practice in pile driving analyi ha been the ue of the analyi of Smith (7). Recently, Purdue engineer (8) propoed an analyi with a number of advancement over the Smith analyi. Initial evaluation of the Purdue analyi uggeted it better predicted pile et given the tatic capacity and data for the pile and driving ytem. In thi chapter, we will dicu how to chooe value to ue for each parameter in the Purdue dynamic driving analyi tep by tep. The input parameter directly ued in the haft and bae reaction model are: 1. Soil denity r; 2. Small-train hear modulu G max ; 3. Poion ratio c; 4. Pile dimenion, pile diameter B and pile length L; 5. Static unit haft reitance, q L ; 6. Static unit bae reitance, q bl ; 7. Soil vicoity parameter, m, m b, n and n b. Thee parameter can be related to fundamental oil variable, uch a relative denity D R and critical tate friction angle j c 9 for andy oil and undrained hear trength u and over-conolidation ratio OCR for clayey oil. 2.2 Advanced Model for Pile Driving Analyi The Purdue pile driving analyi i baed on more advanced haft and bae reaction model, which are formulated baed on the actual phyic and mechanic of the pile driving problem, than are currently ued in practice. Detail of the analyi can be found in Loukidi et al. (8); the key element of the analyi will be ummarized in thi ection. The haft reitance of the pile i aumed to depend on the tiffne of a zone of highly localized train (a hear band) that develop immediately next to the pile, on a zone of intermediate train, where oil repone i nonlinear, urrounding the hear band, and on a far field, in which train are much maller, further out. The haft reaction model i hown in Figure 2.1. To handle oil nonlinearity and hyterei effectively, we will aume that the oil follow a hyperbolic tretrain law in rate form: G max _t~ 2 _c ð2-1þ jt{lit 1zb rev j f ðliz1þjgn ðþ _c : t f {tj where: t f 5 hear trength of the oil in imple hear condition; t rev 5 hear tre at the lat tre reveral; LI 5 loading index, equal to 0 for virgin loading and 1 for unloading and reloading; Figure 2.1 Soil model along pile haft. gn 5 ignum function, equal to 1 if x.0 and 21 if x,0; G max 5 mall-train hear modulu; b f 5 rate of degradation of the hear modulu. A rheological model (9) repreent the oil repone within the hear band along the haft wall. The propoed model conit of a platic lider and a vicou dahpot connected in parallel and placed along the pile haft wall. The trength of the platic lider i equal to the tatic unit limit haft reitance q L. Sliding initiate once the tre t equal q L, at which point the vicou dahpot i activated. The reaction of the vicou dahpot i a power function of the relative velocity between the pile and oil near the pile haft wall. The total reitance produced by thi rheological model i given by: n t f ~q L 1zm _w pile { _w 1 ð2-2þ where m and n are input parameter that are dicued in detail in ection 2.4. The propoed bae reaction model can take into account the nonlinear oil repone below the pile bae and the rate effect on bae reitance and alo ditinguih between different type of damping. The propoed bae reaction model conit of a nonlinear pring connected in parallel to a radiation dahpot (Figure 2.2). By umming up the pring reaction R (S) b and the radiation dahpot reaction R (D) b, the total bae reaction i given a: R b ~R (S) b zr(d) b ~R (S) b zc b _w b ð2-3þ where c b i the radiation damping contant and _w b i the velocity of the pile bae. The nonlinear pring follow a hyperbolic type loadettlement law: _R (S) b ~ K b,max R b {LI 1zb :! 2 _w b ð2-4þ j t b,rev j fb ðliz1þgn ð_w b Þ : R bf {R b where: K b,max 5 maximum bae pring tiffne; 2 Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11

