From Piles to Piled Raft Foundation - Some Observations on Static and Dynamic Analyses

Transcription

1 From Piles to Piled Raft Foundation - Some Observations on Static and Dynamic Analyses Der-Wen Chang Department of Civil Engineering Tamkang University Tamsui, New Taipei City, Taiwan dwchang@mail.tku.edu.tw Department of Construction Engineering National Kaohsiung First University of Science and Technology Kaohsiung, Taiwan, April 21, 2016

2 Why Deep Foundation? Mega-size/high-rise/heavy-load building on soft soils; Large lateral and overturning loads; Large fdt. settlement and differential settlements; Seismic threats and soil liquefaction induced fdt. damages. 2

3 Types of Deep Foundations Piles and Piers; Combined Pile Raft Foundation (CPRF); Caisson; Barrette (Buttress pile/wall) and Grid Walls. 3

4 Offshore foundations 1. Soil-Structure-Fluid Interactions must be considered 2. Cyclic loading effects (both static and dynamic) are significant 4

5 Effects of the steady-state loads M Dynamics controlled 1.0 Stiffness controlled Mass controlled f m < f <2f m f / f m Rotational frequency and Blade Passing frequency must be avoided 5

6 Degradation of fdt. Resistance under cyclic loads P K 1 > K 2 ; 1 < 2 + direction K 1 K 2 - direction U 6

7 Outlines 1. Design procedures and analyses (5) 2. Simplified analysis for seismic behaviors of piles (10) 3. Applications of dynamic pile-to-pile interaction factors (5) 4. Seismic performance of piles PBEE approach (11) 5. Seismic performance of piles RB approach (6) 6. Design and analyses on CPRF (4) 7. Simplified analysis for seismic behaviors of CPRF (9) 8. Foundation behaviors from analyses (17) 9. Concluding remarks (6) 7

8 I. Design procedures and analyses 8

9 Geotechnical Engineering Design Performance-Based Design Conventional Design Reliability-Based methods, Propability-Based Probability-Based methods, Load and Resistance Factor Design. Uncertainties of the design must be analyzed systematically RBM: FORM, FOSM, Monte Carol Simulation, etc. PBM: PBEE analysis LRFD: AASHTO Working Stress Design, Limite State Design 1. Ultimate Limit State External/Internal Foundation Capacities 2. Serviceability Limit State External/Internal Foundation Serviceability 9

10 Design Flow Chart for Pile Fdt. 開 始 資料蒐集 地層狀況 土壤強度性質 設計荷重情形 施工狀況調查 無 安全水平力作用 是否高液化潛能之地盤否選擇基樁形式及材料基樁材料容許應力計算基樁容許支承力計算決定基樁數目 是 地盤改良 包含使用材料 形狀大小 長度, 施工方法等之假定 否 無 利用直樁是計算基樁水平支承力水平承載樁數檢核安全承受拉力是 否 計算斜樁數目及排列 否 基樁配置 基樁容許拉力計算 合適基樁沈陷量計算 不足 承受拉力樁數檢核 過量 無 沈陷量檢核允許表面負摩擦力有 足夠樁帽設計樁基設計圖 負摩擦力計算 否 樁支承力 完 成 安全 10

11 Concerns 1. Vertical capacity of single pile; 2. Lateral capacity of single pile; 3. Negative skin friction of single pile; 4. Pull-out resistance of single pile; 5. Liquefaction effects on single pile and grouped piles; 6. Settlement and lateral deflections of single pile; 7. Effects of pile-to-pile interactions on grouped piles; 8. Pile cap design and safety checks on piles and cap. Problems require further attentions 1. Statically cyclic loads (effects of unload/reload and number of cycles); 2. Dynamically cyclic load (effects of amplitude/period and initial static load); 3. Seismic loading (PGA/duration/dynamic characteristics); 4. Capacities of Piled Raft foundation (external and internal); 5. Serviceability of Piled Raft foundation (external and internal). 11

12 On PBD and PBSD PBSD of pile fdt Performance-Based Design Physical Tests Numerical Modeling Foundation Capacities Foundation Deformations Uncertainties In-situ full scale pile load test, Shake table test, Centrifuge test, Push-over model test FEM analysis, FDM analysis, BDWF modeling, Wave equation modeling Ground conditions, Soil properties parameters, Loads/Displacements of the structure, Measurements and calculation methods, Site construction methods Reliability-Based methods FOSM, FORM, MCS, Probability-Based methods PBEE, LRFD method, Fuzzy Logic, Evidence Theory etc. Method PBEE analysis Monte Carlo Simulation Factor of safety against seismicity Medium Design MCE earthquake earthquake M cr / M max M y / M max M ult / M max cal / R cal / R cal / R Note: M cr = moment when concrete crack starts; M y = moment when steel bar yields; M ult = moment when plastic hinge occurs; M max = calculated maximum bending moment; cal = calculated reliability index; R = required reliability index 12

