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1. Nonlinear 35 1 1 1 1 0 0 1 0 2 0 3 0 4 0 5 Pile deflection in b H 63 kips Figure C 7 Comparison of the pile deflection profiles for the linear and nonlinear runs 92 Nn N Depth ft N n W T Linear Nonlinear 0 0 1 0 2 0 3 0 4 0 5 Pile deflection in Oo Nn c H 94 5 kips Figure C 7 continued The pile head deflections and the maximum bending moments for both linear and nonlinear analyses are listed in Table C 2 The stress ratio contour fill of the nonlinear run is displayed in Figure C 9 ha Nn T N Depth ft 2 5 A EERTE ENEAN II BM te Ba BON Ae aN te a db tdi nds 4 A aes gh Gp eR EEEF TE Oe Nonlinear 0 50 100 150 200 Bending moment kip ft 35 a H 31 5 kips Figure C 8 Comparison of the pile bending moment profiles for the linear and nonlinear runs 93 Depth ft Depth ft 5 Es 10t 15t 7 20 BIER toads TR A e e RIE ro Sey EAE ET EAEE Se e cer SEE o Bead 25 A E A E OS RIO BONES 7 Babe Se Sid ALA O A ye bs dons aradt ta akarana Ade Linear 4 Nonlinear 35 i 1 1 i 1 0 50 100 150 200 Bending moment kip ft b H 63 kips 5 E 10t 15t 20 Pd AR COM e pes A ote ce e AS a a yi Ale De eg Dara 25 30 Linear Nonlinear 35 0 50 100 150 200 Bending moment kip ft c H 94 5 kips Figure C 8 continued 94 Table C 2 OpenSees simulation res
2. displays LPILE 0 24 48 2 0 Paes pee A Linear soil 0 038 20 8 ot i rises H 16 kips sa ig 0 092 323 0 a Load Case 2 LPILE 0 094 100 0 Free Head Linear soil 0 06 96 7 0 Rates M 100 kip ft Son y applied opposite to 59 cn 0 094 96 9 0 shear am 0 T T z A T 5 A bod iat nd Nit tan ect ee oy pce tl 10 7 A ee eens oi ee oe es ea ea 5 y A 20 J 25 30 OpenSees Linear Soil OpenSees Nonlinear Soil LPILE 35 i i 0 05 0 0 05 0 1 0 15 0 2 0 25 0 3 Pile deflection in Figure E 2 Comparison of pile deflection profiles for load case 1 110 ha 1 2 157 Besga A 20 RRA dete canine ae oa esata Totes Heel 257 7 301 7 OpenSees Linear Soil 000 p OpenSees Nonlinear Soil LPILE 35 i i 1 L 1 i 3 5 3 2 5 2 1 5 1 0 5 0 0 5 Rotation rad 107 Figure E 3 Comparison of pile rotation profiles for load case 1 Depth ft 30L OpenSees Linear Soil OpenSees Nonlinear Soil LPILE 35 i 50 40 30 20 10 0 10 20 Bending moment kip ft Figure E 4 Comparison of bending moment profiles for load case 1 111 5 10 215 E 2 A 20 25 30 ae OpenSees Nonlinear Soil LPILE 35 i i 5 0 5 10 15 20 Shear force kips Figure E 5 Comparison of shear force profiles for load case 1 0 S OpenSees Linear Soil gt yO 5 5 OpenSees Nonlinear Soil a ea
3. e eaf 64 0 662 662 662 y 3 ES Ey He ES AE EL A OE Oe DE The number of yield surfaces used for the predefined sands and clays is 20 29 Shear stress Shear strength Number of yield surfaces 5 Shear modulus Peak shear Shear Mass density x strain strain Shear wave velocity Shear Shear stress stress Shear strength Number of yield surfaces 0 Number of yield surfaces 1 Shear modulus Shear Shear modulus Shear Mass density x strain Mass density x strain Shear wave velocity Shear wave velocity Figure 4 9 Soil backbone curve and yield surfaces From Eq 4 2 we can obtain Tr Y max Y A 4 3a Or a Tr Yr Y max G 7 T 4 3b Substituting Eq 4 3a into Eq 4 1 we can obtain G y mE G 1 y a Ty max Take Medium Sand Table 4 1 as an example G 75 000 kPa p 80 kPa p 33 Substituting the above values into Eq 4 2a we can obtain 30 z _ 242 sin 33 f 3 sin 33 80 50 2 kPa 4 5 Substituting the above into Eq 4 4 we can obtain 75000 y 1 1494 L y 4 6 y max Figure 4 10 shows the backbone curves at y 2 5 and 10 based on Eq 4 6 60 50 Shear stress kPa w D S N Ta Ymax gt 2 Opo y 5 max a ta 10 0 f i i i 0 1 2 3 4 5 Shear strain Figure 4 10 Backbone curves for Medium Sand 4 2 3 User
4. 3 54114 m from pile center 4 9586 m from pile center 3042 m from pile center Y Longitudinal plane crossing pile center Transverse plane crossing pile center Tos Figure 7 4 Response time histories window 66 8 Pile Group 8 1 Pile Group Parameters To activate pile group check Pile Group The pile group is defined by the following parameters Figure 8 1 Number of Piles The number of piles along X direction longitudinal and Y direction transverse Note that both numbers do not have to be the same Therefore one can easily build am by n pile group model in OpenSeesPL If 1 is entered for both single pile will be considered Spacing The spacing specified as a factor of the pile diameter between pile centers along X direction longitudinal and Y direction transverse Obviously the spacing must be greater than 1 If Fixed is chosen for the pile head a rigid pile cap will be employed If Free Pinned is chosen the pinned connection is considered for the pile heads of the pile group Pile Pile Head Pile Type Circular y Fixed C Free Pinned N X lt Dir Y Dir Diameter Side Length D fi m Pile Head oO 0 ton Number la 3 3 Total Pile Length 12 im S of Piles Pile Length above Surface 6 rn Axial Load o kN a 3 3 Linear Beam Properties Young s Modulus 30000000 kPa Mass Density 0 ton m3 Moment of Inertia 0 0490873 m4 Re Calculate C Nonlinear Beam Element Aggregator Section
5. C Nonlinear Beam Element Fiber Section j f const Linear Beam Element Figure 8 1 Pile group definition 8 2 Pile Group Meshing 67 To define the finite element mesh for a pile group model click Mesh Parameters button in the Model Input window Figure 5 1 And click Pile Group in the Horizontal Meshing tab to define the controlling parameters in the horizontal directions Figure 8 2 For General Definition and Vertical Meshing Tabs please refer to Chapter 5 Figure 8 3 shows a sample mesh of a 3 x 3 pile group model half mesh configuration General Definition Pile Group E Horizontal Meshing Single Pile Longitudinal x Transverse Y Number of Mesh Layers Between Piles 2 Vertical Meshing Mesh Scaling Ratio of Adjacent Element Width over Distant il Longitudinal Mesh Layer after Length of Mesh Uniform Ratio of Element Pile Group rn Layers Meshing Length over Next 1st Layer after K Interface 2nd Layer in UULU UUEL 3rd Layer 4th Layer 5th Layer fF T T M Use Longitudinal Parameters for Transverse Direction Transverse ist Layer after Interface 2nd Layer 3rd Layer 4th Layer HT 5th Layer o A TT Figure 8 2 Pile group horizontal meshing 68 Figure 8 3 Sample mesh of a 3 by 3 pile group model half mesh configuration 8 3 Output for a Pile Group Model In a pile group analysis output is available for the responses of each
6. ooooonccnnnconocccicoconcnconncconoconocono nooo ccoo cccnocnnncnnnno 5 Figure 2 3 OpenSeesPL copyright message RS ARE ae 6 Figure 2 4 Buttons available in the Finite Element Mesh window ccesceeseseeeteceeeneeeeeeenees 7 Figure 3 1 Definition of pile model AAA A A RN 8 Figure 3 2 Definition of linear pile properties bruselas tio pitillo 9 Figure 3 3 Definition of nonlinear pile properties Aggregator Section oooonocnnccnnncoconcconnconnnos 10 Figure 3 4 Definition of nonlinear pile properties Fiber Section oooooonconoccnnnccnnocconncconoconnconnnos 12 Figure 3 5 Moment curvature response for the pile with default steel and concrete parameters A A A AAA Sets A AAA each EEEa a AE 14 Figure 3 6 Material Parameters of the Concrete01 material Mazzoni et al 2006 15 Figure 3 7 Typical hysteretic stress strain relation of the Concrete01 material Mazzoni et al A O 15 Figure 3 8 Material Parameters of the Steel01 material Mazzoni et al 2006 ooonconnnninnnnn 16 Figure 3 9 Typical hysteretic behavior of model with Isotropic hardening of the Steel01 material Mazzontetal DUO aida yee a A A A E AA Ai 16 Figure 3 10 Schematic of fiber section definition for a circular cross section Mazzoni et al A E pact aaseagls EE E 17 Figure 3 11 Schematic of patch definition for a circular cross section Mazzoni et al 2006 17 Figure 3 12 Schematic of layer definition for a circular cross section M
7. 1f present in the input motion to propagate to the ground surface with more fidelity 5 4 Mesh Scaling The soil domain will be scaled if Re scale Soil Domain in Horizontal Directions checkbox is checked Figure 5 1d Model Length The length of the soil domain along the longitudinal direction to be scaled Model Width The width of the soil domain along the transverse direction to be scaled General Definition Horizontal Meshing Single Pile Mesh Scale Half mesh Pile Group Vertical Meshing Pile Mesh Scaling Num of Slices 16 y Number of Beam Elements above Ground Surface E a General Definition 47 General Definition Horizontal Meshing single Pile Pile Group Vertical Meshing Mesh Scaling a Single Pile Mesh Layer Length of Mesh Uniform From Pile Center rm Layers Meshing Pile Radius 0 5 f Vv 1st Layer after i pp gt Interface E 2nd Layer fi 8 E a 3rd Layer jo f iv 4th Layer o fi lv 5th Layer fo f m 6th Layer fo fi V Outermost Zone fi f Vv Ratio of Element Length over Next o co TT Note Definitions following a O length section will be ignored e g if you do notneed the 3rd layer and beyond enter 0 for the length of the 3rd layer b Horizontal Meshing for Single Pile Models Figure 5 1 Definition of meshing parameters General Definition Vertical Meshing 3 Horizontal Meshing Single Pile Mesh Layer Height Number of
8. 2a h The pile is assumed to be fully embedded in a homogenous isotropic linearly elastic half space with a shear modulus G and a Poisson s ratio vs 0 25 Using Eqs 78 83 and Figure 9 of the above reference the pile response h a 0 1 l a 50 under an applied pure pile head horizontal load is shown in Figure C 4 and Figure C 5 where E Young s Modulus of Pile Gs Shear Modulus of Soil w Pile deflection in H Horizontal load kip z Pile depth ft 88 Normalized Deflection w AaG g Z Yy4da P9ZTTRuIoN 50 under an applied pure pile head Figure C 4 Sample pile deflection h a 1 l a horizontal load Abedzadeh and Pak 2004 89 Normalized Moment Ha 0 0 5 1 1 5 2 2 5 3 Normalized Depth z a Ep Gs 25000 Ep Gs 2500 Figure C 5 Sample pile bending moment h a 1 l a 50 under an applied pure pile head horizontal load Abedzadeh and Pak 2004 90 Appendix C II Nonlinear Response of the Single Pile Model In the nonlinear run the same material properties of the linear run are employed except the soil now assumed to be a clay material with a maximum shear strength or cohesion 5 1 psi in the range of a Medium Clay This maximum shear strength is achieved at a specified strain Ymax 10 The lateral load H is applied at an increment of 0 7875 kips and the final load is 94 5 kips 3 x 31 5 kips The 8 node bri
9. 71 PL Deformed Mesh EEk Due to pushover y disp contour 3D view Play Animation M Endless Zoom In Out Frame xY VE xZ 3D lt gt Up Down M Show Legend Unit m 1 200e 001 1 136e 001 1 071e 001 1 007 e 001 9 430e 002 8 787 e 002 8 144e 002 7 502e 002 6 859e 002 6 216e 002 5 57 4e 002 4 931 e 002 4 289e 002 3 646e 002 3 003e 002 2 361 e 002 1 718e 002 1 075e 002 4 328e 003 2 098e 003 8 524e 003 fe alel Time second fiz Scale Factor 50 Animation Playing Delay millisecond 10 Show Whole model Figure 8 8 Deformed mesh of a pile group model 72 Appendix A How to Define the Soil Finite Element Mesh Step 1 In the user interface click Pile Parameters With reference to Figure 3 1 define the following parameters according to your preference Diameter The pile outer diameter Total Pile Length Starting from the pile head all the way to the pile tip Pile Length above Surface from pile head to mud line ground surface Soil Parameters make sure at least the total Thickness of soil layers is defined This is the total thickness of the ground stratum from the ground surface all the way down to the base of the soil mesh Make sure that the pile tip is within the defined soil domain depth Note Earthquake input motion is imparted along the base of the soil mesh This base is assumed to represent rigid bedrock As such this input earthquake excitation
10. Analysis Increments to Max fi oo Curvature l a 13 Moment Curvature Relationship Moment Curvature Response File mcFile txt b Figure 3 5 Moment curvature response for the pile with default steel and concrete parameters 14 2 pfpeifepsc Figure 3 6 Material Parameters of the Concrete01 material Mazzoni et al 2006 Concrete Stress ksi 0 002 0 000 0 002 0 004 0006 0 008 0 010 0 012 0 014 0 016 Concrete Strain in in Figure 3 7 Typical hysteretic stress strain relation of the Concrete01 material Mazzoni et al 2006 15 stress or force strain or deformation 100 80 Stress ksi 100 0 010 0 000 0 010 0 020 0 020 0 040 0 050 0 060 Strain in n Figure 3 9 Typical hysteretic behavior of model with Isotropic hardening of the Steel01 material Mazzoni et al 2006 16 cover patch core patch y external radius radius Figure 3 10 Schematic of fiber section definition for a circular cross section Mazzoni et al 2006 numSubdivcira 4 Figure 3 11 Schematic of patch definition for a circular cross section Mazzoni et al 2006 17 Figure 3 12 Schematic of layer definition for a circular cross section Mazzoni et al 2006 18 4 Soil Parameters To define soil strata click Soil Parameters in the Model Input window Figure
11. Diameter 16 or Radius a 8 Pile length 52 9 ft Young s Modulus of Pile E 29000 ksi Moment of Inertia of Pile 7 838 2 in Soil Domain In this section the pile is embedded in a uniform soil layer pile top is 0 1 above the ground line Linear and nonlinear soil responses are investigated The Medium density relative granular soil type Lu et al 2006 is selected in this initial attempt The material properties of the soil are listed below At the reference confinement of 80 kPa or 11 6 psi the Shear Modulus of Soil G 10 88 ksi and the Bulk Modulus of Soil B 29 ksi 1 e Poisson s ratio vs 0 33 see Lu et al 2006 Submerged Unit Weight y 62 8 pcf Bowles 1988 For nonlinear analysis the Friction Angle 32 Bowles 1988 and the peak shear stress occurs at a shear strain Ymax 10 at the 11 6 psi confinement 96 Lateral Load The pile head with a free head condition which is 0 1 above the ground surface is subjected to horizontal loads H of 21 kips 31 5 kips and 43 kips Bowles 1988 Finite Element Simulation In view of symmetry a half mesh 2 900 8 node brick elements 23 beam column elements and 207 rigid beam column elements in total is studied as shown in Figure D 1 Length of the mesh in the longitudinal direction is 520 ft with 260 ft transversally in this half mesh configuration resulting in a 520 ft x 520 soil domain in plan view Layer thickness is 80 ft the bottom
12. History Output 7 2 1 Soil Response Time Histories To view the soil response time histories click Soil Response Histories in Menu Display The figures show the response time histories of the soil domain from the ground surface till the bottom at a number of locations which are along the longitudinal direction crossing the pile center The following types of response time histories are available e Longitudinal acceleration time histories Longitudinal displacement rel to base time histories Transvers acceleration time histories Transverse displacement rel to base time histories Vertical acceleration time histories Vertical displacement time histories Excess pore pressure time histories Shear stress xy vs strain amp eff confinement Shear stress yz vs strain amp eff confinement Shear stress zx vs strain amp eff confinement Longitudinal normal stress time histories Transverse normal stress time histories Effective vertical normal stress time histories Shear stress xy time histories Shear stress yz time histories Shear stress zx time histories Longitudinal normal strain time histories Transverse normal strain time histories Vertical normal strain time histories Shear strain xy time histories Shear strain yz time histories Shear strain zx time histories Pile response and deformed mesh output are also available in a base shaking analysis Please refer to Section 6 1 4 65 Response
13. LPILE aa 10 Ligon niet hy RR Gianna Mais E OM oe a Bah Acie Te ae RnR cae tate a tal gt oe ate te a La I E 15 A ER ee ey a a ae eer sS ES A 207 J 25 Badala pna pio A E S a Oa RAN 30 F 7 35 i i 0 1 0 05 0 0 05 0 1 Pile deflection in Figure E 6 Comparison of pile deflection profiles for load case 2 112 5 A 10 15 5g 5 A 20 25 30 D OpenSees Nonlinear Soil PILE 35 i i i i i 2 0 2 4 6 8 10 12 Rotation rad 3 x 10 Figure E 7 Comparison of pile rotation profiles for load case 2 Depth ft 20 OpenSees Linear Soil OpenSees Nonlinear Soil LPILE 35 l l i 100 80 60 40 20 0 20 Bending moment kip ft Figure E 8 Comparison of bending moment profiles for load case 2 113 Nn Depth ft N N Nn 30 OpenSees Nonlinear Soil LPILE 35 i i i i i 5 0 5 10 15 20 25 30 Shear force kips Figure E 9 Comparison of shear force profiles for load case 2 First step Final Figure E 10 Stress ratio contour fill for load case 1 red color shows yielded soil elements First step Final Figure E 11 Stress ratio contour fill for load case 2 red color shows yielded soil elements 114 Appendix F Finite Element Analysis of Caltrans 42 CIDH Pile Using OpenSees for General Comparison with LPILE with Default P Y Multiplier 1 0 Introduction In this study we conduct a fin
14. Shear kips Moment kip ft Load case 1 Fixed head 64 0 Load case 2 Fixed head 128 0 Load case 3 Fixed head 256 0 Load case 4 Free head 64 0 Load case 5 Free head 128 0 Load case 6 Free head 256 0 Finite Element Simulation In view of symmetry a half mesh 2 900 8 node brick elements 19 beam column elements and 180 rigid beam column elements in total is studied as shown in Figure F 1 Length of the mesh in the longitudinal direction is 1360 ft with 680 ft transversally in this half mesh configuration resulting in a 1360 ft x 1360 soil domain in plan view Layer thickness is 60 ft the bottom of the soil domain is 25 ft below the pile tip so as to mimic the analytical half space solution The floating pile is modeled by beam column elements Mazzoni et al 2006 and rigid beam column elements are used to model the pile size diameter The following boundary conditions are enforced D The bottom of the domain is fixed in the longitudinal x transverse y and vertical z directions ID Left right and back planes of the mesh are fixed in x and y directions the lateral directions and free in z direction UD Plane of symmetry is fixed in y direction and free in z and x direction to model the full mesh 3D solution The lateral load is applied at the pile head ground level in x longitudinal direction The above simulations were performed using OpenSeesPL Lu et al 2006 Simulation Results Figures D 2 D