13 Figure 2.2 Propoed oil model at pile bae. R bf 5 limit bae capacity; R b,rev 5 pring reaction R b at lat diplacement reveral; b fb 5 rate of degradation of the bae pring tiffne. Incluion of the rate effect in the model through R bf yield a bae reitance relationhip imilar to that for the limit haft reitance: R bf ~Q bl ð1zm b ð_w b where m b and n b are input parameter controlling the oil vicoity. The radiation dahpot coefficient for the pile bae model i given a: c b ~ Þ n b c Lym c emb c hy R b {LI 1zb :! 2 ð2-6þ j t b,rev j fb ðliz1þ gn ð_w b Þ : R bf {R b where: c Lym 5 radiation dahpot coefficient of Lymer analog; c emb 5 depth factor for radiation damping; c hy 5 hyteretic damping effect on the radiation damping. The olution cheme of 1D pile dynamic analyi i to dicretize the pile into lumped mae with oil reaction applied to each lumped ma (Figure 2.3). The ytem of differential equation decribing the problem i: z½c ½MŠ w pile Š _wpile z½k Þ Š wpile zfrg~0 ð2-7þ where [M], [C] and [K] are the global ma matrix, global damping matrix and global tiffne matrix of the lumped ma ytem. The ytem of equation of motion (2-7) i olved uing Newmark algorithm. 2.3 Determination of Small-Strain Shear Modulu The mall-train hear modulu for andy oil can be etimated uing the correlation propoed by Hardin and Black (10): Figure 2.3 Lumped mae ytem of 1D dynamic analyi. G max ~691 ð2:17{eþ2 pffiffiffiffiffiffiffiffi p 0 p a ð2-8þ 1ze where e i the void ratio, p i the mean effective tre, and p a i a reference tre (the tandard atmopheric preure of 100kPa 5 0.1MPa 5 1kgf/cm 2 5 1tf). For clayey oil, the mall-train hear modulu take the form (11): G max ~323 ð2:97{eþ2 pffiffiffiffiffiffiffiffi ðocrþ k p 0 p a ð2-9þ 1ze The power k to which the over-conolidation ratio OCR i raied i given in Table Determination of Soil Vicoity Parameter The parameter n and n b fall in a relatively narrow range, with mot value being in the vicinity of 0.2 (8). Hence, a ingle value for n 5 n b 50.2 i elected independent of oil type. For and, we will aume m 5 m b 50.3 in accordance with Coyle and Gibon (12) and Randolph (13). TABLE 2.1 Exponent k for Equation (2-9) Platicity Index (PI) $ k Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11 3

14 For clay, the parameter m and m b are related to the undrained hear trength of the oil a propoed by Lee et al. (14): m ~1:65{0:75 u 0 ð2-10þ m b ~1:2{0:63 p a u p a 0 ð2-11þ 2.5 Determination of Static Unit Shaft Reitance For and, the limit haft reitance i evaluated uing UWA-05 method (15). The UWA-05 deign equation for haft capacity of driven pile are expreed a follow: ( " q L ~ f t 0:03q c A 0:3 r,eff max h # ) {0:5 f c B,2 zd 0 rd tan d f ð2-12þ A 3 ~0:64z0:40 ln u 0 v0 2.6 Determination of Static Unit Bae Reitance For and, the tatic unit bae reitance i related to cone penetration reitance, which i etimated uing the equation propoed by Salgado and Prezzi (18): q bl ~q c ~p a 1:64 exp½0:1041w c z 0:841{0:0047DR ð2-18þ h ð0:0264{0:0002w c ÞD R Š p a For clay, the tatic unit bae reitance i aumed to be ten time the undrained hear trength of the oil (19): q bl ~10 u ð2-19þ A r,eff ~1{IFR D 2 i ð2-13þ D " # D i ðmþ 2 IFR mean & min 1, 1:5ðmÞ ð2-14þ D 0 rd ~4GDr ð2-15þ D where: d f 5 Contant volume interface friction angle; h 5 Ditance to the pile tip; D 0 rd 5 Change in radial tre due to loading tre path (dilation); f t 5 1 for compreion and 0.75 for tenion; f c G~185q c q {0:75 c1n with q {0:75 c1n ~ q ð c=p a Þ= 0 v0 =p 0:5; a p a 5 A reference tre equal to 100kPa; 0 v0 5 In-itu vertical effective tre; Dr 5 Dilation, aumed 0.02mm (16). For clay, the limit haft reitance i calculated through the a-method: q L ~a u ð2-16þ The hort term a ST propoed by Bau et al. (17) i ued: a ST ~1:03 A 1 zð1{a 1 Þexp { 0 v0 A2 w p c {w r,min ð2-17þ A where: A 1 ~ 0:75for w c{w r, min ~5 0 0:43for w c {w r, min ~12 0 A 2 ~0:55z0:43 ln u 0 v0 2.7 Determination of Other Parameter The Poion ratio ued in the model i the malltrain Poion ratio. Standard value of 0.15 and 0.22 can be ued for andy and clayey oil without much impact on the analyi reult (8). The oil unit weight i computed from the relative denity for and. The unit weight ued for normally conolidated clay i ued a 17kN/m 3, and the unit weight for over-conolidated clay i 19kN/m PILE DRIVING FORMULAS 3.1 Introduction In thi chapter, we will imulate driving in five type of oil profile to develop the correponding pile driving formula. Thee general cenario are thoe of a floating pile in and, an end-bearing pile in and, a floating pile in clay, an end-bearing pile in clay and a pile penetrating through a normally conolidated clay layer reting on a dene and layer. For and cae, we will control relative denity and pile length to invetigate their effect on the relation between the pile tatic capacity and pile et per blow. For clay cae, the overconolidation ratio, the ratio of undrained hear trength over vertical effective tre for normally conolidated clay, and the pile length are ued a variable. The pile tatic capacity (Q 10% for and and Q L for clay) i calculated a dicued in Chapter 2, and the pile et per blow i obtained from the numerical pile driving analyi. Initially, analye are done for the ICE-42S hammer, whoe parameter are lited in Table 3.1. The pile i a teel cloe-ended pipe pile with an outer diameter of 356mm. The effect of the variability of hammer weight and drop height are taken into account in the final pile driving formula for each oil profile. 4 Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11