13 Pile Design Conventional Design (Ordinary Critical) PBSD Determine V H D L Ar Concerns NO Seismic PBD? YES PBEE approach Conventional Design Seismic Design in options (need to consider soil liquefaction effects) Foundation Capacities Fdt. Deformations Deterministic approach and/or Probability approach? PGAt from hazard carve Seismic record in use Calibrate a(t) for analysis Optional OK Find Umax Mmax Apply PBEE to find λvsumax and λvsmmax Compare Mmax with Mcr/My/Mult Use Mcr My and Mult to find Umc Umy Umm Use LPIPE to compute Mcr My Mult Choose proper tool Calibrate the model parameters Based on seismic design level Compare Umax with Umc/Umy/Umm Check Umax<Umc/Umy/Umm NG NG Redesign OK End of Design 13

14 II. Simplified analysis for seismic behaviors of piles 14

15 EQWEAP (EarthQuake Wave Equation Analysis for Piles) Seismic pile responses Seismic Free-Field Response by LMA Seismic Pile Response by WEA Decoupled motions + Uncoupled analysis 15

16 WEAP under EQ excitations Px Mt () Q ( t ) Q( t ) Px Mt () P x C s M V P( x, t) K s x 2 u ( A x) 2 t V V x M M x P x Discrete pile segments and equilibriums 16

17 EQWEAP Formulas Chang et al. (2014) 1. If ground motions were obtained from free-field analysis 2. If seismic earth pressures were given 3. If ground displacement profiles were prescribed 17

18 EQWEAP Formulas (cont.) 1. For ground motions from free-field analysis: 2. For seismic earth pressures already known: 3. For ground displacement profiles already known: 18

19 Pile Nonlinearity Approximate Bouc-Wen Model : M E I M Z 1 y III II I Iterative analysis is conducted to modify the EI values according to M- relationship 19

20 Moment (kn-m) Moment (kn-m) Effects of Pile Diameter and Ar on Moment Capacities of pile Percentage of Steel = 1.94 % Diameter of Pile = 0.5 m Diameter of Pile = 1 m Diameter of Pile = 2 m 3000 M u,ψ u M u,ψ u 1000 Diameter of Pile = 1m Percentage of Steel = 1.04 % Percentage of Steel = 1.94 % Percentage of Steel = 3.04 % 0 0.0E+0 4.0E-3 8.0E-3 1.2E-2 1.6E-2 Curvature (rad/m) 0 0.0E+0 4.0E-3 8.0E-3 1.2E-2 Curvature (rad/m) 20

21 Depth (cm) Depth (cm) Liquefiable Layer Liquefiable Layer Soil Parameter Reduction Coefficient PWP Model Failure occurred at 7 sec Failure occurred at 7 sec 30 Time at 15 sec Time at 25 sec 30 Time at 15 sec Time at 25 sec Time at 35 sec Time at 35 sec Pile Displacements (cm) Pile displacement at different time step from SPRC model Pile Displacements (cm) Pile displacement at different time step from EPWP model 21

22 Depth (cm) Depth (cm) Liquefiable Layer 12 Liquefiable Layer Direct Earth Pressure 24 Indirect Earth Pressure Failure occurred at 5 sec Failure occurred at 5 sec 30 Time at 15 sec Time at 25 sec 30 Time at 15 sec Time at 25 sec Time at 35 sec Time at 35 sec Pile Displacements (cm) Pile displacement at different time step from direct earth pressure model Pile Displacements (cm) Pile displacement at different time step from indirect earth pressure model 22

23 Depth (cm) 0 6 Liquefiable Layer Observed (No. 9) Observed (No. 2) 30 Predicted (Ishihara and Cubrinovski, 2004) Direct Earth Pressure Model (failure occurred at 4.4 sec) Indirect Earth Pressure Model (failure occurred at 5.4 sec) PWP Model (failure occurred at 7.0 sec) Soil Parameter Reduction Coefficient (failure occurred at 7.0 sec) Pile Displacements (cm) Maximum pile displacement profiles from alternate modeling of EQWEAP analysis and the field observations 23