15. Unit m 2 000e 001 1 898e 001 1 796e 001 1 694e 001 1 592e 001 1 490e 001 1 388e 001 1 286e 001 1 184e 001 1 082e 001 9 795e 002 8 775e 002 7 754e 002 6 734e 002 5 713e 002 4 693e 002 3 672e 002 2 652e 002 1 631 e 002 6 109e 003 4 096e 003 Step No 20 4 gt xlt SA Scale Factor 20 Animation Playing Delay millisecond 10 Show Whole model y Figure 6 10 2D plane Y 0 view of the longitudinal displacement contour in the deformed mesh window 6 2 Eigenvalue Analysis To conduct an Eigenvalue analysis click Eigenvalue and then specify Number of Frequencies in Figure 2 1 And then click Save Model amp Run Analysis Figure 6 11 shows the output window for an Eigenvalue analysis which can be accessed by clicking menu Display and then choosing Deformed Mesh 59 PH Mode Shapes Mode shape disp contour 3D view Play Animation JW Er Zoom In Out Frame xY VE xZ 3D lt gt Up Down M Show Legend 1 122e 002 1 371e 002 1 619e 002 1 868e 002 2 116e 002 2 365e 002 2 614e 002 2 862e 002 Unit m 2 110e 002 1 861e 002 1 613e 002 1 364e 002 1 116e 002 8 670e 003 6 183e 003 3 697 e 003 1 211e 003 1 275e 003 3 761e 003 6 248e 003 8 734e 003 Mode No 1 4 gt f Frequency H2 7 50646 Scale Factor 545 Animation Playing Delay millisecond 10 Show Whole model Figure 6 11 Output for an Eigenvalue analysis 60 7 Base Shaking Analysis 7
16. Zone Residual Shear Strength for Very Loose Material Only fo2 kPa Soil Modulus Variation with Depth P CL CC Youngs Poisson s Modulus kPa Ratio 0 3 ae fis ton m3 po fie 005 Notes FP L and C represents parabolic linear and constant variation of soil modulus with depth respectively cae Figure 4 21 Outermost zone material 45 5 Mesh Generation To define the finite element mesh click Mesh Parameters button in the Model Input window Figure 5 1 5 1 General Mesh Definition Mesh Scale The mesh scale can be quarter mesh half mesh or full mesh to reduce computational effort depending on the situation at hand Number of Slices The number of mesh slices in the circumferential direction Number of Beam Elements above Ground Surface The number of beam elements used for the pile section above the ground surface 5 2 Horizontal Meshing The meshing in the horizontal direction for the single pile definition is controlled by the following parameters Tab Horizontal Meshing Figure 5 1b This section controls mesh refinement along the horizontal direction Length of each soil horizontal layer is defined in the left column Number of mesh elements in each defined is specified in the column Number of Mesh Layers Note that the first mesh layer is starting from the center of the mesh when the pile is located and the length of the first mesh layer is equal to the pile radius Ratio of
17. bottom of the domain is fixed in the longitudinal x transverse y and vertical z directions ID Left right and back planes of the mesh are fixed in x and y directions the lateral directions and free in z direction UD Plane of symmetry is fixed in y direction and free in z and x direction to model the full mesh 3D solution The lateral load is applied at the pile head ground level in x longitudinal direction The above simulations were performed using OpenSeesPL Lu et al 2006 Simulation Results The pile head deflections and the maximum bending moments for the linear and nonlinear analyses are listed in Table 2 along with LPILE results for comparison see Appendix for partial output of LPILE results Figures C 2 C 5 show comparisons of the pile deflection rotation bending moment and shear force profiles respectively for load case 1 Figures C 6 C 9 show comparisons of 108 the pile deflection rotation bending moment and shear force profiles respectively for load case 2 The stress ratio contour fill of the nonlinear runs for load cases 1 amp 2 are displayed in Figures C 10 amp C 11 a Isometric view b Pile head close up Figure E 1 Finite element mesh employed in this study 109 Table E 2 Cal Trans CIDH Pile OpenSees Simulation and LPILE Results Max bending Analysis Pile head O M max Profile type deflection in kip ft depth ft
18. constitutes total motion imparted at this Bedrock level Step 2 Click Mesh Parameters to define additional meshing parameters please refer to Chapter 5 and Figure 5 1 The finite element mesh created with the above default values is shown in Figure A 1 Examples of mesh generation are shown in Figures A 2 A 4 Figure A 1 Finite element mesh created with default values 73 General Definition o a Horizontal Meshing Single Pile Mesh Scale Halt mesh Pile Group j Vertical Meshing Pile Mesh Scaling Num of Slices 32 v Number of Beam Elements above Ground Surface a b Figure A 2 Mesh refinement example 1 a Change Num of Slices to 32 b the resulting mesh Vertical Meshing E General Definition Horizontal Meshing Single Pile Mesh Layer Height Number of Ratio of Top lt Pile Group From m Mesh Uniform ElementHeight Vertical Meshing Topdown Layers Meshing over Bottom Mesh Scaling 1 SUA SUE SUE Si SI a aa 4 TTT TTT xl MTT b Figure A 3 Mesh refinement example 2 a Change Number of Mesh Layers in the vertical direction b the resulting mesh 75 General Definition Horizontal Meshing Single Pile i S Single Pile Mesh Layer Length of Mesh Uniform Ratio of Element Pile Group From Pile Center rm Layers Meshing Length over Next Rare Pile Radius o s f 4 Maa Mesh Scaling 1st Layer after i 2 Interfac
19. curvature procedures for sections in 3D space The moment curvature analysis of the section in this OpenSees example is by creating a zero length rotational spring element This section is subjected to a user defined constant axial load and to a linearly increasing moment to a user defined maximum curvature Mazzoni et al 2006 Laterally Loaded Pile The circular pile is 5 ft in diameter D The pile length above the ground surface is 10 ft Therefore the equivalent pile length is 10 ft Fiber section is used to model the nonlinear behavior of the pile The fiber section properties are listed in Tables F 1 4 The schematic of the fiber section definition is also shown in Figure F 1 also see Figure F 2 for the input interface for fiber section in OpenSeesPL Table H 1 Material parameters of the concrete material Core Cover Concrete Compressive Strength ksi 5 2 4 Concrete Strain at Maximum Strength 0 002885 0 003 Concrete Crushing Strength ksi 1 04 0 8 Concrete Strain at Crushing Strength 0 0144 0 01 Table H 2 Material parameters of the steel material Steel Yield Strength ksi 66 8 Initial Elastic Tangent ksi 29000 Strain hardening Ratio 0 01 133 Table H 3 Patch information for the pile circular cross section Core Cover Number of Subdivisions fibers in the Circumferential Direction amp 8 Number of Subdivisions fibers in the Radial Directio
20. eee edie AAA build a section Silvia Mazzoni amp Frank McKenna 2006 SET UP wipe clear memory of all past model definitions model BasicBuilder ndm 3 ndf 6 Define the model builder ndm dimension ndf dofs set dataDir Data set up name of data directory simple file mkdir dataDir create data directory source LibUnits tcl define units MATERIAL parameters set IDconcCore 1 material ID tag confined core concrete 139 set IDconcCover 2 material ID tag unconfined cover concrete set IDreinf 3 material ID tag reinforcement nominal concrete compressive strength set fc expr 4 0 ksi CONCRETE Compressive Strength ksi Tension Compression set Ec expr 57 ksi sqrt fc psi Concrete Elastic Modulus confined concrete set Kfc 1 3 ratio of confined to unconfined concrete strength set felC expr K fc fc CONFINED concrete mander model maximum stress seteps1C expr 2 fclC Ec strain at maximum stress set fc2C expr 0 2 fc1C ultimate stress set eps2C expr 5 eps1C strain at ultimate stress unconfined concrete set fc1U fe UNCONFINED concrete todeschini parabolic model maximum stress setepslU 0 003 strain at maximum strength of unconfined concrete set fc2U expr 0 2 fc1U ultimate stre
21. load displacement is linearly increasing with steps In a dynamic monotonic pushover users are allowed to define the loading duration 6 1 2 2 Sine Wave Pushover If Dynamic Pushover is chosen a Sine Wave loading pattern is also available Figure 6 2 6 1 2 3 Pushover by User Defined Load Pattern U Push To define your own load pattern U Push click U Push in Figure 6 2 The U Push window is shown in Figure 6 3 Click Select Change Pushover File to change file The user defined pushover file should contain single column data 52 Current U Push File CAProgram Files BridgePBEE motions upusht tt Select Change Pushover File C Program Files BridgePBEE motions upush1 tt U Push Data View Push anta iew Pushover Loading Histo Number of Steps eee ee Starting Point Ending Point 201 4 28718e 007 Max alue Point 128 1 25999 Min Value Point 177 1 75653 OK E Pushover Loading History Horizontal axis Step Vertical axis None Figure 6 3 User defined pushover load pattern U Push 6 1 3 Running the Analysis To run the analysis click Save Model amp Run Analysis in Menu Analyze Upon the user requests to run the analysis OpenSeesPL will check all the entries defined by the user to make sure the model is valid Thereafter a small window Figure 6 4 will show the progress of the analysis 53 By default graphical output windows will be opened upon completion of the ana
22. of fluid phase 2 2x10 kPa for water typically and n the initial porosity Horizontal Permeability The permability along the horizontal direction Vertical Permeability The permability along the vertical direction User Defined Nonlinear Shear Stress Strain Backbone Curve The nonlinear shear stress strain backbone curve can be defined by specifying a G Gmax curve Figure 4 11 To specify the G Gmax curve first enter number of points defining G G max curve and then enter pairs of shear strain and G Gmax values The maximum number of points that can be entered is 13 the backbone curve becomes horizontal after point 13 In addition If the number of points is zero then the built in hyperbolic curve will be used instead If the number of points is 1 the material is elastic perfectly plastic The user defined backbone curve is activated if the number of points is greater than zero In this case the user specified friction angle is ignored Instead is defined as follows 343 0 p sing 6 36 p 3 9 33 where Om is the product of the last modulus and strain pair in the modulus reduction curve Therefore it is important to adjust the backbone curve so as to render an appropriate If the resulting 1is smaller than the phase transformation angle r r is set equal to g Also remember that improper modulus reduction curves can result in strain softening response negative tangent shear modulus which i
23. of the nonlinear run for the fixed head condition red color Shows yielded Sob Clements e bans e e ed 122 Figure F 11 Stress ratio contour fill of the nonlinear run for the free head condition red color shows yielded soil element ivi ii asdaeaaadeateisecaasy 123 Figure F 12 Comparison of pile deflection profiles for the fixed head condition 124 Figure F 13 Comparison of pile rotation profiles for the fixed head condition eee 124 Figure F 14 Comparison of bending moment profiles for the fixed head condition 125 Figure F 15 Comparison of shear force profiles for the fixed head condition c eee 125 Figure F 16 Comparison of pile deflection profiles for the free head condition eee 126 Figure F 17 Comparison of pile rotation profiles for the free head condition eee 126 Figure F 18 Comparison of bending moment profiles for the free head condition 127 vi Figure F 19 Comparison of shear force profiles for the free head condition 0 00 0 cesses 127 Figure G 1 Finite element mesh employed in this study oooonoconicccnocccinccooncconcconc nono connnoconocnnnos 130 Figure G 2 Pile profile response at the axial load of 243 Kips cece eeseeseeeeeeceeeeeseeneeeeeeeeees 131 Figure G 3 Close up of final deformed mesh factor Of 120 ee cesesseeseeeeeeeceeeceeeeneeeneeeeees 131 Figure G 4 Stress ratio contour fill for the nonlinear ana
24. of the soil domain is 27 2 ft below the pile tip so as to mimic the analytical half space solution The floating pile is modeled by beam column elements and rigid beam column elements are used to model the pile size diameter The following boundary conditions are enforced D The bottom of the domain is fixed in the longitudinal x transverse y and vertical z directions ID Left right and back planes of the mesh are fixed in x and y directions the lateral directions and free in z direction HI Plane of symmetry is fixed in y direction and free in z and x direction to model the full mesh 3D solution The lateral load is applied at the pile head ground level in x longitudinal direction The above simulations were performed using OpenSeesPL Lu et al 2006 Simulation Results The pile deflections at the ground line and the maximum bending moments for the linear and nonlinear analyses are listed in Table D 1 along with the experimental measurements for comparison Alizadeh and Davisson 1970 Bowles 1988 Figure D 2 shows the load deflection curve for the linear and nonlinear runs Comparison of the pile deflection profiles for the linear and nonlinear analyses are displayed in Figure D 3a c The bending moment profiles for the 3 load levels are shown in Figure D 4a c along with the observed for comparison Alizadeh and Davisson 1970 The stress ratio contour fill of the nonlinear run is displayed in Figure D 5 Com
25. pile Figures 8 4 8 8 69 PL Pile Response Response profile al of Displacement in Longitudinal direction for Pile 1 Pile 1 q U Pile 2 Displacement Profile for Pile 1 File pdispProf txt pile 3 ile 4 leds Kial ile 6 ile 7 ile 8 ile 9 ile 10 ile 11 ile 12 ile 13 ile 14 ile 15 ile 16 Figure 8 4 Pile response profiles for a pile group model 1 Pile Response e l ile 2 Response Profiles for All Steps ile 43 ias ile 4 File ProfHist txt ios ile 46 ile 7 ile 48 ile 49 ile 10 ile 11 ile 12 ile 13 ile 14 ile 15 ile 16 Figure 8 5 Pile response time histories for a pile group model 70 Pile Response Relationships Load displacement at 14 3 m pile Top in Longitudinal direction for Pile 1 y Pile 1 Pile 2 Load Displacement Curve for Pile 1 14 3 m above grou Bis 3 pile top File load _dispX 14 3m txt Pile 4 Pile 5 Pile 6 et 52 Pile 7 Pile 8 Pile 9 Pile 10 Pile 11 Pile 12 Pile 13 Pile 14 Pile 15 Pile 16 Pile Group Figure 8 6 Pile response relationships for a pile group model Pile Response Relationships Load displacement y 14 3 m pile Top in Longitudinal direction y for Pile Group Load Displacement Curve for Pile Cap File load disp Pile Group Figure 8 7 Pile response relationships at the pile cap for a pile group model
26. stress strain backbone curve can be defined by specifying a G Gmax curve Figure 4 15 The user defined backbone curve is activated if the number of points is greater than zero In this case if the user specifies 0 cohesion c will be ignored Instead c is defined by c sqrt 3 0m 2 where Om is the product of the last modulus and strain pair in the modulus reduction curve Therefore it is important to adjust the backbone curve so as to render an appropriate c If the user specifies gt 0 this will be ignored Instead is defined as follows 38 3 43 o 20 p sing 6 13 0 20 p 3 14 If the resulting lt 0 we set 0 and c sqrt 3 on 2 Also remember that improper modulus reduction curves can result in strain softening response negative tangent shear modulus which is not allowed in the current model formulation Finally note that the backbone curve varies with confinement although the variation is small within commonly interested confinement ranges Backbone curves at different confinements can be obtained using the OpenSees element recorder facility Mazzoni et al 2006 For information about other parameters see Section 4 2 3 1 4 2 3 4 User Defined Clay2 U Clay2 The second type of user defined clay U Clay2 can be defined as shown in Figure 4 16 See Section 4 2 3 2 for information about parameters defining U Clay2 4 2 3 5 User Defined Sand2A U Sand2A The third type of user defined
27. the Fiber Section is only available to circular pile in this version of OpenSeesPL Two materials are available Concrete01 and Steel01 in this version of OpenSeesPL Concrete01 Figure 3 6 is defined by the following parameters for Core and Cover see Figure 3 10 Concrete Compressive Strength The concrete compressive strength at 28 days fpc in Figure 3 6 Concrete Strain at Maximum Strength The concrete strain at maximum strength epsc0 in Figure 3 6 Concrete Crushing Strength The concrete crushing strength fpcu in Figure 3 6 Concrete Strain at Crushing Strength The concrete strain at crushing strength epsU in Figure 3 6 Note that the compressive concrete parameters should be input as negative values Typical hysteretic stress strain relation of the Concrete01 material is shown in Figure 3 7 Steel01 is defined by the following parameters Figure 3 8 and Figure 3 9 Yield Strength The yield strength of steel Initial Elastic Tangent The initial elastic tangent of steel Strain hardening Ratio The strain hardening ratio ratio between post yield tangent and initial elastic tangent Patch Figure 3 10 is defined by the following parameters for both Core and Cover Number of Subdivisions fibers in the Curcumferential Direction The number of subdivisions fibers in the circumferential direction of the pile circular cross section SnumSubdivCirc in Figure 3 11 Number of Subdivisions fibers in the Radial Dir
28. vertical gravity factor is applied at the first run through the soil element body force factor 3 Switching from elastic soil properties to nonlinear soil properties The actual defined soil properties in every part of the mesh are activated and nonlinear if specified properties are activated as well The dynamic solver is used similar to item 1 above and Kmatrix1 is used for convergence Own weight is applied in 5 steps time step is set to 50 000 secs A convergence tolerance of 0 0001 is used displacement norm The boundary conditions for this step remain those of BC1 4 Including the beam column elements and their own weight A new mass and stiffness matrix is built based on the latest tangent soil stress strain state and the linear properties of the beam column elements A convergence tolerance of 0 0001 is used displacement norm The load is applied in 20 steps by default the user can modify this value in the the OpeSees Parameters section from Analysis Options The stiff matrix is not updated The dynamic solver is used similar to Section 2 and 5 time steps are allowed with no additional input excitation to ensure convergence to a stable static solution The boundary conditions for this step remain those of BC1 80 5 Solution Phase Solution is started with a stiffness matrix based on the latest soil and beam column stress strain state Four different analysis scenarios are possible Static Push over analys