15 TABLE 3.1 Specification of ICE-42S Hammer Name Value TABLE 3.2 Simulation Cae for Floating Pile in Sand Name Relative Denity (%) Pile Length (m) Ram weight lbf (18.2kN) Drop height 16.4ft (5m) Maximum tranferred energy lbf?ft (56.7kNm) Energy ratio 62.4% Source: (20). 3.2 Floating Pile in Sand In thi ection, we conider the cae of floating pile in a uniform and layer, a hown in Figure 3.1. The relative denity of the and and the length of the pile are ued a the two main variable to develop the pile driving formula. The relative denity of the and layer i allowed to vary from 10% to 90%, with 90% and being an unrealitic cae, except perhap for very hort pile, ued to bound the reult from above. In routine onhore practice, the driven pile length i uually in the range of 10m to 50m. To incorporate the length effect of the pile into the pile driving formula, imulation with pile length equal to 10m, 20m, 30m and 40m are done. Table 3.2 ummarize the imulation performed to develop the pile driving formula for a floating pile in and. To properly conolidate the reult of the imulation in to a ueful equation, we will firt normalize the pile et by dividing it by the pile length. The pile capacity and the normalized pile et can be fitted a a erie of power function in the form: Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Sand-FL , 20, 30, 40 Q 10% ~A B ð3-1þ L The multiplier, exponent and coefficient of correlation for each cae are lited in Table 3.3. To propoe a unified pile driving formula in term of relative denity and normalized pile et, the parameter A for the power function i fitted a an exponential function (Figure 3.2) of relative denity, and the parameter B i fitted a a linear function (Figure 3.3) of relative denity. The final pile driving formula for floating pile in and i given a: Q 10% D R, ~ L 9:27 exp 3:11 D R D R ð3-2þ 0: {0: L Figure 3.4 how the plot of the propoed driving formula with all the imulated data point. To clearly evaluate the accuracy of the propoed formula, each cae i plotted eparately a hown in Figure 3.5 to Figure Equation (3-2) can be normalized with the reference p a (100kPa 5 0.1MPa 5 1kgf/cm 2 5 1tf) and the reference length L R (1m ft in.) to obtain a nondimenional equation a follow: Figure 3.1 Floating pile in and. TABLE 3.3 Value of A and B in Pile Driving Formula for Floating Pile in Sand Name A B R 2 Sand-FL Sand-FL Sand-FL Sand-FL Sand-FL Sand-FL Sand-FL Sand-FL Sand-FL Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11 5

16 Figure 3.2 and. Multiplier A veru relative denity for floating pile Figure 3.4 Simulated data (point) and propoed pile driving formula (line) for floating pile in and. Q 10% p a L 2 ~ 0:093 exp 3:11 D R R 100 D R 0: {0:68 ð3-3þ L 3.3 End-Bearing Pile in Sand The relative denity of the and layer along the pile haft i aumed a 30% to imulate a relatively looe oil tate. To characterize an end-bearing pile, the relative denity of the pile bae i from 40% to 90% (Figure 3.14). Table 3.4 ummarize the imulation cae performed to develop the pile driving formula for an end-bearing pile in and. Following the ame technique dicued in ection 3.2, the multiplier, exponent and coefficient of correlation of the power function for each cae are lited in Figure %. Pile driving formula with imulated data for D R Figure 3.3 Exponent B veru relative denity for a floating pile in and. Figure %. Pile driving formula with imulated data for D R 6 Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11