24 Grouped Piles 24

25 III. Applications of Dynamic pile-to-pile interaction factors 25

26 Dynamic pile-to-pile interaction factor Dobry and Gazetas (1988) 26

27 Pile-to-Pile Interactions 27

28 Use of superposition theory 28

29 Lateral load distributions (Chang et al, 2009) 29

30 Load ratio varied at frequencies and the timedependent history (Chang et al. 2009) 30

31 IV. Seismic performance of piles PBEE approach 31

32 Seismic Performance Requirements Seismic Performance Concerns for Transportation Structures (after Chen et al., 2006) Performance Safety Serviceability Level I Level II Level III structure remained elastic restricted local damages, recoverable superstructure and main body collapse prohibited same as before recoverable w/ shortterm remedies urgent remedies applicable, limited speed/weight for vehicles Short term not needed urgent remedy method applicable Replacing elements, structural reinforcements undertaken Rehabilitation Long term routine monitoring, protections existing remedy method applicable closed for constructions Seismic Performances and Return Periods for Transportation Structures (after Chen et al., 2006) Hazard Level Embankment Bridge pile foundation Underground structures ordinary important ordinary important S 30 Level I Level I Level I S 475 Level III Level III Level II Level III Level II S 2500 N/A N/A Level III N/A Level III 32

33 Annual Probability of Exceedance(1/year) Local seismic hazard curve Cheng (2002) 1E+0 台北市 PGA (g) 1E-1 新竹市台中市嘉義市台南市 City\TR 30 yr TR1 475 yrs TR yrs TR3 1E-2 1E-3 Taipei 30yr 高雄市恆春鎮宜蘭市花蓮市 台東市 Taichung 475yr Taipei Hsinchu Taichung Chiayi Tainan yr Kaoshiung E-4 Kaohsiung Pingtung I-lan E Intensity Measures, PGA(g) Hualian Taitung If Seismic Design Code is followed, PGA t are 0.06g, 0.24g and 0.32g in Taipei 33

34 Probability Method - PBEE Analysis Total probability P for the occurrence of a event can be computed as an integral of all the probabilities that could occur. For the occurrence of consecutive scenarios such as a, b and c, the total probability of occurrence P can be computed as P = 0.6*0.4*0.2 =

35 PBEE (Performance Based Earthquake Engineering) Analysis A probability based approach suggested by US PEER Excellent summary can be found in Kramer (2008) DV N N N DM EDP IM DV P DV dv DM dm P k DM > dm EDP edp k j k 1 j 1 i 1 j i IM i P EDP edp IM im im : Annual Rate (probability) of Exceedance DV: Decision Variable (costs of the hazard) DM: Damage Measure (maximum bending moment) EDP: Engineering Demand Variable (maximum pile displacement) IM: Intensity Measure (mostly used - PGA) 35

36 KEY - Seismic Hazard Curve λ=σσσυp[ IM>im M =m, R= r] P[M =m] P[R= r] k IM im 0 k 36

37 Demand curve Fragility curve 37

38 Displacement, EDP (cm) Annual Probability of Exceedance (1/year) EDP vs IM vs EDP 1/b -k 2 2 EDP, a, b, k, k, EDP k k f a exp 2 b EDP E E-1 1E-2 40 PGA=0.12g PGA=0.29g PGA=0.51g 1E PGA, IM (g) 1E Displacement, EDP (cm) 38

39 Maximum Moment (10^2kN-m) Annual Probability of Exceedance (1/year) DM vs EDP vs DM -k 1 b d 2 1 DM k DM ( DM ) k 0 exp d 2 2 R D a c 2b d 400 1E E E-1 1E PGA=0.12g PGA=0.29g PGA=0.51g 1E Maximum Displacement (cm) 1E Maximum Moment (10^2kN-m) 39

40 Annual Probability of Exceedance (1/year) Annual Probability of Exceedance (1/year) PBEE Analysis I Annual rate of exceedance vs. Max. pile displacements at various EQ levels 1E+0 1E+0 1E-1 1E-1 1E-2 1E-2 1E-3 1E-3 1E-4 1E Displacement, EDP (cm) Displacement, EDP (cm) 40

41 Annual Probability of Exceedance (1/year) Annual Probability of Exceedance (1/year) PBD Findings II (Mcr= 7300 kn-m, My= kn-m, Mult= kn-m) Annual rate exceedance vs. Maximum pile moment at various EQ levels 1E+1 1E+1 1E+0 1E+0 1E-1 NG 1E-1 NG 1E-2 OK 1E-2 OK 1E-3 OK 1E-3 OK 1E Maximum Moment (10^2kN-m) 1E Maximum Moment (10^2kN-m)