29. 0 4 0 5 0 6 0 7 Pile deflection in Figure F 16 Comparison of pile deflection profiles for the free head condition 0 ha T Nn T Depth ft N T OpenSees Linear Soil 64 kips OpenSees Linear Soil 128 kips OpenSees Linear Soil 256 kips 30 7 OpenSees Nonlinear Soil 64 kips Pd OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips N Nn T 35 5 4 3 2 1 0 1 Rotation in 3 Figure F 17 Comparison of pile rotation profiles for the free head condition 126 ha T ha Nn T Depth ft N T S OpenSees Linear Soil 64 kips OpenSees Linear Soil 128 kips OpenSees Linear Soil 256 kips gob OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips N Nn T 35 200 0 200 400 600 800 1000 1200 1400 Bending moment kip ft Figure F 18 Comparison of bending moment profiles for the free head condition Depth ft a gt N N Nn OpenSees Linear Soil 128 kips OpenSees Linear Soil 256 kips 30 1 OpenSees Nonlinear Soil 64 kips J OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips 200 100 0 100 200 300 400 Shear force kips Figure F 19 Comparison of shear force profiles for the free head condition 12
30. 0 boro ec WIICALICEOS AQUA OO OpenSees Nonlinear Soil LPILE 50 Experimental 50 0 50 100 150 200 Bending moment kip ft b H 31 5 kips 0 E 10t J 2201 5 a A 30 40 _ OpenSees Linear Soil OpenSees Nonlinear Soil Se LPLE 50 Experimental 50 0 50 100 150 200 250 300 Bending moment kip ft c H 43 kips Figure D 7 continued 106 Appendix E Finite Element Analysis of Standard CalTrans 16 CIDH Pile Using Opensees for General Comparison with LPILE with Default P Y Multiplier 1 0 Introduction In this study we conduct a finite element simulation of the standard Caltran 16 CIDH pile using the 3D OpenSeesPL interface The simulated pile responses are compared with LPILE results Laterally Loaded Pile Pile Data The geometric and elastic material properties of the pile are listed below Diameter D 16 Pile length 35 ft Moment of Inertia of Pile J 850 inf Young s Modulus of Pile E 4030 ksi In this initial study the pile was modeled to remain linear also in view of the applied load levels Soil Domain Linear and nonlinear soil responses are investigated The Medium relative density granular soil type Lu et al 2006 is selected in the analyses The material properties of the soil are listed below At the reference confinement of 80 kPa or 11 6 psi the Shear Modulus of Soil G 10 88 ksi and the Bulk Modulus of Soil B 29 ksi 1 e Poisso
31. 00 000 kPa and initial lateral vertical confinement ratio Ko 0 9 by default and a default global very large permeability coefficient 100 m s by default the permeability will be changed to the user specified value before the dynamic run Default is global elastic modulus 600 000 kPa by default and global initial lateral vertical confinement ratio Ko 0 9 by default for the entire soil domain These specified global values will be used for the top soil layer For all other soil layers including the pile zone and the interfacing zone the elastic modulus employed is equal to the above global value 600 000 kPa by default times the ratio of the mass density of the current soil layer over the top soil layer These elastic soil properties are used to define an elastic stiffness matrix Kmatrix1 A default convergence tolerance of 0 0001 is used displacement norm which the user can specify in the OpeSees Parameters section from Analysis Options Boundary conditions BC1 Lateral boundaries Rollers are used on the lateral boundaries to prevent lateral deformation and vertical displacement is allowed Base Rollers are used to prevent vertical displacement but lateral deformation is allowed 2 Model inclination If the model is inclined an extra run for applying the horizontal gravity factor is added The horizontal gravity factor is applied at the based nodes as acceleration input the base nodes have to be fixed before this run The
32. 02 Linear load 1002 0 0 0 0 0 0 0 0 0 0 1 0 Compute curvature increment set dK expr maxK numIncr Use displacement control at node 1002 for section analysis dof 6 integrator DisplacementControl 1002 6 dK 1 dK dK Do the section analysis set ok analyze numIncr set IDctrINode 1002 set IDctrIDOF 6 set Dmax maxK set Diner dK set TolStatic 1 e 9 set testTypeStatic EnergyIncr set maxNumlterStatic 6 set algorithmTypeStatic Newton if Sok 0 if analysis fails we try some other stuff performance is slower inside this loop set Dstep 0 0 set ok 0 while Dstep lt 1 0 amp amp ok 0 set controlDisp nodeDisp IDctrINode IDctrIDOF set Dstep expr controlDisp Dmax set ok analyze 1 this will return zero if no convergence problems were encountered if Sok 0 reduce step size if still fails to converge set Nk 4 reduce step size set DincrReduced expr Dincr Nk integrator DisplacementControl IDctrINode IDctrIDOF DincrReduced for set ik 1 ik lt Nk incr ik 1 set ok analyze 1 this will return zero if no convergence problems were encountered if Sok 0 if analysis fails we try some other stuff performance is slower inside this loop global maxNunmlterStatic max no of iterations performed before failure to converge is ret d puts Trying Newton with Initial Tangent test NormDispIncr TolStatic 2000 0 algorithm Newton initial set ok analyz
33. 1 Initial Elastic Tangent 200000000 Strain hardening Ratio 29000 l 22332 am 0000 200000000 0 01 Circular Shape Number of Subdivisions fibers in the Circumferential Direction Number of Subdivisions fibers in the Patch Radial Direction Internal Radius External Radius iii 0 457 0 61 m Number of Reinforcing Bars along Layer il Layer Area of Individual Reinforcing Bar 0 00014 m2 Radius of Reinforcing Layer 0 457 m Cancel View Moment Curvature Response Figure 3 4 Definition of nonlinear pile properties Fiber Section 12 The moment curvature response for the pile is shown in Figure 3 5 for default steel and concrete parameters Moment Curvature Analysis Material Concrete Cover 22332 kPa 0 002 Compressive Strength Strain at Max Strength Crushing Strength kPa 1 Strain at Crushing Strength 0 006 Material Steel Yield Strength 460000 kPa Initial Elastic Tangent 200000000 kPa Strain hardening Ratio Patch Number of Fibers in Circumferential Direction Number of Fibers in Radial Direction Internal Radius External Radius 0 45 o 1 g 1 I lt arn _ a y A Pro O az m i Layer Number of Reinforcing Bars along Layer 16 Area of Individual Reinforcing Bar 0 0001 4 m2 Radius of Reinforcing Layer 0 457 m Axial Load fi 00 kN Maximum Curvature 0 3937 rad m Number of
34. 1 Base Shaking 7 1 1 Step by Step Time Integration OpenSeesPL employs the Newmark time integration procedure with two user defined coefficients B and y Newmark 1959 Chopra 2004 Standard approaches may be adopted by appropriate specification of these constants Figure 7 1 Default values in OpenSeesPL are y 0 55 and B y 4 4 Computations at any time step are executed to a convergence tolerance of 10 Euclidean Norm of acceleration vector normalized by the first iteration Error Norm predictor multi corrector approach Note An additional fluid phase Chan 1988 time integration parameter 0 is set to 0 6 in the data file B 1 4 y 1 2 B 1 6 y 1 2 Linear acceleration conditionally stable scheme Average acceleration or trapezoidal rule unconditionally stable scheme in linear analyses B 1 12 y 1 2 Fox Goodwin fourth order accurate 157 a tabl unconditional non stable oo stability N J s SS x sx S 8 Ns conditional a stability N 0 0 H 0 0 0 5 1 0 15 2 0 Figure 7 1 Newmark Time Integration 61 7 1 2 Input Motion One two and three directions of excitations are available longitudinal transverse and vertical directions Figure 2 1 and Figure 7 2 The bedrock is assumed to be rigid the input motion is total motion Base seismic excitation can be defined by either of the following two methods i Via a built in input motion library Th
35. 29 a Isometric view Se KOS gt A ISS SS AS TER AI ee a I ES A rica b Pile head close up Figure G 1 Finite element mesh employed in this study 130 Depth ft N N Nn o Nn Oo 0 18 0 16 0 14 0 12 0 1 0 08 O 100 200 Vertical displacement in Axial force kips Figure G 2 Pile profile response at the axial load of 243 kips Figure G 3 Close up of final deformed mesh factor of 120 131 9 17De 001 8 509e 001 7 648e 001 7 167e 001 6 526e 001 5 864e 001 5 203e 001 4 542e 001 3 881 e 001 3 220e 001 2 559e 001 9 170e 001 8 509e 001 646e 001 167e 001 6 526e 001 5 664e 001 5 203e 001 4 542e 001 3 631 e 001 3 220e 001 2 559e 001 b Side view Figure G 4 Stress ratio contour fill for the nonlinear analysis red color shows yielded soil elements 132 Appendix H Moment Curvature Analysis of Circular Nonlinear RC Beam Fiber Section Introduction In this study we compare with an OpenSees moment curvature pushover analysis input file see appendix A single circular reinforced concrete column is rigidly attached to the soil mesh for that purpose The soil domain is assumed rigid so as to simulate a cantilever beam scenario The OpenSees input file is Example 9 listed in the OpenSees Example Manual http opensees berkeley edu OpenSees manuals ExamplesManual HTML This OpenSees example introduces the moment
36. 4 1 Soil Strata Soil Layer From Thickness eae Residual Shear Strength topdown m oil Type kPa ie 22 U Clay2 PressurelndependMultivield i gt IJV O 3 3 4 TT PNT o a E E A E A a NE 4 5 6 a 8 9 0 1 2 Manan 23533310 l Saturated Soil Analysis Water Table Depth Below Ground Surface fo rm Activate Pile Zone FT Activate Interfacing Layer F Activate Outermost Zone M Activate Tension Cutoff for Cohesive Soil Note P Land C represents Parabolic Linear increasing and Constant variation of soil modulus with depth respectively Cancel Figure 4 1 Soil strata definition 4 1 Soil Parameters A total of 10 soil strata can be defined in OpenSeesPL Figure 4 1 The profile of the soil strata can be defined by using the follow parameters Thickness The thickness for a soil layer Definitions following a zero height will be ignored In other words the total number of soil layers in use will be equal to the number of the last soil layer that contain no zero values e g if you need 5 strata enter nonzero heights for Stratum 1 through Stratum 5 To perform a liquefaction analysis check the checkbox Saturated Soil Analysis Figure 4 1 and specify the water table depth 19 Water Table Depth The Water Table Depth refers to the depth below ground surface e g 0 0 corresponds to a fully saturated soil profile 1 0 is 1m below ground surface Dry sites shou
37. 5 show comparisons of the pile deflection rotation bending moment and shear force profiles respectively for the fixed head condition load cases 1 2 amp 3 along with LPILE results for comparison Figures D 6 D 9 show comparisons of the pile deflection rotation bending moment and shear force profiles respectively for the free head condition load cases 4 5 amp 6 also along with LPILE results for comparison The 116 stress ratio contour fill of the nonlinear runs for the fixed and free head conditions are displayed in Figures D 10 amp D 11 Comparisons of the linear and nonlinear responses using OpenSees are shown in Appendix Figures D 12 D 19 a Isometric view E 1 re a SS eae ea ee ee ea E E e a as ee er a b Pile head close up Figure F 1 Finite element mesh employed in this study 117 Depth ft OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips 7 OpenSees Nonlinear Soil 256 kips LPILE 64 kips N Nn T 30 PARRA i A a eG ah E PILE 108 kips A a al R pta ae A fll i LPILE 256 kips 35 F i i f 1 i 0 1 0 0 1 0 2 0 3 0 4 0 5 0 6 Pile deflection in Figure F 2 Comparison of pile deflection profiles for the fixed head condition 0 5 SS A GAS Aoki AN IE AN wrote pr 10t 7 2 157 7 S p A 20 ET E Rete cee See aes OpenSees Nonlinear Soil 64 ki 25 OpenSees Nonlinea
38. 7 Appendix G Finite Element Analysis of Standard CalTrans 16 CIDH Pile Subjected to Axial Load Introduction In this study we conduct a finite element simulation of the standard Caltran 16 CIDH pile using the 3D OpenSeesPL interface The simulated pile is subjected to axial load Axially Loaded Pile Pile Data The geometric and elastic material properties of the pile are listed below Diameter D 16 Pile length 35 ft Moment of Inertia of Pile J 850 inf Young s Modulus of Pile E 4030 ksi In this initial study the pile was modeled to remain linear also in view of the applied load levels Soil Domain Nonlinear soil response is investigated The Medium relative density granular soil type Lu et al 2006 is selected in the analyses The material properties of the soil are listed below At the reference confinement of 80 kPa or 11 6 psi the Shear Modulus of Soil G 10 88 ksi and the Bulk Modulus of Soil B 29 ksi 1 e Poisson s ratio vs 0 33 see Lu et al 2006 Effective Unit Weight y 110 pcf given by CalTrans For nonlinear analysis the Friction Angle 33 given by CalTrans and the peak shear stress occurs at a shear strain Ymax 10 at the 11 6 psi confinement The parameter Ymax along with the shear modulus define the nonlinear soil stress strain curve Other values Of Ymax Should be explored in the future Axial Load 128 An axial load of 243 kips is applied at the pile hea
39. Crushing Strength Concretel1 Concrete Strain at Crushing Strength Yield Strength Steel01 Initial Elastic Tangent Strain hardening Ratio Circular Shape Number of Subdivisions fibers in the Circumferential Direction Number of Subdivisions fibers in the Patch Radial Direction Internal Radius External Radius Number of Reinforcing Bars along Layer Layer Area of Individual Reinforcing Bar Radius of Reinforcing Layer Figure H 2 Material properties for the Fiber section 135 Figure H 3 Finite element mesh employed in this study 8000 7000 6000 5000 o T o 5 O OpenSeesPL OpenSees Example 0 0000 0 0002 0 0004 0 0006 0 0008 0 0010 0 0012 Curvature rad in Figure H 4 Comparison of the moment curvature curves calculated by using OpenSeesPL and OpenSees Example 136 a Longitudinal displacement b Moment in the longitudinal plane 137 c Longitudinal shear force Figure H 5 Displacement response profiles histories of the pile Figure H 6 Lateral longitudinal shear versus displacement at the pile head 138 Figure H 7 Moment curvature relation at the maximum moment location ground surface in OpenSeesPL Appendix OpenSees Moment Curvature Pushover Analysis Input File Available at http opensees berkeley edu OpenSees manuals ExamplesManual HTML Source code of file ex9f tcl PP fei ence a eee ee
40. Defined Materials User defined materials include user defined sand U Sand1 and U Sand2 with confinement dependent material properties and user defined clay U Clay1 and U Clay2 with properties independent of confinement variation To define the parameters of a user defined material click the list of soil materials and select U Sand1A U Sand1B U Clay1 U Clay2 U Sand2A or U Sand2B accordingly Figure 4 8 31 4 2 3 1 User Defined Sand1A U Sand1A Sandy soil PressureDependMulti Yield with confinement dependent shear response can be defined by specifying the following parameters see Figure 4 6 and Figure 4 11 U Sand1A PressureDependMultiYield for Soil Layer 1 Reset All Based on gt Please select v Soil Elastic Properties Saturated Mass Density Reference Pressure Pressure Dependence Coefficient 2 ton m3 80 kPa 05 100000 kPa 300000 kPa Soil Nonlinear Properties Peak Shear Strain Friction Angle Fluid Properties Fluid Mass Density Combined Bulk Modulus Horizontal Permeability Vertical Permeability 10 35 degree 1 ton m3 2200000 kPa 0 0001 m s 0 0001 m s Modulus Reduction Curve Number of Points Defining Curve Shear strain 0 0001 0 0003 0 001 l i 0 0 0 0 0 0 0 1 o a co a o om A wo J et co o co a o aw o Figure 4 11 U Sand1A Dilatancy Liquefaction
41. Element Length over Next is used to obtain a gradually changing element size within a layer if Uniform Meshing is unchecked obviously this option is only valid if the of mesh layers is 2 or larger 5 3 Vertical Meshing The meshing in the vertical direction is controlled by the following parameters Tab Vertical Meshing Figure 5 1c This section defines the soil profile layering along the vertical direction starting from the ground surface downwards looking at the side view from the top downwards Height thickness of each soil layer is defined in the left column Number of mesh elements in each defined is specified in the column Number of Mesh Layers at least equal to 1 to define a soil profile consisting of a single type of soil Height thickness of this layer must be equal to the entire soil stratum height Note that the number of mesh layers in the upper zone where the pile foundation is embedded will automatically define the number of beam column elements of this pile below ground surface As such it is generally advisable to select an adequate number of 46 mesh layers in this zone Note If there is any error during mesh generation please follow the error message instructions to adjust the controlling parameters and then try again Note Element size is a parameter that affects frequency content of the ground response Smaller size elements particularly along the soil domain height will permit higher frequencies
42. Fixed Vert Bedrock Type Rigid Bedrock Model Inclination along Longitudinal Direction Ground Surface Inclination Angle 0 30 deg fo Whole Model Inclination Angle 0 10 deg fo Figure 7 2 Definition of 3D base excitation and boundary conditions 63 U Shake Current User Defined Input Motion U Shake File CAProgram Files OpenSeesPL Single Pile imotionsiscsmwl bd CAProgram Files OpenSeesPL Single Pile motions scsmv1 bd Detail Motion Information Please change if necessary 6000 SUMEA ete ot Response will be computed for Time seconds Acc Value g 29995 SSCONBE Starting Point Sa 00956 Ending Point 29995 0 0197 Output at interval of Maximum Acc Paint 6 425 os oor ooo Minimum Acc Point 7 035 0 703 View Motion Horizontal axis Time second Vertical axis Acc g Cancel Figure 7 3 User defined input motion U Shake 7 1 3 Model Inclination Inclined models can be defined by the following parameters Figure 2 1 Ground Surface Inclination Angle along Longitudinal Direction The inclination angle of the ground surface along the longitudinal direction in degrees zero degree represents level ground surface 64 Whole Model Inclination Angle along Longitudinal Direction The inclination angle in degrees of the whole model zero degree represents level ground For mildly inclined infinite slopes suggested values are from 0 to 10 degrees 7 2 Time