17 Figure %. Pile driving formula with imulated data for D R Figure %. Pile driving formula with imulated data for D R Figure %. Pile driving formula with imulated data for D R Figure %. Pile driving formula with imulated data for D R Figure %. Pile driving formula with imulated data for D R Figure %. Pile driving formula with imulated data for D R Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11 7

18 TABLE 3.5 Parameter for Power Function for End-Bearing Pile in Sand Name A B R 2 Sand-EB Sand-EB Sand-EB Sand-EB Sand-EB Sand-EB Figure %. Pile driving formula with imulated data for D R Figure 3.15 Multiplier A veru relative denity ratio for endbearing pile in and. Table 3.5. The regreion of the multiplier and exponent for all the cae are hown in Figure 3.15 and Figure 3.16, which aim to relate them to the bae-haft relative denity ratio. The final pile driving formula for an end-bearing pile in and i: Figure 3.14 End-bearing pile in and. TABLE 3.4 Simulation Cae for End-Bearing Pile in Sand Name Bae Relative Denity (%) Shaft Relative Denity (%) Pile Length (m) Sand-EB , 20, 30, 40 Sand-EB , 20, 30, 40 Sand-EB , 20, 30, 40 Sand-EB , 20, 30, 40 Sand-EB , 20, 30, 40 Sand-EB , 20, 30, 40 Figure 3.16 Exponent B veru relative denity ratio for endbearing pile in and. 8 Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11

19 Figure 3.17 Simulated data (point) and propoed pile driving formula (line) for end-bearing pile in and.! D Rbae, ~ D Rhaft L!! 5:33 exp 1:11 D D R bae Rbae 0:10 D Rhaft L Q 10% D Rhaft {0:76 ð3-4þ Equation (3-4) can be normalized with repect to the reference tre p a and the reference length L R to obtain a nondimenional equation a:!! Q 10% p a L 2 ~ 0:053 exp 1:11 D D R bae Rbae 0:10 D {0:76 Rhaft ð3-5þ R D Rhaft L Figure 3.17 how the plot of the propoed driving formula together with all the imulated data. To clearly ee the accuracy of the propoed formula, we plot the Figure 3.19 Propoed pile driving formula for end-bearing pile in and: D Rb 5 50%. formula with imulated data for each cae eparately in Figure 3.18 through Figure Floating Pile in Clay A contant ratio of theundrained hear trength over vertical effective tre u 0v i aumed for a normally conolidated clay layer to imulate the floating pile in clay a hown in Figure Table 3.6 ummarize the imulation cae conidered to develop the pile driving formula. For each cae, we ue a different pile length in the 10m to 40m range. The form for the pile driving formula for a floating pile in clay i: u Q L, ~ 34:10 u 0:67 u z2:55 0 {1:29 0 v L 0 v ð3-6þ v L Figure 3.18 Propoed pile driving formula for end-bearing pile in and: D Rb 5 40%. Figure 3.20 Propoed pile driving formula for end-bearing pile in and: D Rb 5 60%. Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11 9

20 Figure 3.21 Propoed pile driving formula for end-bearing pile in and: D Rb 5 70%. Equation (3-6) can be normalized with the reference tre p a and the reference length L R a follow: Q L p a L 2 ~ 0:34 u 0:67 u z0:026 0 {1:29 R 0 v ð3-7þ v L Figure 3.25 how the correponding plot with imulated data. In Figure 3.25, the pile capacitie for different u 0v at the ame pile et do not vary much. To maximize eae of ue by engineer, a ingle equation i ued to repreent the entire range of condition aumed: Q L ðþ~10:94 {1:12 ð3-8þ The nondimenional form of Equation (3-8) i: Q L {1:12 p a L 2 ~0:11 ð3-9þ R L R Figure 3.23 Propoed pile driving formula for end-bearing pile in and: D Rb 5 90%. TABLE 3.6 Simulation Cae for Floating Pile in Clay Name u 0 v Pile Length (m) Clay-FL , 20, 30, 40 Clay-FL , 20, 30, 40 Clay-FL , 20, 30, 40 Clay-FL , 20, 30, 40 Clay-FL , 20, 30, 40 The coefficient of correlation of (3-8) with all the imulated data i cloe to a hown in Figure 3.26, which mean that the imple form of (3-8) i accurate enough to ubtitute for the more complex form (3-6). where L R i the reference length (1m53.28ft). Figure 3.22 Propoed pile driving formula for end-bearing pile in and: D Rb 5 80%. Figure 3.24 Floating pile in clay. 10 Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11