42 Alternative Procedure From the moment capacities to find the design probabilities, then use to determine allowable pile displacements, U mc, U my and Mmm Ductility Index, R =1.5 42

43 V. Seismic performance of piles Reliability approach 43

44 Reliability Approach - MCSM Probability of failure P f = n f /n total Assuming normal distribution or log-normal distribution, reliability index can be computed from mean value m and standard deviation of the scenarios. Variability of seismic records, soil parameters and the geological conditions could be considered. It was found that the seismic input is especially significant to the results. 44

45 Monte Carlo Simulation based on Weighted PGA For PGA t, compute all the scenarios including variability of soil parameters and all possible seismic intensities PGA i PGA t. The seismic records for the acceleration time history of the site can be achieved using specific methods. Then, P ft at PGA i PGA t = P fi W i Total probability of failure, P ft represents for the total potential influences of all possible EQs under the design EQ level is suggested. 45

46 Calculating the weights d d dra ( ) ( ) (1 ( ) ) ( a P ) A a FA a RA a da da da Design Life = 50 years 1- = cumulated probability of EQ PGA t I II III 46 PGA

47 Weighted Intensities (Chang et al, 2014) PGA (g) Return period (year) (%) Probability of occurrence for a > PGA Probability of occurrence for a PGA Numerator of the central difference formula Weights E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 47

48 Weighted intensities (continued) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 48

49 Factor of Safety (Chang et al., 2014) Method Factor of safety, F P and F R Moderate EQ Design EQ MCE quakes PBEE M cr /M max M y /M max M ult /M max MCSM obt. / R obt. / R obt. / R Whitman (1984) R = 2.4 for foundations 49

50 VI. Design and analyses on CPRF 50

51 ISSMGE TC212 CPRF Guidelines 51

52 Load carried by the piles 0.5 The optimized design 52

53 Numerical modeling for Capacities and Serviceability P stiff soils P all P all soft soils P ult P ult : ultimate load P all : allowable load u all u all : allowable displacement u 1. Ultimate capacity of the foundation could be estimated from Load-displacement relationship of the foundation. 2. Displacements (or deformations) are controlled to avoid the Structural damages. 3. Blind guess of the FS is not required. 53

54 3D FEM analysis as the tool Examinations of numerical model, material model, material parameters, loads, environment and construction procedures 54

55 VII. Simplified analysis for seismic responses of CPRF 55

56 Analyses for Piled Raft Fdt. Poulos (2001) 1. Simplified calculation methods (Poulos-Davis- Randolph) 2. Approximate computer-based methods 3. Rigorous computer-based methods Matsumoto (2013) 56

57 Simplified modeling for seismic responses of raft fdt. Uncoupled motions of the slab Underneath Impedances y z x Subjected to horizontal seismic motion 57

58 Motions of equivalent pier pile-soil-pile elements equivalent pier 58

59 Analytical/discrete equations EA 2 u x 2 dx = ρadx 2 u t 2 + k sb(u u g ) + k ep u u ep + k st 1 R u + m st R 2 u t 2 u i, j + 1 = 2F 2 B C + D H F u i, j + 1 u i + 1, j F + 1 F u i 1, j u i, j 1 + C F u ep i, j + B F u g(i, j) where F = ρ x2 k st x EA E t 2 + m str x EA t 2 ; B = k sb x EA ; C = k ep x EA ; D = k st xr EA ; H = ; x = spatial increment in x direction; t = time increment. 59

60 Numerical example strip fdt. on piles 300m 60m 60m 60m Seismic direction plan view 30m 60m 60m 60m 60m 30m equivalent pier 60

61 Seismic input (a) (a)(a) (c) (b) (d) 3D FEM Modeling (a) (b) (c) 61

62 Comparisons and Observations (a) 108cm 102cm (b) -102cm -112cm 62

63 Influences of bevel angle y z Underneath Impedances 63

64 Time efficiency Method Computer features Computation time (sec) EQPR analysis 3D Midas- GTS analysis CPU: Intel Xeon E3-1231v3 RAM: 16GB 60 sec based on time increments of sec (computations required for EQWEAP analysis is included) 9hr 25min 10sec for elements based on time increments of 0.02 sec 64

65 VIII. Foundation behaviors from analyses 65

66 Study on spread raft on piles Load distributions of piles 27m 23m 66

67 v and h affected by loads and S/D Sand-clay-sand model is used in monitoring 67