43. Live Internet Computation of Seismic Ground Response 2004 Z Yang J Lu and A Elgamal Advances in Engineering Software 35 249 259 Earth Dams on Liquefiable Foundation Numerical Prediction of Centrifuge Experiments 2004 Z Yang A Elgamal K Adalier and M Sharp J Engineering Mechanics ASCE 130 10 1168 1176 Dynamic Response of Saturated Dense Sand in Laminated Centrifuge Container 2005 A Elgamal Z Yang T Lai B L Kutter and D Wilson J Geotechnical and Geoenvironmental Engineering ASCE 131 5 598 609 Modeling Soil Liquefaction Hazards for Performance Based Earthquake Engineering 2001 S Kramer and A Elgamal Pacific Earthquake Engineering Research PEER Center Report No 2001 13 Berkeley CA 147
44. OpenSeesPL 3D Lateral Pile Ground Interaction User Manual Beta 1 0 http cyclic ucsd edu openseespl Jinchi Lu Ahmed Elgamal and Zhaohui Yang University of California San Diego Department of Structural Engineering December 2011 For conversion between SI and English Units please check http www unit conversion info 1 kPa 0 1450378911491 psi 1 psi 6 89475 kPa Table of Contents TABLE OF FIGURES IV 1 INTRODUCTION 1 1 1 OVERVIEW 1 2 SYSTEM REQUIREMENTS 1 3 INSTALLATION 1 4 ACKNOWLEDGMENTS 2 GETTING STARTED 4 2 1 START UP 2 2 INTERFACE 2 2 1 Menu Bar 2 2 2 Model Input Window 2 2 3 Finite Element Mesh Window 3 PILE MODEL 8 3 1 PILE PARAMETERS 3 2 PILE PROPERTIES 3 2 1 Linear Beam Element 3 2 2 Nonlinear Beam Element 4 SOIL PARAMETERS 19 4 1 SOIL PARAMETERS 4 1 1 Analysis Options 4 1 2 Additional Viscous Damping 4 2 SOIL PROPERTIES 4 2 1 Theory of Soil Models 4 2 2 Predefined Materials 4 2 3 User Defined Materials 4 2 4 Material Properties for Pile Zone 4 2 5 Pile Soil Interfacing Layer Properties 4 2 6 Outermost Zone Properties Si MESH GENERATION46 5 1 GENERAL MESH DEFINITION 5 2 HORIZONTAL MESHING 5 3 VERTICAL MESHING 5 4 MESH SCALING 6 PUSHOVER amp EIGENVALUE ANALYSES 50 6 1 PUSHOVER ANALYSIS 6 1 1 Analysis Types 6 1 2 Load Pattern 6 1 3 Running the Analysis 6 1 4 Output for Pushover Analysis 6 2 EIGENVALUE ANALYSIS 7 BASE SHAKING ANALYSIS 61 7 1 BASE SHAKING 7 1 1 Step by Step T
45. PL main window 2 2 Interface There are 3 main regions in the OpenSeesPL window menu bar the model input window and the finite element mesh window 2 2 1 Menu Bar The menu bar shown in Figure 2 2 offers rapid access to most of OpenSeesPL s main features OpenSeesPL Untitled File Execute Display Help DSH E OpenSeesPL Untitled ES Execute Display Help New Model OpenSeesPL Untitled Open Model File QA Display Help Close Model Save Model amp Run Analysi EA D _ Save Model aRun Analysis Save Model As c Model Summary b OpenSeesPL Untitled File Execute EJEA Help OpenSeesPL Untitled File Execute Display El Soil Response Histories Deformed Mesh D ci Gd 2 6 Openseesht Website Pile Response Profiles About OpenSeesPL Pile Response Relationships Model Input Link Internal Forces d Figure 2 2 OpenSeesPL s menu bar and submenu bars a menu bar b menu File c menu Execute d menu Display and e menu Help OpenSeesPL s main features are organized into the following menus e File Controls reading writing and printing of model definition parameters and exiting OpenSeesPL e Execute Controls running analyses e Display Controls displaying of the analysis results e Help Visits OpenSeesPL website and display the copyright info Figure 2 3 About OpenSeesPL OpenSeesPL Beta 1 0 November 2011 Copyright C 2011 The Regen
46. Parameters Phase Transformation 30 Angle degree Contraction param Dilation parami Dilation param2 Liquefaction parami Liquefaction param2 Liquefaction param3 Cancel View Backbone Curve Saturated Mass Density The saturated mass density of the cohesionless soil Reference Pressure The reference mean effective confining pressure p at which soil appropriate soil properties below are defined Gmax The reference low strain shear modulus G specified at a reference mean effective confining pressure p 32 Bmax The reference bulk modulus B specified at a reference mean effective confining pressure P Pressure Dependence Coefficient d A positive constant defining variations of G and B as a function of instantaneous effective confinement p Ceci B B 2 P y 4 7 r r Peak Shear Strain An octahedral shear strain at which the maximum shear strength is reached specified at a reference mean effective confining pressure p The suggested values are between 0 001 and 20 Friction Angle The friction angle 4 at peak shear strength in degrees The suggested values are between 5 and 65 degrees Fluid Mass Density The mass density of the fluid which is usually 1 0 ton m Combined Bulk Modulus The combined undrained bulk modulus B relating changes in pore pressure and volumetric strain may be approximated by B By n 4 8 where By is the bulk modulus
47. Profiles To view the pile response click Pile Response Profiles in Menu Display The figures show the response time histories and response profiles of the pile Seven types of response are available Figure 6 7 e Displacement e Acceleration e Rotation e Moment e Shear e Pressure 55 NAAA Re ponse profile y of Displacement y in Longitudinal direction y Response profile X Displacement y Longitudinal direction y Longitudinal direction Response profile Transverse direction Vertical direction Bending Moment Shear Force Pressure Response Summa Figure 6 7 Response time histories and profiles for pile 6 1 4 3 Pile Response Relationships To view the pile response relationships click Pile Response Relationships in Menu Display The figures show the response relationships of the pile Two types of response are available Figure 6 8 e Load displacement e Moment curvature To zoom in or zoom out use mouse to select a window Click fill to get back to the original figure 56 1 Pile Response Relationships Loag displacement Ela 6 m pile Top y in Longitudinal direction y Load displacement fDi ge a E Longitudinal direction gt direction v Longitudinal direction gt top File Load displacement i gg Longitudinal direction Transverse direction Kil Figure 6 8 Response relationships for pile 6 1 4 4 Deformed Mesh By default the defo
48. Ratio of Top Pile Group From m Mesh Uniform Element Height Vertical Meshing Topdown Layers Meshing over Bottom Mesh Scaling _ 1 E E a 0 9 fo f jz o fo f Iv fi fo IV f fll nn a A fo f Iv fi fo v f 10 o IV fi fo f z f c Vertical Meshing Mesh Scaling i General Definition Horizontal Meshing Single Pile Scale Soil Domain in Horizontal Directions Single Pile Only Pile Group E a e 200 wWericalMeshin Model Length Longitudinal Direction m Mesh Scaling Model Width Transverse Direction fi 50 m d Mesh Scaling Figure 5 1 continued 49 6 Pushover amp Eigenvalue Analyses In a pushover or base shaking analysis four runs are conducted in sequence in order to achieve convergence and simulate the actual loading situation 1 1 run Gravity of soil domain is applied in this run all soil materials are prescribed as linear during this run 2 2 run Soil elements are changed to nonlinear if Nonlinear is chosen in Analysis Options see Section 4 1 1Error Reference source not found 3 3 run Pile elements are added and gravity of the pile structure is applied in this run 4 4 run Pushover or base shaking analysis is started 6 1 Pushover Analysis 6 1 1 Analysis Types To conduction a pushover analysis click Pushover and then click Define Pattern in Figure 2 1 Two types of pushover analyses are available Figure 6 1 Static and Dynamic Pushover 6 1 1 1 Force Based Metho
49. Time Histories Longitudinal displacement rel to base time hist y at 0 0 m pile center bas v in Longitudinal plane crossing pile center fp Longitudinal acceleration time histories i Longitudinal displacement rel to base time historiei Transvers acceleration time histories Transverse displacement rel to base time historie Vertical acceleration time histories Vertical displacement time histories Excess pore pressure time histories Shear stress xy vs strain amp eff confinement Shear stress yz vs strain amp eff confinement Shear stress 2x vs strain amp eff confinement Longitudinal normal stress time histories Transverse normal stress time histories Effective vertical normal stress time histories Shear stress xy time histories Shear stress yz time histories Shear stress 2x time histories Longitudinal normal strain time histories Transverse normal strain time histories Vertical normal strain time histories Shear strain xy time histories Shear strain yz time histories Shear strain 2x time histories 0 5 m from pile center 1 m from pile center 5 m from pile center 4071 m from pile center 3 54114 m from pile center 4 9586 m from pile center 6 73042 m from pile center 8 9452 m from pile center 11 7137 m from pile center 15 1743 m from pile center 9 5 m from pile center 0 5 m from pile center 1 m from pile center 1 15 m from pile center 2 40717 m from pile center
50. ak Shear Strain 0 001 20 13 Number of Yield Surfaces 0 30 20 Advanced Options M Use KO for Elastic Own Weight m F Young s Modulus for Elastic Own Weight kPa Figure 4 18 U Sand2B 4 2 4 Material Properties for Pile Zone The pile zone refers to the pile domain under the ground surface The material for the pile zone Figure 4 19 can be selected from an available menu of cohesionless and cohesive soil materials including the elastic isotropic material In addition user defined cohesionless and cohesive soil materials U Sand1A U Sand1B U Clay1 U Clay2 U Sand2A and U Sand2B are also available to choose If an elastic isotropic material is selected the user is requested to specify Young s Modulus Poisson s Ratio Mass Density Permeability of the material used for the pile zone 43 Pile Zone Material for Pile Zone e Residual Shear Strength for be Very Loose Material Only kPa Soil Modulus Variation with Depth EP CL C Youngs E Poisson s b3 Modulus kPa Ratio Mess T horma Pame as Notes P L and C represents parabolic linear and constant variation of soil modulus with depth respectively cae Figure 4 19 Pile zone material 4 2 5 Pile Soil Interfacing Layer Properties The material for the pile soil interfacing layer Figure 4 20 can be selected from an available menu of cohesionless and cohesive soil materials including the elastic isotropic material In addition u
51. are enforced I The bottom of the domain is fixed in the longitudinal x transverse y and vertical z directions ID Left right and back planes of the mesh are fixed in x and y directions the lateral directions and free in z direction ID Plane of symmetry is fixed in y direction and free in z and x direction to model the full mesh 3D solution The lateral load is applied at the pile head ground level in x longitudinal direction The above simulations were performed using OpenSeesPL Lu et al 2006 Simulation Results and Comparison with Elastic Solution Deflection and bending moment response profiles obtained from OpenSees are shown in Figure C 2 and Figure C 3 along with the analytical elastic solution by Abedzadeh and Pak 2004 for comparison note that the elastic solution was obtained by performing a linear interpolation of the normalized deflections and moments shown in Figure C 4 and Figure C 5 for Ep Gs 3634 The pile head deflection and the maximum bending moment from OpenSees and the elastic solution are also listed in Table C 1 In general the numerical results match well with the analytical elastic solution The pile head deflection from the 20 node element mesh 0 043 is almost identical to the elastic solution 0 042 84 For nonlinear run please see Appendix C II a Isometric view b Pile head close up Figure C 1 Finite element mesh employed in this study 85 Table C 1 Comp
52. arison of OpenSees results and the analytical elastic solution Openbecs Results Elastic solution by 8 node element 20 node Abedzadeh and Pak 2004 element Pile head deflection in 0 039 0 043 0 042 Maximum moment Minax kip ft 30 31 27 Depth where Max occurs ft 2 87 2 87 23 0 5 10 S157 Y en o 20 A 25 301 Elastic solution by Abedzadeh and Pak 2004 OpenSees using 8 node brick element e OpenSees using 205 node brick element 35 0 0 005 0 01 0 015 0 02 0 025 0 03 0 035 0 04 0 045 Pile deflection in Figure C 2 Comparison of pile deflection profiles v 25 l a 50 86 N Nn o Pile depth ft N Nn 30 EEEE EEE ETE OpenSees using 8 node brick element OpenSees using 20 node brick element 3 5 fi 5 0 5 10 15 20 25 30 35 Bending Moment kip ft Figure C 3 Comparison of pile bending moment profiles v 25 l a 50 87 Appendix C I Elastic Solution of the Response of a Laterally Loaded Pile in a Semi Infinite Soil Medium with Constant Modulus along Depth For details please see Farzad Abedzadeh and Y S Pak 2004 Continuum Mechanics of Lateral Soil Pile Interaction Journal of Engineering Mechanics Vol 130 No 11 November pp 1309 1318 Consider a flexible cylindrical pipe pile of radius a length Z a wall thickness h a note that the moment of inertia J
53. as developed by Dr Jinchi Lu jinlu ucsd edu Dr Ahmed Elgamal elgamal ucsd edu and Dr Zhaohui Yang yangaaa gmail com The OpenSees geotechnical simulation capabilities were developed by Dr Zhaohui Yang and Dr Ahmed Elgamal For more information please visit http cyclic ucsd edu opensees OpenSeesPL operates in SI and English units NOTE Seismically induced deformations are complex mechanisms Much expertise and sound engineering judgment are necessary in interpreting the OpenSeesPL computational results 1 2 System Requirements OpenSeesPL runs on PC compatible systems using Windows NT V4 0 2000 XP Vista or Windows 7 The system should have a minimum hardware configuration appropriate to the particular operating system Internet Explorer 3 0 or above or compatible Browser with Java Applet enabled is needed to view the graphic results For best results your system s video should be set to 1024 by 768 or higher 1 3 Installation After downloading the OpenSeesPL installation file OQpenSeesPL_ Setup exe double click on the icon and the installation procedure will start Once installed the default case in OpenSeesPL is a good way to go through the steps involved in conducting an OpenSeesPL analysis The interface will allow the user to prepare and save an input file to run the analysis and to display the response Note Tcl tk 8 5 must be installed in order to run OpenSeesPL Please restart the computer after the i
54. ation profiles for load case Z ooonooniconicniccnicioccconononononcnnnnnncns 113 Figure E 8 Comparison of bending moment profiles for load case 2 ooooocnccniccnncnicccocanoncnnnnnnns 113 Figure E 9 Comparison of shear force profiles for load Case 2 cooconcococnonocinocnnccconcnononancnnnnnnons 114 Figure E 10 Stress ratio contour fill for load case 1 red color shows yielded soil elements 114 Figure E 11 Stress ratio contour fill for load case 2 red color shows yielded soil elements 114 Figure F 1 Finite element mesh employed in this Study ooooooccniccninccnoncconncconcconc nono connnocnocnnnos 117 Figure F 2 Comparison of pile deflection profiles for the fixed head condition e 118 Figure F 3 Comparison of pile rotation profiles for the fixed head condition eee 118 Figure F 4 Comparison of bending moment profiles for the fixed head condition 119 Figure F 5 Comparison of shear force profiles for the fixed head condition 1 0 0 0 eeeeeeeees 119 Figure F 6 Comparison of pile deflection profiles for the free head condition cee 120 Figure F 7 Comparison of pile rotation profiles for the free head condition 0 00 00 cesses 120 Figure F 8 Comparison of bending moment profiles for the free head condition 121 Figure F 9 Comparison of shear force profiles for the free head condition 0 0 0 ceeeeeeeeeeees 121 Figure F 10 Stress ratio contour fill
55. azzoni et al 2006 18 Figure 4 1 A a ai a aden Me ata see ease 19 Figure 422s Analysis Options A A A A ad 21 Figure 4 3 Rayleigh damping coefficients icc sccccyiscsucteansveevaovsdecensh iecengsuagecth ondvansesseancausbsaeveaseazes 22 Figure 4 4 OpenSees parameters rai 23 Figure 4 5 Multi yield surfaces in principal stress space and deviatoric plane Prevost 1985 Parra 1996 Yang 2000 A A E AA 24 Figure 4 6 Shear effective confinement and shear stress strain response Yang and Elgamal 2002 Yang etal 2003 Lt RA 25 Figure 4 7 Von Mises multi surface kinematic plasticity model Yang 2000 Yang et al 2003 ice a EE EE ESE O LN 26 Figure 4 8 Soil materials in OpenSeesPL lt 2s cese ccssscccadesccescessavesnseccseactteusuvtecuevestannceusdedcueatesecsens 27 Figure 4 9 Soil backbone curve and yield surfaces oooooonicnnncnnccnocnocnnoncnnncononononnnoncconnconc cn ncnn nono 30 Figure 4 10 Backbone curves for Medium Sand ccescesessceeseeseeeseceseceeeeeeeseeeeeeeeeeseenaeenaeens 31 Figure 4 11 U Sani lAs i etatai eie i iaaa aae Tasia 32 Figure 4 12 Initial yield domain at low levels of effective confinement Yang et al 2003 36 Figure 4 13 Schematic of constitutive model response showing a octahedral stress 7 effective confinement p response b octahedral stress 7 octahedral strain y response and c configuration of yield domain Yang et al 2003 ooooococccinccnocccoccnnoncconncconocono nono
56. ck element mesh is employed in this nonlinear analysis Figure C 1 Simulation Results Figure C 6 shows the load deflection curve for the nonlinear run along with the linear result for the 8 node brick element mesh the final lateral load is also extended to 94 5 kips as described in the previous sections for comparison It is seen from Figure C 6 that nearly linear behavior is exhibited in the nonlinear run for only low levels of applied lateral load less than 10 kips 90 80 70 60 50 Load kips 40 30 20 10 Linear Nonlinear 0 0 05 0 1 0 15 0 2 025 03 035 04 045 0 5 Pile head deflection in Figure C 6 Comparison of the load deflection curves for the linear and nonlinear runs 91 The pile deflection profiles for both linear and nonlinear cases are displayed in Figure 7 For comparison the linear and nonlinear responses at the lateral load of 31 5 kips 63 kips 2 x 31 5 and 94 5 kips 3 x 31 5 are shown Figure C 7 The bending moment profiles for the 3 load levels are shown in Figure C 8a c 0 T T T T 5 Lea ote Ge fe 8 ote Sig IO 10 a EE E etc cept ty Sil SN ace De GM Oa Se le At ete Darts oh Me a irate nS E et Oe ta 2a 15 Ea AAA Soe 6 a AS o A a A Bee N AEBS i E A 20 T 25F 30 Linear Nonlinear 35 fi 1 1 i 1 0 0 1 0 2 0 3 0 4 0 5 Pile deflection in a H 31 5 kips 0 5 10 215 sg 290 A 25 301 Linear