21 TABLE 3.7 Simulation Cae for End-Bearing Pile in Clay Name OCR u 0 v Pile Length (m) Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Clay-EB , 20, 30, 40 Figure 3.25 Simulated data (point) and propoed pile driving formula (line) for floating pile in clay. 3.5 End-Bearing Pile in Clay To imulate the cae of an end-bearing pile in clay, the pile i imulated to penetrate through a normally conolidated clay layer and ret on an over-conolidated clay layer with higher OCR a hown in Figure Table 3.7 ummarize all the cae conidered. If we were to fit the data eparately for each value of OCR, for OCR 5 4, the pile driving formula i in the form: Q L u 0 v, L ~ 15:78 u z1:32 0 v L 0:13 u 0 v {0:73 ð3-10þ Equation (3-10) can be normalized with repect to the reference tre p a and the reference length L R a follow: Q L p a L 2 R ~ 0:16 u z0:013 0 v L 0:13 u 0 v {0:73 ð3-11þ For OCR 5 10, the pile driving formula ha the form: u Q L, ~ 35:26 u 0:51 u {2:27 0 {0:80 0 v L 0 v ð3-12þ v L The nondimenional form of Equation (3-12) i: Q L p a L 2 ~ 0:35 u 0:51 u {0:028 0 {0:80 R 0 v ð3-13þ v L A hown in Figure 3.28, all the data point follow the trend of a ingle power function with coefficient of correlation equal to regardle of the value of the over-conolidation ratio. Thu, we propoe a impler equation a the driving formula for end-bearing pile in clay: Q L ~7:90 {1:18 ð3-14þ The nondimenional form of Equation (3-14) i propoed a: Figure 3.26 Pile driving formula for floating pile in clay. Figure 3.27 End-bearing pile in clay. Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11 11

22 Figure 3.28 Simulated data (point) and propoed pile driving formula (line) of all OCR value for end-bearing pile in clay. 3.6 Clay over Sand Q L {1:18 p a L 2 ~0:079 ð3-15þ R L R In thi cae, the pile i aumed to cro a normally conolidated clay layer and ret on a relatively dene and layer. The relative denity of the bae and layer varie from 40% to 90%. To incorporate the effect of the pile length into the pile driving formula, the pile length ued i 10m, 20m, 30m and 40m (Figure 3.29). Table 3.8 ummarize the imulation cae performed to develop the pile driving formula for thi cae. The multiplier, exponent and coefficient of correlation of the power function for each cae are lited in Table 3.9. The regreion of the multiplier and exponent for all the cae are hown in Figure 3.30 and Figure The coefficient of correlation of multiplier A and exponent B among all cae are both a high a The final pile driving formula for a pile croing a clay layer and bearing on a and layer can be written a: Q 10% D R, ~ L 2:81 exp 4:22 D R D 0:40 R ð3-16þ 100 {0: L Equation (3-16) can be normalized with repect to the reference tre p a and the reference length L R to obtain thi nondimenional form: Q 10% p a L 2 R ~ 0:028 exp 4:22 D R 100 D 0:40 R L 100 {0:77 ð3-17þ Figure 3.32 how the plot of the propoed driving formula (line) together with all the imulated data (point). 3.7 Effect of Hammer Weight and Drop Height The pile driving formula propoed in Section 3.2 to 3.6 are developed by uing an ICE-42S hammer with the following propertie: 18.2kN hammer weight, 5m drop height and 62.4% hammer efficiency. In practice, a variety of hammer, each with it own hammer weight and drop height could be ued in a given pile driving project. A general pile driving formula need to contain hammer parameter. In order to include hammer parameter in the pile driving formula developed earlier, we have conidered ix combination of hammer weight and drop height (lited in Table 3.10). The reference force W R (100kN lbf kip) and the reference length L R (1m ft in.) are ued to non-dimenionalize the pile driving formula. TABLE 3.8 Simulation Cae for End-Bearing Pile Penetrated through Clay and Reted on Sand Name Bae Relative Denity (%) Shaft Clay OCR Pile Length (m) Figure 3.29 End-bearing pile penetrated through clay and reted on and. ClayOverSand , 20, 30, 40 ClayOverSand , 20, 30, 40 ClayOverSand , 20, 30, 40 ClayOverSand , 20, 30, 40 ClayOverSand , 20, 30, 40 ClayOverSand , 20, 30, Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11