68 Vertical displacements of raft Stage load w/o consolidation long-term w/ consolidation long-term short-term 68

69 Horizontal displacements of raft long-term short-term 69

70 Axial loads of piles Consolidation 70

71 Skin frictions of piles Consolidation 71

72 t-z and Q-z curves Center Edge Corner Corner Edge Center 72

73 Lateral resistances along pile shafts Consolidation Stage loading (drained) Stage loading (undrained) 73

74 p-y curves Center Side edge Front edge Rear corner Front corner 74

75 Study on physical model data (Unsever et al., 2014) Vertical loading Horizontal loading 75

76 Axial forces Moments Shears 76

77 Behaviors of piled raft foundation 77

78 Comparisons on Midas and EQWEAP analyses 78

79 PBEE analysis from EQWEAP OK OK NG 79

80 Behaviors of ring-shaped grouped piles 80

81 Comparisons on Midas and EQWEAP analyses 81

82 PBEE analysis from EQWEAP OK OK OK 82

83 VIIII. Concluding Remarks 83

84 On methodologies 1. Accuracy of the pile analysis and design relies on the knowledge of site soils. 2. The load effects need further investigations. 3. PBD and PBSD became more important to design practice of deep foundation. 4. Unless the uncertainties of design parameters are considered, the analysis in monitoring the foundation behaviors performance-based analysis. 5. Load-displacement relationships of the fdt. should be analyzed using 3D FEM analysis. Both capacities and serviceability of CPRF could be revealed. 6. Simplified analyses are very helpful in the stage of preliminary design. 7. Simplified analyses will make PBSD more accessible. 84

85 On static foundation behaviors 1. Long-term settlements are larger than short-term settlements of deep fdt. where soft soils are encountered. 2. Unless time-dependent effects are interested, staged loads can be used to compute the fdt. displacements. 3. For matrix oriented pile foundation, larger settlements - fdt. center, smaller settlements - fdt. corners. Loading patterns of the piles are just the opposite. 4. Load sharing will be significantly affected by S/D and the length of pile which appear to be the most dominant factors in design. 5. Loads carried by piles also will be affected by geological conditions of the site. Sandy soils and clayey soils will yield different results. 85

86 On seismic load influences 1. Seismic impacts from the ground soils onto the foundation should be carefully modeled 2. Seismic load influences to all the piles in grouped pile foundation and CPRF are about the same. 3. Smaller pile diameter will result in larger relative foundation displacements w.r.t. the ground. 4. Reducing the length of piles will enlarge the foundation displacement. 5. The number of piles is highly related to S/D ratio. The corresponding effects should be monitored carefully. 86

87 On seismic load influences (contd.) 6. Stiffness and thickness of the softs will not affect much of foundation displacement when end-bearing piles were encountered. Nevertheless, stiffer and thicker soft soils will help to reduce slightly the foundation displacement. 7. Direction of the horizontal seismic load w.r.t. foundation seems to be insignificant. Foundation displacements caused by longitudinal ground excitation is slightly smaller than those occurred along the transverse direction. 8. Existence of the superstructure will generally make smaller foundation displacements. The more rigid the superstructure is (superstructure displacement becomes negligible), the less the foundation displacement will be. 87

88 On PBSD 1. PBEE approach is certainly a good tool to PBSD of pile foundation and CPRF. 2. Seismic forces is the most dominant design factor compared to variations of the soil parameters and geological conditions. 3. Moment capacities could be used to guide the design. 4. Productions of artificial EQs become rather important in this case. 5. If Reliability Based approach is interested, MCS can be used. In that case, weights of the IMs must be obtained. 6. Factor of safety of PBSD could be defined. They should be in similar order from PB and RB approaches. 88

89 References Byrne, B. and Houlsby, G. (2013) Foundations for Offshore Wind Turbines, Supergen Wind, 7 th Training Event, U. of Oxford. Frank, R. (2008) Design of Pile Foundations following Eurocode 7 Section 7. Workshop Eurocodes: background and applications. Hannigan et al. (2006) Design and Construction of Driven Pile Foundations- Volume 1, Report FHWA-NHI Orr, T. (2013) Eurocodes: Background and Applications, Worked Examples Design of Pile Foundations. Poulos, H.G. (2001) Method of Analysis of Piled Raft Foundations, TC18 Report, ISSMGE. Tomlinson M. and Woodard, J. (2008), Pile Design and Construction Practice, Taylor & Francis. 陳正興 (2014) 性能設計的理念與架構 台灣省土木技師公會基樁設計與施工新觀念研討會 陳正興, 黃俊鴻 (2016) 基礎性能設計, 財團法人地工技術研究發展基金會叢書 交通部運研所 (2014) 碼頭耐震性能設計手冊, MOT-IOT-103- H1DB006a 89

90 The End Thanks for your attentions! 90