57. ction of the soil hysteretic elasto plastic shear response including permanent deformation In this material plasticity is exhibited only in the deviatoric stress strain response The volumetric stress strain response is linear elastic and is independent of the deviatoric response This constitutive model simulates monotonic or cyclic response of materials whose shear behavior is insensitive to the confinement change Plasticity is formulated based on the multi surface nested surfaces concept with an associative flow rule according to the well known Provost approach In the clay model the nonlinear shear stress strain back bone curve is represented by the hyperbolic relation Kondner 1963 defined by the two material constants low strain shear modulus and ultimate shear strength The material type for the cohesive soils in OpenSees is called PressureIndependMultiYield ME O 2 3 1 3 rece Po Deviatoric plane O Principal effective stress space Figure 4 5 Multi yield surfaces in principal stress space and deviatoric plane Prevost 1985 Parra 1996 Yang 2000 24 Figure 4 6 Shear effective confinement and shear stress strain response Yang and Elgamal 2002 Yang et al 2003 a Von Mises multi surface 25 b Hysteretic shear response Figure 4 7 Von Mises multi surface kinematic plasticity model Yang 2000 Yang et al 2003 4 2 2 Predefined Materials As shown in Figure 4 1 t
58. d The force based method is used if the Force Based Method radio button is chosen Longitudinal X Force The force applied in the longitudinal direction Transverse Y Force The force applied in the transverse direction Vertical Z Force The force applied in the vertical direction Moment of X The applied bending moment about the longitudinal direction Mx Moment of Y The applied bending moment about the longitudinal direction My Moment of Z The applied bending moment about the longitudinal direction M3 6 1 1 2 Displacement Based Method The displacement based method is used if the Displacement Based Method radio button is chosen Longitudinal Displacement The displacement applied in the longitudinal direction Transverse Displacement The displacement applied in the transverse direction 50 Vertical Displacement The displacement applied in the vertical direction Rotation around X The applied rotation around the longitudinal axis X Rotation around Y The applied rotation around the transverse axis Y Rotation around Z The applied rotation around the vertical axis Z Pushover Type Pattern Static Pushover Monotonic Pushover Loading Duration 20 sec C Dynamic Pushover Frequency fi Hz Loading Afterward Method AE Duration Mo sec Keep C Remove Force Based Method Amplitude Increasing Slope fo C Displacement Based Method C U Push Siei m Force Increment Per Step or Tim
59. d free head connection Finite Element Simulation In view of symmetry a half mesh 2 900 8 node brick elements 19 beam column elements and 180 rigid beam column elements in total is studied as shown in Figure G 1 Length of the mesh in the longitudinal direction is 520 ft with 260 ft transversally in this half mesh configuration resulting in a 520 ft x 520 soil domain in plan view Layer thickness is 60 ft the bottom of the soil domain is 25 ft below the pile tip so as to mimic the analytical half space solution The floating pile is modeled by beam column elements Mazzoni et al 2006 and rigid beam column elements are used to model the pile size diameter The following boundary conditions are enforced D The bottom of the domain is fixed in the longitudinal x transverse y and vertical z directions ID Left right and back planes of the mesh are fixed in x and y directions the lateral directions and free in z direction UD Plane of symmetry is fixed in y direction and free in z and x direction to model the full mesh 3D solution The axial load is applied at the pile head ground level in z vertical direction The above simulations were performed using OpenSeesPL Lu et al 2006 Simulation Results The pile vertical displacement and axial force profiles at the axial load of 243 kips are shown in Figure G 2 The final deformed mesh is shown in Figure G 3 Figure G 4 displays the stress ratio contour fill 1
60. dium silt permeability 8 Sat cohesionless medium sand permeability 9 Sat cohesionless medium gravel permeability 10 Sat cohesionless medium dense silt permeability 11 Sat cohesionless medium dense sand permeability 12 Sat cohesionless medium dense gravel permeability 13 Sat cohesionless dense silt permeability 14 Sat cohesionless dense sand permeability 15 Sat cohesionless dense gravel permeability 16 Cohesive soft 17 Cohesive medium 18 Cohesive stiff 19 U SandlA PressureDependMultivield 20 U Sand1B PressureDependMultivield 21 U Clay1 PressurelndependMultiVield 22 U Clay2 PressurelndependMultivield 23 U Sand2A PressureDependMultiYieldO2 24 U Sand2B PressureDependMultivield02 Figure 4 8 Soil materials in OpenSeesPL 27 Table 4 1 Predefined soil materials in OpenSeesPL Reference bulk icti pecan Permeability Mas a density 3 coeff m s ton m Reference shear modulus Cohesionless Soil G kPa at modulus B angle kPa at degrees a 1 p 80kPa p 80kPa Very loose silt permeability Very loose sand permeability Very loose gravel permeability Loose silt permeability Loose sand permeability Loose gravel permeability Medium silt permeability Medium sand permeability Medium gravel permeability Medium dense silt permeability Medium dense sand permeability Medium dense gravel permeability De
61. e g a f 2nd Layer fi 8 e E 0 8 3rd Layer fo fi Vv fi 4th Layer o fi Vv fi 5th Layer fo fi Vv fi 6th Layer o i Iv fi Outermost Zone fi fi z fi Note Definitions following a O length section will be ignored e g if you do not need the 3rd layer and beyond enter 0 for the length of the 3rd layer a b Figure A 4 Mesh refinement example 3 a Change meshing controlling parameters in the horizontal direction b the resulting mesh Appendix B Own Weight Application with Dry and Saturated Soil Cases Boundary Conditions The boundary conditions available in OpenSeesPL include Shear Beam Rigid Box and Periodic Boundary 1 Shear Beam In this case the front and back nodes at any depth move together horizontal and vertical directions The Shear Beam boundary condition if it s chosen is enforced for all runs Rollers are used for lateral and base boundaries for all gravity runs The base nodes are fixed after the first run If Fixed Vert is checked all nodes at lateral boundaries will be fixed in vertical direction before the dynamic run 2 Rigid Box In gravity runs lateral boundaries are fixed in both horizontal directions and free in vertical direction Rollers are used for base nodes which will be fixed after the first run If Fixed Vert is checked all nodes at lateral boundaries will be fixed in vertical direction before the dynamic run 3 Periodic Boundary In this case each node on the front bounda
62. e 1 test testTypeStatic TolStatic maxNumlterStatic 0 algorithm algorithmTypeStatic if Sok 0 puts Trying Broyden algorithm Broyden 8 set ok analyze 1 143 algorithm algorithmTypeStatic if Sok 0 puts Trying NewtonWithLineSearch algorithm NewtonLineSearch 0 8 set ok analyze 1 algorithm algorithmTypeStatic if ok 0 stop if still fails to converge puts format fmtl PROBLEM IDctrINode IDctrIDOF nodeDisp SIDctrINode IDctrIDOF LunitTXT return 1 end if end for integrator DisplacementControl IDctrINode IDctrIDOF Dincr bring back to original increment end if 3 end while loop bh endifok 0 a Neel ha E E he eet ee ee eee Ps ee ee global LunitTXT load time unit text if info exists LunitTXT 1 set LunitTXT Length set blank if it has not been defined previously set fmtl s Pushover analysis CtrINode 31 dof 1i Curv 4f s format for screen file output of DONE PROBLEM analysis if Sok 0 puts format fmtl PROBLEM IDctrlNode IDctrIDOF nodeDisp IDctrINode SIDctrIDOF LunitT XT else puts format fmtl DONE IDctrINode IDctrIDOF nodeDisp IDctrINode SIDctrIDOF LunitT XT 144 References M Alizadeh and M T Davisson 1970 Lateral Load Tests on Piles Arkansas River Project JSMFD ASCE Vol 96 SM5 September pp 31 40 J E Bowles 1988 Foundation Analysis and D
63. e Step Displacement Increment Per Step or Time Step Logitudinal lt Force Roo kN Longitudinal Displacement pao m Transverse Y Force fo kN Transverse Displacement Eoo m Vertical 2 Force fo kN Vertical Displacement fo m Moment of x Rotation around x ft rad Moment of Y Rotation around Y po fred Moment of Z Rotation around Z pp rad Surface Load Applied at Pile Zone Ground Surface Level Per Step Logitudinal lt fo Transverse Y fo Vertical Z fo kPa Total Analysis Time Steps Static Pushover Number of Steps 20 Dynamic Pushover Computation Time 20 sec Time Step fo sec Applied Location d C ShearBeam Starting from Surface o m Cancel Shear Beam by Profile Ratios z hange Profile Applied Range Height Figure 6 1 Pushover analysis 51 6 1 2 Load Pattern To conduct a pushover analysis a load pattern must be defined The load pattern is shown in Figure 6 2 Pattern C Monotonic Pushower Loading Duration sec Frequency 1 Hx3 poeding Afterward Sine Wave Dtos Cy sec Keep r Amplitude Increasing Slope 0 Remove C U Push Figure 6 2 Pushover load pattern 6 1 2 1 Monotonic Pushover If Static Pushover is chosen the pushover options include monotonic pushover as well as pushover by a user defined loading pattern U Push Please see Section 6 1 2 3 for how to define a U Push In a monotonic pushover the pushover
64. e ali ccacessec ancsusep sca scccacgeaatacasieg etenetes dasmateonseieeacaees 60 Figure 7 1 Newmark Time Integration A NA 61 Figure 7 2 Definition of 3D base excitation and boundary conditions oooooconoccnocanoccnoccnncnononnnonos 63 Figure 7 3 User defined input motion U Shake ooooocinncciocococccocccooncconncconocon cono nono noconccnnnconnnoo 64 Figure 7 4 Response time histories window a Acicisc digs aisaetieesad eta nes 66 Figure 8 1 Pile group definition a te 67 Figure 8 2 Pile group horizontal meshing nd taba oa a o ibas 68 Figure 8 3 Sample mesh of a 3 by 3 pile group model half mesh configuration 0 0 0 0 69 Figure 8 4 Pile response profiles for a pile group MOdel cece eeceeeeceseceeeeneeeseeeeeeeeeeseenseeaeeess 70 Figure 8 5 Pile response time histories for a pile group model oooononccnnccnoccnococonancnnncconocannconnoos 70 Figure 8 6 Pile response relationships for a pile group model oooooonccninccnoccniccconcnconncconaconcnonnnon 71 Figure 8 7 Pile response relationships at the pile cap for a pile group model eee 71 Figure 8 8 Deformed mesh of a pile group model 00 cece ceeceesceesceceseceteeeeeeeeseecsaecnteeseeeenseees 12 Figure A 1 Finite element mesh created with default Values ooooonconicnnonncnncncnocnnoncnrncononononnos 73 Figure A 2 Mesh refinement example 1 a Change Num of Slices to 32 b the resulting mesh A a A A vlads beatae 74 Figure A 3 Mesh refin
65. e on the front boundary moves the same as the analogous node on the back boundary and the vertical is free but can be fixed by the user 82 Appendix C Benchmark Linear Finite Element Analysis of Laterally Loaded Single Pile Using OpenSees 8 Comparison with Analytical Solution Introduction In this study I The response of a laterally loaded pile obtained using the OpenSeesPL interface is compared with the analytical elastic solution proposed by Abedzadeh and Pak 2004 Detailed information about the analytical elastic solution is provided in Appendix C I please see this end of Appendix C ID Based on the linear analysis presented below nonlinear soil response is addressed in Appendix C II please see this end of Appendix C Laterally Loaded Pile Pile Data The pile employed in the OpenSees simulation is circular with a diameter of 16 radius a 8 while the one for the analytical elastic solution is a cylindrical pipe pile of the same radius and a wall thickness h 0 1a Both cases have the same pile length 33 3 ft Va 50 The cross sectional moment of inertia of the pipe pile J xa h 1286 8 in which will be used for the circular pile in the OpenSees simulation In summary the geometric and elastic material properties of the pile are listed below Radius a 8 Pile length 33 3 ft Young s Modulus of Pile E 29000 ksi Moment of Inertia of Pile 1286 8 inf Soil Domain The pile is assumed t
66. ear Nonlinear 30 l i i 0 0 2 0 4 0 6 0 8 Pile deflection in e H 31 5 kips Figure D 3 Comparison of the pile deflection profiles for the linear and nonlinear runs 100 10 ha Nn Depth ft N N N T Linear Nonlinear UY 0 0 2 0 4 0 6 0 8 Pile deflection in f H 43 kips Figure D 3 continued 3 D 20H O E T E E TEE E E 020 AET EET A 25 AE EAN o e A ay Ay tA Ea SNR OS ea Linear 30t Nonlinear Experimental 35 i 1 1 0 50 100 150 Bending moment kip ft a H 21 kips Figure D 4 Comparison of the pile bending moment profiles for the linear and nonlinear runs 101 5F Si 7 10 2 151 S o 20 Decl eo A a ee EA a s a Belgas A A rd Neal Linear 30 AN gite IE A las att ys las DaN g hy A o Nonlinear la oed Experimental 35 0 50 100 150 Bending moment kip ft b H 31 5 kips 0 5 b 10F 15 3 D A EA E ETE ESENES EAEE ELETE ok bee bee he A I 25 pastes ie of Me ae eae es re RE en ats Bek it oe fe Dh ns ns Ae oe ain kieran au wages Sed 30 ee EN VEENI EET dee Bet arene Ss or amp S98 bowed eere Za Nonlinear a Experimental 35 l 0 50 100 150 Bending moment kip ft c H 43 kips Figure D 4 continued 102 a First step b H 21 kips c H 31 5 kips d H 43 kips Figure D 5 Stress ratio contour fill of the nonlinear run at differen
67. ection The number of subdivisions fibers in the radial direction of the pile circular cross section numSubdivRad in Figure 3 11 Internal Radius The internal radius of the patch intRad in Figure 3 11 External Radius The external radius of the patch extRad in Figure 3 11 The values of yCenter and zCenter y amp z coordinates of the center of the circle as shown in Figure 3 11 are zeros And the startAng starting angle and endAng ending angle are set to 0 and 360 degrees respectively in OpenSeesPL since only a full mesh is available for fiber section nonlinear beam element 11 Layer is defined by the following parameters Figure 3 12 Number of Reinforcing Bars along Layer The number of reinforcing bars along layer numBars in Figure 3 12 Area of Individual Reinforcing Bar The area of individual reinforcing bar Radius of Reinforcing Layer The radius of reinforcing layer radius in Figure 3 12 The values of yCenter and zCenter y amp z coordinates of the center of the circle as shown in Figure 3 12 are zeros And the startAng starting angle and endAng ending angle are set to 0 and 360 degrees respectively in OpenSeesPL since only a full mesh is available for fiber section nonlinear beam element Fiber Section Material Concrete Compressive Strength Concrete0j Concrete Strain at Maximum Strength Concrete Crushing Strength Concrete Strain at Crushing Strength Yield Strength 460000 Steel0
68. ects and liquefaction induced lateral loading Slopes and pile systems embedded in sloping ground are also currently being simulated 1 1 Overview OpenSeesPL is a FE user interface for 3D lateral pile ground interaction response This interface allows conducting pushover pile analyses as well as seismic earthquake simulations The FE analysis engine for this interface is the Pacific Earthquake Engineering Research PEER Center OpenSees Framework developed under the leadership of Professor Gregory Fenves of UC Berkeley For more information please visit http opensees berkeley edu OpenSeesPL allows simulations for any size of pile and pile diameter The pile cross section can be circular or square Linear and nonlinear material properties options are available for pile definition OpenSeesPL allows for definition of multiple soil strata Nonlinearity of soil materials is simulated by incremental plasticity models to allow for modeling permanent deformation and for generation of hysteretic damping In addition OpenSeesPL allows including user defined soil materials OpenSeesPL allows for convenient pre processing and graphical visualization of the analysis results including the deformed mesh ground response time histories and pile responses OpenSeesPL makes it possible for geotechnical and structural engineers researchers to quickly build a model run FE analysis and evaluate the performance of the pile ground system OpenSeesPL w
69. ement example 2 a Change Number of Mesh Layers in the vertical direction a A a an eh ote Rta gh Pare os a uae os 75 Figure A 4 Mesh refinement example 3 a Change meshing controlling parameters in the horizontal direction b the resulting mesh ooonccnincnnoccnonacinccconoconcnonnnconncconocnnn cono cconncconocons 76 Figure C 1 Finite element mesh employed in this Study cccecccesseceseceeeeeeeceeeeeeeeeteeeeeeenseees 85 Figure C 2 Comparison of pile deflection profiles v 25 A 50 ceecceseeteeseeeseeeeeeteenseeeeees 86 Figure C 3 Comparison of pile bending moment profiles v 25 l a 50 0 eeeeseeeeeeseeeteeneeees 87 Figure C 4 Sample pile deflection h a 1 l a 50 under an applied pure pile head horizontal load Abedzadeh and Pak 200 ad ds 89 Figure C 5 Sample pile bending moment h a 1 l a 50 under an applied pure pile head horizontal load Abedzadeh and Pak 2004 ooooooocccnoccconococcoooccoonnncconononononoconononononccnnncnnnnnos 90 Figure C 6 Comparison of the load deflection curves for the linear and nonlinear runs 91 Figure C 7 Comparison of the pile deflection profiles for the linear and nonlinear runs 92 Figure C 8 Comparison of the pile bending moment profiles for the linear and nonlinear runs 93 Figure C 9 Stress ratio contour fill of the nonlinear run at different load levels red color shows yielded SOL ld ii o Ad cada 95 Figure D 1 Finite element mesh em
70. er fc1U eps1U fc2U eps2U Slambda ftU Ets build cover concrete unconfined uniaxialMaterial Steel02 IDreinf F y Es Bs RO cR1 cR2 build reinforcement material section GEOMETRY set DSec expr 5 ft Column Diameter set coverSec expr 5 in Column cover to reinforcing steel NA set numBarsSec 16 number of uniformly distributed longitudinal reinforcement bars set barAreaSec expr 2 25 in2 area of longitudinal reinforcement bars set SecTag 1 set tag for symmetric section Generate a circular reinforced concrete section 140 with one layer of steel evenly distributed around the perimeter and a confined core confined core by Michael H Scott 2003 it it Notes The center of the reinforcing bars are placed at the inner radius The core concrete ends at the inner radius same as reinforcing bars The reinforcing bars are all the same size The center of the section is at 0 0 in the local axis system Zero degrees is along section y axis Sh He He Hk EOE set ri 0 0 inner radius of the section only for hollow sections set ro expr DSec 2 overall outer radius of the section set nfCoreR 8 number of radial divisions in the core number of rings set nfCoreT 8 number of theta divisions in the core number of wedges set nfCoverR 4 number of radial divisions in the cover set nfCoverT 8 number of th