23 TABLE 3.9 Parameter of Power Function for Pile in Clay over Sand Name A B R 2 ClayOverSand ClayOverSand ClayOverSand ClayOverSand ClayOverSand ClayOverSand Figure 3.32 Simulated data (point) and propoed pile driving formula (line) of end-bearing pile through clay on and. individual imulation. For floating pile in and and pile croing a clay layer and reting on and, the following form may be ued for the pile driving formula: Figure 3.30 Multiplier A veru relative denity for pile in clay over and. For each W - H pair, a pecific pile driving formula W R L R can be developed baed on the imulation reult. A unified pile driving formula hould contain thee two hammer variable W and H adequately reproduce the W R L R Q 10% p a L 2 ~ R e h a W b H c exp d D! R D e R W R L R 100 L 100 zf ð3-18þ Similarly, for end-bearing pile in and, the following form may be ued for the pile driving formula: Q 10% p a L 2 ~ R e h a W b!! H c exp d D D R bae Rbae e W R L R D Rhaft L D Rhaft zf ð3-19þ For floating pile in clay and end-bearing pile in clay, the following form may be ued for the pile driving formula: Q L p a L 2 ~e h a W b! H c ðþ d w w ze 0 ð3-20þ R W R L R Solving for variable a, b, c, d, e, and f in Equation (3-18) and (3-19) (a, b, c, d, and e in Equation (3-20)) i TABLE 3.10 Hammer Parameter Variable Hammer Figure 3.31 Exponent B veru relative denity for pile in clay over and. W W R H L R Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11 13

24 a typical optimization problem, for which the objective function i to obtain the maximum value for the coefficient of correlation between the data predicted from the pile driving formula and the data calculated baed on the propertie of the oil profile. Thi problem can be et, in mathematical term, a: max R 2 SS err ~ max 1{ SS tot ð3-21þ where: SS tot ~ P ðy i {y Þ 2 5 um of quare of the difference i between the pile capacity for each oil profile and the average of thee capacitie; SS err ~ P ðf i {y i Þ 2 5 um of quare of the difference between the pile capacitie predicted uing the pile i driving formula and thoe calculated uing tatic method applied to the oil profile; y i 5 pile capacity calculated baed on the propertie of oil profile; y5 average of calculated pile capacitie baed on the propertie of oil profile; f i 5 pile capacity predicted by propoed pile driving formula. Thi type of optimization problem can be olved by uing the Microoft Office Excel (21) optimization olver. A ummary of the olution to Equation (3-21) for each typical oil profile can be found in Table The coefficient of correlation R 2 of the olution for each typical oil profile i over 0.97, which indicate the propoed pile driving formula can accurately predict the pile capacity for the oil profile conidered in thi report. For floating pile in and, the pile driving formula i expreed in term of five variable: the hammer efficiency, the normalized hammer weight, the normalized hammer drop height, the relative denity of the and and the pile et: Q 10% p a L 2 ~ R e h 0:39 W 0:59 H 0:38 exp 2:29 D! R ð3-22þ D 0:12 R 100 {0:60 W R L R 100 L A comparion of the relationhip between normalized pile capacity veru normalized pile et obtained from the pile driving formula and the dynamic analyi for Figure 3.33 Comparion between imulated data by dynamic analyi and predicted value by propoed pile driving formula for floating pile in and. Figure 3.34 Comparion between imulated data and predicted value by propoed pile driving formula for floating pile in and: Hammer 1 (W/W R and H/L R 5 2.5). floating pile in and for all even hammer i hown in Figure The ame comparion i made pecifically for each hammer in Figure 3.34 through Figure The comparion are clearly very favorable. For end-bearing pile in and, the pile driving formula i expreed in term of five variable: the TABLE 3.11 Summarie of Solution to Equation (3-21) for Typical Soil Profile Variable Soil Profile a b c d e f R 2 FLSand EBSand FLClay N/A EBClay N/A ClayOverSand Joint Tranportation Reearch Program Technical Report FHWA/IN/JTRP-2012/11