71. eral load 128 kips left plan view right side view c lateral load 256 kips left plan view right side view Figure F 10 Stress ratio contour fill of the nonlinear run for the fixed head condition red color shows yielded soil elements 122 a lateral load 64 kips left plan view right side view 38660001 b lateral load 128 kips left plan view right side view X c lateral load 256 kips left plan view right side view Figure F 11 Stress ratio contour fill of the nonlinear run for the free head condition red color shows yielded soil elements 123 Appendix F I OpenSees Simulation Results On Si 10 6 157 E 2 Q 20 byl 1 OpenSees Linear Soil 64 kips 25 1 OpenSees Linear Soil 128 kips 7 i OpenSees Linear Soil 256 kips A racecars ests OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips 35 i i 0 0 05 0 1 0 15 0 2 0 25 Pile deflection in Figure F 12 Comparison of pile deflection profiles for the fixed head condition 0 5 AAA cet te SP AN Ay Be EN es Jes ot lorie tat Te aN A Y SoA as Seat a th vel al ta E 10F 7 amp 151 7 sS p A 20 AA A a eee Ge TE aes ete ee 25 OpenSees Linear Soil 128 kips i 7 OpenSees Linear Soil 256 kips 30 L T OpenSees Nonlinear Soil 64 kips 1 Vol OpenSees Nonlinear So
72. esign 4 Edition McGraw Hill Book Co New York NY 10020 Farzad Abedzadeh and Y S Pak 2004 Continuum Mechanics of Lateral Soil Pile Interaction Journal of Engineering Mechanics Vol 130 No 11 November pp 1309 1318 Iwan W D 1967 On a class of models for the yielding behavior of continuous and composite systems J Appl Mech ASME 34 612 617 Kondner R L 1963 Hyperbolic stress strain response Cohesive soils Journal of the Soil Mechanics and Foundations Division 89 SM1 115 143 Mazzoni S McKenna F and Fenves G L 2006 Open system for earthquake engineering simulation user manual Pacific Earthquake Engineering Research Center University of California Berkeley http opensees berkeley edu OpenSees manuals usermanual Mroz Z 1967 On the description of anisotropic work hardening Journal of Mechanics and Physics of Solids 15 163 175 Parra E 1996 Numerical modeling of liquefaction and lateral ground deformation including cyclic mobility and dilation response in soil systems PhD Thesis Department of Civil Engineering Rensselaer Polytechnic Institute Troy NY Prevost J H 1985 A simple plasticity theory for frictional cohesionless soils Soil Dynamics and Earthquake Engineering 4 1 9 17 Yang Z 2000 Numerical modeling of earthquake site response including dilation and liquefaction PhD Thesis Department of Civil Engineering and Engineering Mec
73. essing keys of LEFT ARROW RIGHT ARROW UP ARROW or DOWN ARROW respectively The view can be zoomed in by pressing key F9 out by pressing key F10 or frame by pressing key F11 PE Deformed Mesh DER 2D X 15 1743 m Disp contour fill 2D Y 19 5 m isp 2D Y 15 1743 m Unitm 2D Y 0 m 2 000e 001 2D Z 0 m 1 898e 001 Z 0 503883 m 1 796e 001 2 1 06375 m 1 694e 001 Pore pressure PP contour Excess PP EPP contour EPP ratio contour Longitudinal stress contour Transverse stress contour Vertical stress contour Shear stress xy contour Shear stress yz contour Shear stress 2x contour Stress ratio contour 8 775e 002 Eff confinement contour 7 754e 002 Longitudinal strain contour 6 734e 002 Transverse strain contour 5 713e 002 Vertical strain contour 4 693e 002 Shear strain xy contour 3 672e 002 Shear strain yz contour 2 652e 002 Shear strain 2x contour 1 631 e 002 Rigid link axial force 6 109e 003 Link hori shear force 4 096e 003 Link vert shear force 2 1 68583 m 1 592e 001 2 2 37703 m 1 490e 001 Z 3 14503 m 1 388e 001 2 3 99836 m 1 286e 001 1 184e 001 1 082e 001 9 795e 002 OSOUODODODODODO Scale Factor 77 Animation Playing Delay millisecond 10 Show Whole model v Figure 6 9 Deformed mesh and contour fill 58 AA Due to pushover disp contour 2D Y 0 m y Play Animation Y Endless Zoom In Out Frame paci Laue Sa ata BIB lt gt Up Down Show Legend
74. eta divisions in the cover Define the fiber section section fiberSec SecTag set rc expr ro coverSec Core radius patch circ 1DconcCore nfCoreT nfCoreR 0 0 ri rc 0 360 Define the core patch patch circ IDconcCover nfCoverT nfCoverR 0 0 rc ro 0 360 Define the cover patch set theta expr 360 0 numBarsSec Determine angle increment between bars layer circ IDreinf numBarsSec barAreaSec 0 0 rc theta 360 Define the reinforcing layer assign torsional Stiffness for 3D Model set SecTagTorsion 99 ID tag for torsional section behavior set SecTag3D 3 ID tag for combined behavior for 3D model uniaxialMaterial Elastic SecTagTorsion Ubig define elastic torsional stiffness section Aggregator SecTag3D SecTagTorsion T section SecTag combine section properties source ex9 tcl Source code of file ex9 tcl Ge Nae A A A A Moment Curvature analysis of section Silvia Mazzoni amp Frank McKenna 2006 define procedure source MomentCurvature3D tcl O A ee set P expr 1800 kip Tension Compression set maximum Curvature set Ku expr 0 01 in set numIncr 100 Number of analysis increments to maximum curvature default 100 Call the section analysis procedure MomentCurvature3D SecTag3D P Ku numIncr 141 Source code of file MomentCurvature3D tcl proc MomentCurvature3D secTag axialLoad maxK numIncr 100 PARAHA ARAARA TET TEETER TET EET TTT TET A
75. fuge Tests 1996 E Parra K Adalier A W Elgamal M Zeghal and A Ragheb Eleventh World Conference on Earthquake Engineering Acapulco Mexico June 23 28 Numerical Modeling of Liquefaction and Lateral Ground Deformation Including Cyclic Mobility and Dilation Response in Soil Systems 1996 Ender Parra PhD Thesis Dept of Civil Engineering Rensselaer Polytechnic Institute Troy NY Identification and Modeling of Earthquake Ground Response II Site Liquefaction 1996 M Zeghal A W Elgamal and E Parra Soil Dynamics and Earthquake Engineering Vol 15 523 547 Elsevier Science Ltd Soil Dilation and Shear Deformations During Liquefaction 1998a A W Elgamal R Dobry E Parra and Z Yang Proc 4th Intl Conf on Case Histories in Geotechnical Engineering S Prakash Ed St Louis MO March 8 15 pp1238 1259 Liquefaction Constitutive Model 1998b A W Elgamal E Parra Z Yang R Dobry and M Zeghal Proc Intl Workshop on The Physics and Mechanics of Soil Liquefaction Lade P Ed Sept 10 11 Baltimore MD Balkema Modeling of Liquefaction Induced Shear Deformations 1999 A Elgamal Z Yang E Parra and R Dobry Second International Conference on Earthquake Geotechnical Engineering Lisbon Portugal 21 25 June Balkema Numerical Modeling of Earthquake Site Response Including Dilation and Liquefaction 2000 Zhaohui Yang PhD Thesis Dept of Civil Engineering and Enginee
76. g parameters Am and Ax are obtained by solving the follow equations simultaneously A _ A az baggy tah A E AT f 2 Direct Specification of Am and Ay The user can also directly define Rayleigh damping coefficients Am and Ax Figure 4 3 21 Damping Coefficients Current Damping Coefficients Mass Proportional Coeff 2 1842e 001 Stiffness Proportional Coeff 9 0946e 004 The above coefficients can be changed by using either of the following two methods By Defining Damping Ratios C By Defining Rayleigh Damping Coeff Frequency 0 1 10 Hz Damping Ratio 0 2 20 Rayleigh Damping Coefficients fi 2 Mass Proportional Coeff 2 15428 001 2 le 2 Stiffness Proportional Coeff 8 09468 004 Re calculate amp View Damping Curve Update amp Close Window Do Not Update amp Close Window E Damping Curve Figure 4 3 Rayleigh damping coefficients 22 OpenSees Parameters Parameters for Dry Soil Analysis 1st Run Tolerance tol for OpenSees command 0 0001 Max number of iterations fipo test NormDispincr maxNumlter Number of steps for OpenSees 1 Time step dt 50000 command analyze Run for Horizontal Gravity Application Activated if Model Inclination Degree is not zero Number of steps for linearly 5 Time step dt 50000 increasing loading part Number of steps for constant loading part afterwards 2nd Run Number of steps for OpenSees Time ste
77. hanics Columbia University New York NY Yang Z and Elgamal A 2002 Influence of permeability on liquefaction induced shear deformation Journal of Engineering Mechanics 128 7 720 729 Yang Z Elgamal A and Parra E 2003 A computational model for cyclic mobility and associated shear deformation Journal of Geotechnical and Geoenvironmental Engineering 129 12 1119 1127 145 OpenSeesPL Related References Numerical Analysis of Seismically Induced Deformations In Saturated Granular Soil Strata 1994 Ahmed M Ragheb PhD Thesis Dept of Civil Engineering Rensselaer Polytechnic Institute Troy NY Identification and Modeling of Earthquake Ground Response 1995 A W Elgamal M Zeghal and E Parra First International Conference on Earthquake Geotechnical Engineering IS TOKYO 95 Vol 3 1369 1406 Ishihara K Ed Balkema Tokyo Japan Nov 14 16 Invited Theme Lecture Prediction of Seismically Induced Lateral Deformation During Soil Liquefaction 1995 T Abdoun and A W Elgamal Eleventh African Regional Conference on Soil Mechanics and Foundation Engineering International Society for Soil Mechanics and Foundation Engineering Cairo Egypt Dec 11 15 Liquefaction of Reclaimed Island in Kobe Japan 1996 A W Elgamal M Zeghal and E Parra Journal of Geotechnical Engineering ASCE Vol 122 No 1 39 49 January Analyses and Modeling of Site Liquefaction Using Centri
78. he soil materials can be selected from an available menu of cohesionless and cohesive soil materials Figure 4 8 There are 18 predefined materials using the PressureDependMultiYield soil model Basic model parameter values for these materials are listed in Table 4 1 If Cohesionless very loose is chosen the user is allowed to define the residual shear strength 0 2 kPa is specified by default The cohesionless very loose soil is same as the cohesionless loose soil except the user is allowed to specify the residual shear strength for the very loose one In addition user defined cohesionless and cohesive soil materials U Sand1A U Sand1B U Clay1 U Clay2 U Sand2A and U Sand2B are also available to choose U Sand1A and U Sand1B use PressureDependMultiYield model while U Sand2A and U Sand2B use PressureDependMultiYield02 model As shown in Figure 4 1 parabolic variation of soil modulus with depth is used if P is selected Linear variation of soil modulus with depth is used if L is selected And the constant soil modulus with depth is used if C is selected 26 lr Sat cohesionless very loose silt permeability 1 Sat cohesionless very loose silt permeability 2 Sat cohesionless very loose sand permeability 3 Sat cohesionless very loose gravel permeability 4 Sat cohesionless loose silt permeability 5 Sat cohesionless loose sand permeability 6 Sat cohesionless loose gravel permeability 7 Sat cohesionless me
79. ial lateral vertical stress ratio also known as coefficient of lateral earth pressure at rest Ko Ko is related to Poisson s ratio by the following relation Ky v 1 v The suggested range for Ko is between 0 1 and 0 9 Cohesion The suggested range is between 0 and 5000000 kPa See Section 4 2 3 1 for more information Friction Angle The suggested range is between 5 and 65 degrees See Section 4 2 3 1 for more information Peak Shear Strain The suggested range is between 0 001 and 20 See Section 4 2 3 1 for more information Number of Yield Surfaces NYS The suggested range is between 0 and 30 In particular NYS 0 dictates an elastic shear response Cohesion Friction Angle and Peak Shear Strain are ignored see Figure 4 9 NYS 1 indicates an elastic perfectly plastic shear response Peak Shear Strain is ignored see Figure 4 9 Advanced Options Use KO for Elastic Own Weight If checked users can specify the initial lateral vertical confinement ratio KO which will be used for the application of own weight at the elastic stage first run Young s Modulus for Elastic Own Weight The elastic modulus used for the application of own weight at the elastic stage 4 2 3 3 User Defined Clay1 U Clay1 Non liquefiable clay with shear response properties independent of confinement variation can be defined as shown in Figure 4 7 and Figure 4 15 Cohesion The apparent cohesion at zero effective confinement The nonlinear shear
80. ield domain radius 34 Tp Y 3 12 1 Yah cos l defines the effective confining pressure e g 10 kPa below which the mechanism is in effect Lis actually p in Figure 4 12 Smaller values should be assigned to denser sands defines the maximum amount of perfectly plastic shear strain developed at zero effective confinement during each loading phase 1 is actually y in Figure 4 12 Smaller values should be assigned to denser sands Maximum extent of biased loading yield domain y is actually y in Figure 4 12 Vw LY 4 13 L defines the maximum amount of biased perfectly plastic shear strain y accumulated at each loading phase under biased shear loading conditions as y 1 x l y is actually y and is R in Figure 4 13 Typically Z takes a value between 0 0 and 3 0 Smaller values should be assigned to denser sands Table 4 2 Suggested values for contraction and dilation parameters Loose Sand Medium Sand Medium dense Sand Dense Sand 15 35 35 65 65 85 85 100 cl 35 Figure 4 12 Initial yield domain at low levels of effective confinement Yang et al 2003 a b Ys Ya ly SRY Translated ne Enlarged Figure 4 13 Schematic of constitutive model response showing a octahedral stress 7 effective confinement p response b octahedral stress 7 octahedral strain y response and c configuration of yield domain Ya
81. igure F 6 Comparison of pile deflection profiles for the free head condition 0 l A NGE edene nie eniai Node s3 eS 7 te eae 10F 7 amp 151 7 sS p A 20 loo oro pb Peking e o ty ee A eee OpenSees Nonlinear Soil 64 kips 25 OpenSees Nonlinear Soil 128 kips 7 OpenSees Nonlinear Soil 256 kips Aia LPILE 64 kips uss A A LPILE 128 kips LPILE 256 kips 35 i i i i 10 8 6 4 2 0 2 Rotation in 107 Figure F 7 Comparison of pile rotation profiles for the free head condition 120 10 3 151 J 3 2 A 20 E o DENS 25 L A ME NTE hat Open Nonlinear Soil 6 kips vl OpenSees Nonlinear Soil 128 kips pl OpenSees Nonlinear Soil 256 kips 30 Y LPILE 64 kips J LPILE 128 kips LPILE 256 kips 35 0 500 1000 1500 2000 2500 3000 Bending moment kip ft Figure F 8 Comparison of bending moment profiles for the free head condition Nn Depth ft N N Nn T OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 Bi LPILE 64 kips LPILE 128 kips LPILE 256 kips 200 100 0 100 200 300 400 Shear force kips 30 F Figure F 9 Comparison of shear force profiles for the free head condition 121 oT Ted 3 901e 001 a lateral load 64 kips left plan view right side view oT Te 3 901 e 001 b lat
82. il 128 kips OpenSees Nonlinear Soil 256 kips r 35 i i i i i i i 14 12 10 8 6 4 2 0 2 Rotation rad 107 Figure F 13 Comparison of pile rotation profiles for the fixed head condition 124 5 A A A ARA 10t 2151 3 D A 20 A A A A a Rh E rd tb fo TE OpenSees Linear Soil 64 kips 25 OpenSees Linear Soil 128 kips OpenSees Linear Soil 256 kips 30 7 OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips 35 2000 1500 1000 500 0 500 Bending moment kip ft Figure F 14 Comparison of bending moment profiles for the fixed head condition 0 Nn N T Depth ft oa DETRE TE a AI i OpenSees Linear Soil 64 kips Eo OpenSees Linear Soil 128 kips OpenSees Linear Soil 256 kips 30 A 1 OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips N Nn T 50 0 50 100 150 200 250 300 Shear force kips Figure F 15 Comparison of shear force profiles for the fixed head condition 125 Depth ft OpenSees Linear Soil 64 kips OpenSees Linear Soil 128 kips 7 OpenSees Linear Soil 256 kips A ee 7 OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips N Nn T 35 i 0 1 0 0 1 0 2 0 3
83. ime Integration DO Up UND O 00 46 46 46 47 50 50 52 53 54 59 61 61 7 1 2 Input Motion 62 7 1 3 Model Inclination 64 7 2 TIME HISTORY OUTPUT 65 7 2 1 Soil Response Time Histories 65 8 PILE GROUP 67 8 1 PILE GROUP PARAMETERS 67 8 2 PILE GROUP MESHING 67 8 3 OUTPUT FOR A PILE GROUP MODEL 69 APPENDIX A HOW TO DEFINE THE SOIL FINITE ELEMENT MESH 73 APPENDIXB OWN WEIGHT APPLICATION WITH DRY AND SATURATED SOIL CASES 77 APPENDIX C BENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES amp COMPARISON WITH ANALYTICAL SOLUTION 83 APPENDIX D FINITE ELEMENT ANALYSIS OF ARKANSAS TEST SERIES PILE 2 USING OPENSEES WITH LPILE COMPARISON 96 APPENDIX E FINITE ELEMENT ANALYSIS OF STANDARD CALTRANS 16 CIDH PILE USING OPENSEES FOR GENERAL COMPARISON WITH LPILE WITH DEFAULT P Y MULTIPLIER 1 0 107 APPENDIX F FINITE ELEMENT ANALYSIS OF CALTRANS 42 CIDH PILE USING OPENSEES FOR GENERAL COMPARISON WITH LPILE WITH DEFAULT P Y MULTIPLIER 1 0 115 APPENDIX G FINITE ELEMENT ANALYSIS OF STANDARD CALTRANS 16 CIDH PILE SUBJECTED TO AXIAL LOAD 128 APPENDIX H MOMENT CURVATURE ANALYSIS OF CIRCULAR NONLINEAR RC BEAM FIBER SECTION 133 REFERENCES 145 OPENSEESPL RELATED REFERENCES 146 ili Table of Figures Figure 2 1 OpenSeesPL main MI A a en oia 4 Figure 2 2 OpenSeesPL s menu bar and submenu bars a menu bar b menu File c menu Execute d menu Display and e menu HelD
84. including material properties Meshing parameters are also defined e Analysis Types Controls analysis options pushover analysis Eigenvalue analysis or base shaking simulation e Boundary Conditions Controls boundary conditions e Model Inclination Controls the inclination angles for the ground surface and the whole model 2 2 3 Finite Element Mesh Window The finite element mesh window Figure 2 1 displays the mesh generated Once the mesh window is focused the mesh can be rotated by dragging the mouse moved in 4 directions by pressing keys of LEFT ARROW RIGHT ARROW UP ARROW or DOWN ARROW respectively The view can be zoomed in by pressing key F9 out by pressing key F10 or frame by pressing key F11 To display a 2D view press key F2 for Plane XY where X is the longitudinal directon Y the transverse direction F3 for Plane YZ where Z is the vertical direction or F4 for Plane XZ An isometric view of the mesh can be achieved by pressing key F5 Alternatively users can press the corresponding button shown in Figure 2 4 Finite Element Mesh Re Generate P Pile Only Zoomin Figure 2 4 Buttons available in the Finite Element Mesh window 3 Pile Model To define pile geometry click Pile Parameters in the Model Input window The pile geometry is defined by the following parameters Figure 3 1 Pile Pile Head l Pile Group Pile Type Circular Fixed C Free Pin
85. is The dynamic solver is used similar to item 1 above with a convergence tolerance of 0 0001 displacement norm that the user can modify in the OpeSees Parameters section from Analysis Options Boundary conditions for this case are Default is fixed boundaries everywhere but the user can change that to Shear Beam or Periodic Boundary Dynamic push over analysis In this case a dynamic solver is used modified Newton Raphson with the time integration parameters y 0 6 and B 0 3025 and the actual user specified time step Note that the user can also modify the Rayleigh mass and stiffness proportional viscous damping parameters which are set by default to 2 at the frequencies of 1 Hz and 6 Hz After the dynamic load has been applied analysis can proceed for a user specified number of seconds so that the free vibration response can be assessed if so desired Boundary conditions for this case are Default is fixed boundaries everywhere but the user can change that to Shear Beam or Periodic Boundary Dynamic Base earthquake excitation In this case a dynamic solver is used modified Newton Raphson with the time integration parameters y 0 6 and B 0 3025 and the actual user specified time step The convergence tolerance of 0 0001 is the default but the user can modify this value displacement norm in the OpeSees Parameters section from Analysis Options Note that the user can also modify the Rayleigh mass a
86. is library includes near fault soil surface motions as well as long duration rock outcrop motions recorded during past strong earthquakes worldwide ii U Shake a user defined input motion Figure 7 3 The input motion file to be defined should consist of two columns Time seconds and Acceleration g delimited by SPACE S Below is an example of a user defined input motion file 0 00 0 000 0 02 0 005 19 98 0 004 20 00 0 000 Note that the user defined input motion file must be placed in the subfolder motions This subfolder also contains all provided built in input motion files The amplitude of the input motion can be scaled by a factor ranging from 0 01 to 1 0 In addition if 0 2g sinusoidal motion is chosen the user must specify excitation frequency and number of cycles Figure 2 1 Scale Factor The amplitude of the input motion is multiplied by the Scale Factor The Scale Factor may be positive or negative Frequency The Frequency in Hz has to be specified if harmonic sinusoidal motion is chosen Number of Cycles The Number of Cycles has to be specified if sinusoidal motion is chosen 62 Base Shaking ie mon x en 0 2g sinusoidal motion f Y Tapered 0 2g sinusoidal motion Z Tapered 0 2g sinusoidal motion Frequency 0 5 5Hz p poau Poo Number of Cycles 3 30 fi 0 fio fi 0 Scale Factor 0 01 1 fi fi fi Boundary Conditions B C Type Rigid Box v
87. ite element simulation of a CalTrans 42 CIDH pile using the 3D OpenSeesPL interface The simulated pile responses are compared with LPILE results Laterally Loaded Pile Pile Data The geometric and elastic material properties of the pipe pile are listed below Diameter D 42 or radius a 21 Wall thickness h 0 75 Pile length 35 ft Moment of Inertia of Pile 7 na h 21 821 in Young s Modulus of Pile E 29 000 ksi In this initial study the pile was modeled to remain linear also in view of the applied load levels Soil Domain Linear and nonlinear soil responses are investigated The Medium relative density granular soil type Lu et al 2006 is selected in the analyses The material properties of the soil are listed below At the reference confinement of 80 kPa or 11 6 psi the Shear Modulus of Soil G 10 88 ksi and the Bulk Modulus of Soil B 29 ksi 1 e Poisson s ratio vs 0 33 see Lu et al 2006 Unit Weight y 110 pcf For nonlinear analysis the Friction Angle y 33 and the peak shear stress occurs at a shear strain Ymax 10 at the 11 6 psi confinement The parameter ymax along with the shear modulus define the nonlinear soil stress strain curve Other values of Ymax Should be explored in the future 115 Lateral Load A total of six load cases Table 1 are studied The loads are applied at the pile head Table F 1 Load cases for the study Pile head condition
88. ld specify water table depth to be equal to the entire model depth 4 1 1 Analysis Options First some important master control options are defined by clicking Analysis Options as shown in Figure 2 1 This will display the interface shown in Figure 4 2 Here you can 1 Select to keep the soil properties as defined by their linear properties or opt to conduct nonlinear soil computations note that the default is Linear 2 Select among a number of available Brick elements in OpenSees 3 Apply own weight of the soil using a global lateral stress coefficient and a single value of Young s modulus that is user defined this will reduce initial shear stresses in the mesh due to own weight application but generally will have minimal impact on the subsequent earthquake computations anyway 4 Apply own weight of the soil using a global permeability horizontal amp vertical e g one can specify a large permeability value for the application of own weight in a saturated soil analysis 5 by clicking Rayleigh Damping Figure 4 3 you can change the viscous damping characteristics of the model and 6 by clicking OpenSees Parameters Figure 4 4 you can OpenSees analysis parameters advanced feature please exercise with care 4 1 2 Additional Viscous Damping In OpenSeesPL additional viscous Rayleigh type damping is available of the form C AnM A K where M is the mass matrix C is the viscous damping matrix K is the initial stiffness
89. lexural Rigidity My Mz The Flexural Rigidity of the pile which is equal to the product of Young s Modulus E and the Moment of Inertia J My corresponds the moment curvature about section local y axis and Mz corresponds the moment curvature about section local z axis Yield Moment The Yield Moment of the pile Kinematic Hardening Parameter The Kinematic Hardening Modulus Isotropic Hardening Parameter The Isotropic Hardening Modulus Shear Rigidity Vy amp Vz The Shear Rigidity of the pile which is equal to the product of the Shear Modulus G and the area of the pile cross section A Vy corresponds the shear force deformation along section local y axis and Vz corresponds the shear force deformation along section local z axis Torsional Rigidity T The Torsional Rigidity of the pile which is equal to the product of the Shear Modulus G and J Axial Rigidity P The Axial Rigidity of the pile which is equal to the product of Young s Modulus E and the area of the pile cross section A EN Aggregator Section Flexural Rigidity El 158600 KN m2 Yield Moment ETS kN m Kinematic Hardening Parameter 0 kN m Isotropic Hardening Parameter 0 kN m2 Shear Rigidity GA 3378000 KN Torsional Rigidity GJ 42200 kN m2 Axial Rigidity EA 8785000 kN Cancel Figure 3 3 Definition of nonlinear pile properties Aggregator Section 3 2 2 2 Fiber Section 10 The dialog of defining Fiber Section is shown in Figure 3 4
90. lysis Analysis in Progress Dry Case Pushover Run 4 of 4 Pushover analysis V Open output windows when analysis is complete Stop Figure 6 4 Analysis running progress window 6 1 4 Output for Pushover Analysis 6 1 4 1 Tips on Manipulating Graphs Response time histories and profiles are displayed by X Y plot using Java Applet Therefore make sure to enable Java Applet in your web browser Internet Explorer You may also view the digital data by clicking on the link under the X Y plot If occasionally the graph becomes crooked you can click on the Fill button to refresh it To zoom in on any region of the plot select a box with the mouse pointer Figure 6 5 Start at the upper left corner of the region you wish to view in more detail and drag downwards and to the right To bring the graph to the original scale click on the fill button at the upper right corner a Select a box using the mouse pointer b Then release the mouse Figure 6 5 Zoom in 54 a Select a box using the mouse pointer b Then release the mouse Figure 6 6 Zoom out To zoom out drag the mouse pointer upwards Figure 6 6 When zooming out a reference box is drawn that will represent the current view and dragging will cause a box to be displayed that represents the new view Again click on the fill button at the upper right corner to bring the graph to the original scale 6 1 4 2 Pile Response Time Histories and
91. lysis red color shows yielded soil A es OE RnR te Oe Ne ae et MIE eT RP Pe Oe ee eee 132 Figure H 1 Schematic of the fiber section definition for the circular pile cross section 135 Figure H 2 Material properties for the Fiber section apa 135 Figure H 3 Finite element mesh employed in this Study oooonoccniccnnocccoccconncconocono nono connnoconocnoos 136 Figure H 4 Comparison of the moment curvature curves calculated by using OpenSeesPL and OpensSees EXample Ns 136 Figure H 5 Displacement response profiles histories of the pile o ooonoconncnncninncnnnccconccconocnnos 138 Figure H 6 Lateral longitudinal shear versus displacement at the pile head 138 Figure H 7 Moment curvature relation at the maximum moment location ground surface in OE A EE EE EEA EE ce aigatio ss a sed EE us oo E sak sa 139 Vil 1 Introduction OpenSeesPL is a graphical user interface GUI for three dimensional 3D ground and ground structure response The OpenSees Finite Element FE Computational Analysis framework http opensees berkeley edu is employed to conduct all analyses The OpenSeesPL graphical interface pre and post processor is focused on facilitating a wide class of 3D studies with additional capabilities yet under development In the current version OpenSeesPL may be employed to study a number of geometries and configurations of interest including Linear and nonlinear incremental plasticit
92. matrix Am and Ax are two user specified constants The damping ratio curve f is calculated based on the following equation A _ A 7 af f where f is frequency 20 Analysis Options Unit System Soil Materials Solid Element Con s SI Units Linear Elastic 20 Node Brick oo C English Units Nonlinear x r staBrick or 9 C Node B Bar Brick Element bbarBrick Cancel Advanced Options Analysis with no gravity weight applied Not good for pressure dependent structural or soil materials and also not good for inclined model or inclined ground surface Application of Own Weight for Soil Domain M Use Global Elastic Material Initial Lateral Vertical Confinement ES MV Use Global Permeability Ratio 0 1 0 9 7 Young s Modulus 600000 kPa Horizontal Permeability 100 m s Vertical Permeability fi oo m s Pile and Rigid Links Mesh Display Remove pile and rigid links from mesh Show Axes 5 iate N l t Rigid Link Stifness Pile Stiness 10000 Show Intermediate Nodes for 20 Node Elemen Pile Radius Expansion fo m Rayleigh Damping OpenSees Parameters Figure 4 2 Analysis options 1 Specification of Am and A By Defining Damping Ratios The user can define damping coefficients Figure 4 3 by specifying two frequencies f and f must be between 0 1 and 50 Hz and two damping ratios and amp suggested values are between 0 2 and 20 The Rayleigh dampin
93. n s ratio v 0 33 see Lu et al 2006 Effective Unit Weight y 110 pef given by CalTrans For nonlinear analysis the Friction Angle 33 given by CalTrans and the peak shear stress occurs at a shear strain Ymax 10 at the 11 6 psi confinement The parameter Ymax along with the shear modulus define the nonlinear soil stress strain curve Other values of Ymax Should be explored in the future 107 Lateral Load Two load cases Table 1 are studied The loads are applied at the pile head Table E 1 Load cases for the study Shear kips Moment kip ft Axial load kips Load case 1 16 0 52 Load case 2 19 8 100 52 Fixed pile head connection Apply moment in opposite direction of shear Finite Element Simulation In view of symmetry a half mesh 2 900 8 node brick elements 19 beam column elements and 180 rigid beam column elements in total is studied as shown in Figure E 1 Length of the mesh in the longitudinal direction is 520 ft with 260 ft transversally in this half mesh configuration resulting in a 520 ft x 520 soil domain in plan view Layer thickness is 60 ft the bottom of the soil domain is 25 ft below the pile tip so as to mimic the analytical half space solution The floating pile is modeled by beam column elements Mazzoni et al 2006 and rigid beam column elements are used to model the pile size diameter The following boundary conditions are enforced D The
94. n 8 4 Internal Radius in 0 25 External Radius in 25 30 Table H 4 Layer information for the pile circular cross section Number of Reinforcing Bars along Layer 16 Area of Individual Reinforcing Bar in 225 Radius of Reinforcing Layer in 25 Pile head lateral displacement of 0 69 in is applied in 25 equal steps An axial load of 1800 kips is applied at the pile head free head connection during loading Simulation Results The finite element mesh employed is shown in Figure F 3 As mentioned before the soil domain is rigid therefore the meshing of the soil domain is insignificant 10 nonlinearBeamColumn elements are used for the pile The comparison of the moment curvature curves is shown in Figure F 4 Both curves match quite well Response profiles of the single pile are shown in Figure F 5 A shear load of 662 kips is reached at the pile head longitudinal displacement of 0 69 in Figure F 5 amp F 6 The maximum moment reached 6609 kip ft occurring at the ground surface Figure F 6 The moment curvature curve of the single pile at the ground surface location is shown in Figure F 7 134 Internal radius for cover also external radius for core Figure H 1 Schematic of the fiber section definition for the circular pile cross section Fiber Section Material Concrete Compressive Strength 5 2 4 ksi Concrete Strain at Maximum Strength 0 002885 0 003 Concrete
95. ncel Figure 4 15 U Clayl 40 View Backbone Curve U Clay2 PressurelndependMultiYield for Soil Layer 1 Initial Lateral vertical Confinement Ratio 0 Figure 4 16 U Clay2 41 U Sand2A PressureDependMultiYield02 for Soil Layer 1 Reset All Based on gt Please select Soil Elastic Properties Modulus Reduction Curve Dilatancy Liquefaction Parameters Saturated Mass Number of Points 1 9 Density ton m3 Defining Curve Reference Pressure les kPa Pressure Dependence 05 Coefficient Phase Transformation 25 5 degree Angle Contraction pararn 1 0 045 Contraction pararn 3 0 06 MS 0 i o o gt oO 2 2 g x as kk 100000 kPa 233000 kPa gt 2 2 2 o o E o o o ow a i Soil Nonlinear Properties Peak Shear fio Strain 10 Friction Angle 335 degree Fluid Properties Fluid Mass Density l ton m3 Combined 2200000 Bulk Modulus Horizontal 0 0001 Permeability i m s Vertical 0 0001 Permeability Duel Dilation param 3 i kPa o TAT Cancel il Figure 4 17 U Sand2A 42 U Sand2B PressureDependMultiYield02 for Soil Layer 1 Mass Density E ton m3 Reference Mean Confinement io kPa Reference Shear Wave Velocity 300 m s Confinement Dependence Coeff 0 1 1 0 o5 Cancel Poisson s Ratio 04 Cohesion o kPe Friction Angle 5 65 degrees 33 5 Pe
96. nd stiffness proportional viscous damping parameters which are set by default to 2 at the frequencies of 1 Hz and 6 Hz After the dynamic load has been applied analysis can proceed for a user specified number of seconds so that the free vibration response can be assessed if so desired Boundary conditions for this case are Default is fixed boundaries everywhere with the base moving according to the applied base excitation The user might wish to activate alternate boundary conditions along the lateral boundaries in the form of Shear beam boundary conditions where the front and back nodes at any depth move together or a periodic boundary condition where each node on the front boundary moves the same as the analogous node on the back 81 boundary and the vertical is free but can be fixed by the user Eigenvalue analysis In this step the mass and stiffness matrices corresponding to the latest stress strain state after application of own weight of the beam column elements are used to compute natural frequencies and mode shapes using a dynamic solver Boundary conditions for this case are Default is fixed boundaries everywhere with the base moving according to the applied base excitation The user might wish to activate alternate boundary conditions along the lateral boundaries in the form of Shear beam boundary conditions where the front and back nodes at any depth move together or a periodic boundary condition where each nod
97. ned Diameter Side Length D Pile Head Bene Mace 0 ton Ei E Total Pile Length Pile Length above Surface Axial Load 0 kN Linear Beam Properties Young s Modulus 30000000 kPa Mass Density 0 ton m3 Moment of Inertia 0 0490873 m4 Re Calculate C Nonlinear Beam Element Aggregator Section C Nonlinear Beam Element Fiber Section Linear Beam Element Figure 3 1 Definition of pile model 3 1 Pile Parameters Parameters to define the geometrical configurations of the pile include refer to Figure 3 1 Pile Type The pile cross section can be circular or square Pile Diameter Side Length D The diameter if a circular pile is chosen or the side length if a square pile is chosen of the pile cross section The value entered must be greater than zero Total Pile Length The total length of the pile The value entered must be greater than zero Pile Length above Surface The height of the pile above the ground surface The value entered must be greater than zero Fixed or Free Head Free Head or Fixed Head can be chosen Pile Head Mass The mass applied at the pile head Axial Load The axial load applied at the pile head positive as compression If checkbox Pile Group is enabled note that the pile group option might not be available in the version you have users can activate pile group by checking Pile Group Please see Chapter 8 for the detailed information 3 2 Pile Properties In OpenSeesPL the element t
98. ng et al 2003 36 4 2 3 2 User Defined Sand1B U Sand1B The second type of user defined sandy soil PressureDependMultiYield U Sand1B can be defined by specifying the following parameters Figure 4 14 U Sand1B PressureDependMultiYield for Soil Layer 1 Mass Density 2 1 ton m3 Reference Mean Confinement feo kPa Reference Shear Wawe Velocity 300 m s Confinement Dependence Coeff 0 1 1 0 0 5 Cancel Poisson s Ratio Cohesion ES Friction Angle 5 55 degrees Backbone Curve Peak Shear Strain 0 001 20 Number of Yield Surfaces 0 30 Advanced Options M Use KO for Elastic Own Weight m M Young s Modulus for Elastic Own Weight kPa Figure 4 14 U Sand1B Note All parameters shown in Figure 4 14 are defined at the reference mean confinement p Mass Density The mass density of the cohesionless soil p The suggested range of values are between 1 and 3 ton m Reference Shear Wave Velocity The reference shear wave velocity V The suggested range is between 10 and 6000 m s The reference shear modulus G p Vs Reference Mean Confinement The reference mean confinement This is the confinement level at which shear wave velocity and peak shear strain are defined The suggested range is between 10 kPa or larger 37 Confinement Dependence Coeff The confinement dependence coefficient The suggested range is between 0 1 and 10 Initial Lateral Vertical Confinement Ratio The init
99. nonn nono nocnnnos 36 Fig re 414 NS at Baa aa ecg St as Na Nag No ale ee Pha ad At eet Be 37 A sic wae A O secs ae ones ed oe ex ods Season na oa A 40 Figure 16 Ue ay 2 sk cacy A A EA 4 Figure 4 17 U Samd 2A titi 42 iv E 4 18 U S nd2 Birine aia ahi cabelas eter l GG aie eel the cee aces 43 Fioure 4 19 Pile one ti dad ARO 44 Figure 4 20 Pile soil interfacing layer material ooononincninconocccooononnnconccconoconn nono nonnnoconocnnnconnnoos 45 Figure 4 21 Outermost zone material a as A di ricas 45 Figure 5 1 Definition of meshing parameter 48 Figure 6 1 Pushover analysis ini ln doaducdeensVantionssicaesavesseungeans 51 Fig re 6 2 Pushover load pat a i i a a e a a ee his 52 Figure 6 3 User defined pushover load pattern U Push ooonconicnnncnnccnncconccoconononanconananananonnnonos 53 Figure 6 4 Analysis running progress WINdOW ccccceesseeeseceteceeeeesseecsaeceseeeeeeeeseecsaecneeeeeeensees 54 FUGUES O52 ZooM MA la glad Ea a aed O aAA 54 PU Ure 0 07 ZOOM OU sas A ii 55 Figure 6 7 Response time histories and profiles for pile ooononnncniconicnnncnocononononconanoncnrcnononononnos 56 Figure 6 8 Response relationships for Pl as 57 Figure 6 9 Deformed mesh and contour Allis cc s cccccisdescvscas nies cotecevecssayvacvedssncsciagnacedeiadersevaazeeres 58 Figure 6 10 2D plane Y 0 view of the longitudinal displacement contour in the deformed MES WII Wa ads 59 Figure 6 11 Output tor an Eigenvalu
100. nse silt permeability Dense sand permeability Dense gravel permeability Shear modulus Bulk Cohesion Permeability Mag Ss density Cohesive Soil modulus B 5 3 G kPa kPa c kPa coeff m s ton m 1 Where p is the reference mean effective confining pressure at which soil appropriate soil properties are defined 2 Friction angles for cohesionless soils are based on Table 7 4 p 425 of Das B M 1983 3 Permeability values are based on Fig 7 6 p 210 of Holtz and Kovacs 1981 4 Mass density is based on Table 1 4 p 10 of Das 1995 5 Cohesion for cohesive soils are based on Table 7 5 p 442 of Das 1983 28 Backbone Curve At a constant confinement p the shear stress r octahedral shear strain y octahedral nonlinearity is defined by a hyperbolic curve backbone curve see Figure 4 9 _ GY KA 4 1 r T 1 where G is the low strain shear modulus see 4 2 3 1 and y satisfies the following equation at Py 2v2sing G Yma for sands 4 2 ane a e en E and _2v2sing 2V2 Gr Y max for cl 13 sin alee 14 Vmax Vr pera oe where Tp is the peak octahedral shear strength is the friction angle c is the cohesion and Y max 18 the maximum shear strain 10 is employed in OpenSeesPL The octahedral shear stress 7 is defined as 1 1 2 T lo 0y j le O i o Cy y 60 60 60 and the octahedral shear strain y is defined as
101. nstallation of Tcl tk 8 5 for the change to take effect To download Tcl tk 8 5 please visit http cyclic ucsd edu openseespl 1 4 Acknowledgments OpenSeesPL is based on research underway since the early 1990s and a partial list of related publications is included in the Appendix section The OpenSeesPL graphical interface is written in Microsoft Visual C 2005 with the Microsoft Foundation Class MFC libraries The Java Applet package used to display graphical results in OpenSeesPL is obtained from the website http ptolemy eecs berkeley edu GIF images are generated with GNUPLOT for MS Windows 32 bit Version 3 7 available at http www gnuplot org 2 Getting Started 2 1 Start Up On Windows start OpenSeesPL from the Start button or from an icon on your desktop To Start OpenSeesPL from the Start button 1 Click Start and then select Programs 2 Select the OpenSeesPL folder 3 Click on OpenSeesPL The OpenSeesPL main window is shown in Figure 2 1 PL OpenSeesPL Untitled File Execute Display Help DSW H gt P Model Input aan Model Definition _ Mesh Paremeters Analysis Options Analysis Type Pushover Define Pattern C Eigenvalue ber of Frequencies C Base Shaking Boundary Conditions B C Type Rigid Box v Fixed Vert Model Inclination along Longitudinal Direction Ground Surface Inclination Angle 0 30 deg Whole Model Inclination Angle 0 10 deg Figure 2 1 OpenSees
102. o be fully embedded in a homogeneous isotropic linearly elastic half space The elastic properties of the soil are assumed constant along the depth in order to compare with the analytical elastic solution and are listed below Shear Modulus of Soil G 7 98 ksi Bulk Modulus of Soil B 13 288 ksi 1 e Poisson s ratio vs 0 25 Submerged Unit Weight y 62 8 pcf The ratio of Young s Modulus of Pile Ep to the Shear Modulus of Soil G E G 3634 which will be used later to obtain the analytical elastic solution by 83 interpolation Lateral Load The pile head free head condition which is located at the ground surface is subjected to a horizontal load H of 31 5 kips Finite Element Simulation In view of symmetry a half mesh is studied as shown in Figure C 1 For comparison both 8 node and 20 node elements are used 2 900 8 node brick elements 20 beam column elements and 189 rigid beam column elements in total in the OpenSeesPL simulation Length of the mesh in the longitudinal direction is 520 ft with 260 ft transversally in this half mesh configuration resulting in a 520 ft x 520 ssoil domain in plan view Layer thickness is 66 ft the bottom of the soil domain is 32 7 ft below the pile tip so as to mimic the analytical half space solution The floating pile is modeled by beam column elements and rigid beam column elements are used to model the pile size diameter The following boundary conditions
103. oundaries in the form of Shear beam boundary conditions where the front and back nodes at any depth move together or a periodic boundary condition where each node on the front boundary moves the same as the analogous node on the back boundary and the vertical is free but can be fixed by the user Eigenvalue analysis In this step the mass and stiffness matrices corresponding to the latest stress strain state after application of own weight of the beam column elements are used to compute natural frequencies and mode shapes using the static solver Boundary conditions for this case are Default is fixed boundaries everywhere with the base moving according to the applied base excitation The user might wish to activate alternate boundary conditions along the lateral boundaries in the form of Shear beam boundary conditions where the front and back nodes at any depth move together or a periodic boundary condition where each node on the front boundary moves the same as the analogous node on the back boundary and the vertical is free but can be fixed by the user Dry soil case with mildly inclined ground and soil with water table specified 1 Application of soil own weight with elastic soil properties A dynamic solver is used and own weight is applied in 5 steps time step is set to 50 000 secs and gamma y and beta parameters are set to 1 5 and 1 in order to obtain a static solution with 79 elastic soil properties elastic modulus 6
104. p dt 50000 command analyze 3rd Run Tolerance tol for OpenSees command Max number of iterations fiso test NormDisplncr maxNumiter Number of steps for linearly Time step dt 50000 increasing loading part Number of steps for constant loading part afterwards Last Run Tolerance tol for OpenSees command Max number of iterations 50 test NormDisplncr maxNumiter Newmark Integrator gamma Time step dt Cancel Figure 4 4 OpenSees parameters 4 2 Soil Properties 4 2 1 Theory of Soil Models In OpenSees the soil model Figure 4 5 for cohesionless soils is developed within the framework of multi yield surface plasticity e g Prevost 1985 In this model emphasis is placed on controlling the magnitude of cycle by cycle permanent shear strain accumulation Figure 4 6 in clean medium to dense sands Parra 1996 Yang 2000 Yang et al 2003 Furthermore appropriate loading unloading flow rules were devised to reproduce the observed strong dilation tendency and resulting increase in cyclic shear stiffness and strength the Cyclic Mobility mechanism The material types for the cohesionless soils in OpenSees are called PressureDependMultiYield and PressureDependMultiYield02 23 Clay material is modeled as a nonlinear hysteretic material Parra 1996 Yang 2000 Yang et al 2003 with a Von Mises multi surface Iwan 1967 Mroz 1967 kinematic plasticity model Figure 4 7 In this regard focus is on reprodu
105. parison with LPILE is included in Appendix D I 97 a Isometric view b Pile head close up Figure D 1 Finite element mesh employed in this study 98 Table D 1 OpenSees Simulation Results and Experimental Measurements Pite Max bending i deflection at M max Profile Analysis type moment M max j ground line kip ft depth ft displays in H 21 kips Experimental 0 17 62 4 Case Linear soil 0 085 35 1 3 1 Figures Case 2 Nonlinear soil 0 31 70 5 6 8 3a amp 4a H 31 5 kips Experimental 0 26 85 5 Case 3 Linear soil 0 13 52 6 3 1 Figures Case 4 Nonlinear soil 0 56 115 5 6 8 3b amp 4b H 43 kips Experimental 0 4 120 5 Case 5 Linear soil 0 17 70 1 3 1 Figures Case 6 Nonlinear soil 0 89 164 7 6 8 3c amp 4c 60 Load kips Linear Nonlinear 0 2 0 4 0 6 0 8 y Pile deflection at ground line in 1 2 1 4 Figure D 2 Comparison of the load deflection curves for the linear and nonlinear runs 99 Na aa eee aoe Dad 5 k 4 10 7 E 15 O A 20 25 Lat a A E ward tab ae ales ees TO 2 uy ly Ng th yg Foo iu E EET al Nonlinear 30 i l l 0 4 0 6 0 8 Pile deflection in d H 21 kips 0 L i f y f 4 5 A RI eat ip diets Bh SRM Ys alte AS A Ste A E ok Gh mM ea Maat aka at Se Ae 107 E E 15 be o o A o e a to to ao o io te O e Bl O A 20 Let A EA ES A N E E A RR 25 7 Lin
106. ployed in this study ooonooccnoccnocccinccconacononononcnnno cono cnncconnnoon 98 Figure D 2 Comparison of the load deflection curves for the linear and nonlinear runs 99 Figure D 3 Comparison of the pile deflection profiles for the linear and nonlinear runs 100 Figure D 4 Comparison of the pile bending moment profiles for the linear and nonlinear runs EI LENA AT ASA AE Wd dea AA AAN Readily TA AA EN 101 Figure D 5 Stress ratio contour fill of the nonlinear run at different load levels red color shows yielded soil im ds 103 Figure D 6 Comparison of the pile deflection profiles for the linear and nonlinear runs 104 Figure D 7 Comparison of the pile bending moment profiles for the linear and nonlinear runs AAA ANA AA A AAN E At E 105 Figure E 1 Finite element mesh employed in this StUdY ooconconnccnncnoconocconncononononanonncnnncnnccnnoo 109 Figure E 2 Comparison of pile deflection profiles for load case 1 1 ce eseeseeeeeteceeeneeeeeeeees 110 Figure E 3 Comparison of pile rotation profiles for load case Lu ce eeeeseeceeeeceteceeeeneeeeeeeeees 111 Figure E 4 Comparison of bending moment profiles for load case 1 eee eeeeceeseeeteeneeeteeeeees 111 Figure E 5 Comparison of shear force profiles for load case 1 eeeeeceseeseereeeeeceseeneeeneeenees 112 Figure E 6 Comparison of pile deflection profiles for load case Z ooooonnonccnicinicnoncnoconancnnnnnnons 112 Figure E 7 Comparison of pile rot
107. procedure for performing section analysis only does moment curvature but can be easily modified to do any mode of section reponse it MHS October 2000 modified to improve convergence by Silvia Mazzoni 2006 it Arguments secTag tag identifying section to be analyzed axialLoad axial load applied to section negative is compression maxK maximum curvature reached during analysis numIncr number of increments used to reach maxK default 100 it Sets up a recorder which writes moment curvature results to file section secTag out the moment is in column 1 and curvature in column 2 Define two nodes at 0 0 node 1001 0 0 0 0 0 0 node 1002 0 0 0 0 0 0 Fix all degrees of freedom except axial and bending fix 1001111111 fix 1002011110 Define element tag ndI ndJ secTag element zeroLengthSection 2001 1001 1002 secTag Create recorder recorder Node file data Mphi out time node 1002 dof 6 disp output moment col 1 amp curvature col 2 Define constant axial load pattern Plain 3001 Constant load 1002 axialLoad 0 0 0 0 0 0 0 0 0 0 Define analysis parameters integrator LoadControl 0 1 0 0 system SparseGeneral piv Overkill but may need the pivoting test EnergyIncr 1 0e 9 10 numberer Plain constraints Plain algorithm Newton analysis Static Do one analysis for constant axial load analyze 1 Define reference moment 142 pattern Plain 30
108. r Soil 128 kips 7 OpenSees Nonlinear Soil 256 kips BO T LPILE 64 kips be the wate daa teats ae ease tet OE j A TE LPILE 128 kips LPILE 256 kips 35 i 1 1 L 2 3 2 1 5 1 0 5 0 0 5 Rotation rad 107 Figure F 3 Comparison of pile rotation profiles for the fixed head condition 118 5 Leste Gah gh Gist A II A OA A 10 2 15p S D A 20 E A A o ae OpenSees Nonlinear Soil 64 kips 25 OpenSees Nonlinear Soil 128 kips OpenSees Nonlinear Soil 256 kips Besa LPILE 64 kips a a ee LPILE 128 kips LPILE 256 kips 3 5 i I L 2500 2000 1500 1000 500 0 500 1000 Bending moment kip ft Figure F 4 Comparison of bending moment profiles for the fixed head condition 0 Depth ft aA S N N Nn OpenSees Nonlinear Soil 128 kips 7 OpenSees Nonlinear Soil 256 kips 30 Whoo ct LPILE APS o i LPILE 128 kips LPILE 256 kips 35 i 1 I i i 100 50 100 150 200 250 300 Shear force kips Figure F 5 Comparison of shear force profiles for the fixed head condition 119 Nn Depth ft N KER OpenSees Nonlinear Soil 64 kips OpenSees Nonlinear Soil 128 kips 7 OpenSees Nonlinear Soil 256 kips 3 rneer eese ne cee gt LPILE 64 kips od LPILE 128 kips LPILE 256 kips 35 l i 0 5 0 0 5 1 1 5 2 Pile deflection in N Nn T F
109. ring 146 Mechanics Columbia University NY New York Dynamic Soil Properties Seismic Downhole Arrays and Applications in Practice 2001 A W Elgamal T Lai Z Yang and L He 4 International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics S Prakash Ed San Diego California USA March 26 31 Computational Modeling of Cyclic Mobility and Post Liquefaction Site Response 2002 A Elgamal Z Yang and E Parra Soil Dynamics and Earthquake Engineering 22 4 259 271 Influence of Permeability on Liquefaction Induced Shear Deformation 2002 Z Yang and A Elgamal J Engineering Mechanics ASCE 128 7 720 729 Numerical Analysis of Embankment Foundation Liquefaction Countermeasures 2002 A Elgamal E Parra Z Yang and K Adalier J Earthquake Engineering 6 4 447 471 Modeling of Cyclic Mobility in Saturated Cohesionless Soils 2003 A Elgamal Z Yang E Parra and A Ragheb Int J Plasticity 19 6 883 905 Application of unconstrained optimization and sensitivity analysis to calibration of a soil constitutive model 2003 Z Yang and A Elgamal Int J for Numerical and Analytical Methods in Geomechanics 27 15 1255 1316 Computational Model for Cyclic Mobility and Associated Shear Deformation 2003 Z Yang A Elgamal and E Parra J Geotechnical and Geoenvironmental Engineering ASCE 129 12 1119 1127 A Web based Platform for
110. rmed mesh is for the dynamic analysis if Due to Seismic Excitation is chosen or the pushover analysis if Due to Pushover is chosen However the deformed mesh due to gravity is also available Due to Gravity is chosen Types of results in the deformed mesh include Figure 6 9 e Deformed Mesh Displacement Contour Fill Longitudinal Displacement Contour Fill X disp contour Transverse Displacement Contour Fill Y disp contour Vertical Displacement Contour Fill Z disp contour Pore Pressure Contour Fill Excess Pore Pressure EPP Contour Fill EPP Ratio Contour Fill Vertical Stress Contour Fill Shear Stress Contour Fill Stress Ratio Contour Fill Effective Confinement Contour Fill The deformed mesh can be viewed in 3D or 2D can be selected from a list of 2D cut planes see Figure 6 10 57 To view the animation of any given type click the Play Animation button The text of the button will change to Stop Animation when the animation is being played To stop the animation click the Stop Animation button The Scale Factor can be changed to improve the viewing effects The time between playing two frames can be defined by specifying the Animation Playing Delay in millisecond Note that the animation will not be played if the current time step is in the last step and Endless Playing is unchecked At any time the deformed mesh can be rotated by dragging the mouse moved in 4 directions by pr
111. ry moves the same as the analogous node on the back boundary horizontal and vertical directions The Periodic boundary condition if it s chosen is enforced for all runs For gravity runs rollers are used for lateral and base boundaries The base nodes are fixed after the first run If Fixed Vert is checked all nodes at lateral boundaries will be fixed in vertical direction before the dynamic run Dry soil case with level ground 1 Application of soil own weight with elastic soil properties At first the defined soil properties are used to set up the soil constitutive model A static solver is used and own weight is applied in one step with elastic soil properties Default is global elastic modulus 600 000 kPa by default and global initial lateral vertical confinement ratio Ko 0 9 77 by default for the entire soil domain These elastic soil properties are used to define an elastic stiffness matrix Kmatrix1 A default convergence tolerance of 0 0001 is used displacement norm which the user can specify in the OpeSees Parameters section from Analysis Options Boundary conditions BC1 Lateral boundaries Rollers are used on the lateral boundaries to prevent lateral deformation and vertical displacement is allowed Base Rollers are used to prevent vertical displacement but lateral deformation is allowed 2 Switching from elastic soil properties to nonlinear soil properties The actual defined soil properties in every par
112. s not allowed in the current model formulation Finally note that the backbone curve varies with confinement although the variations are small within commonly interested confinement ranges Backbone curves at different confinements can be obtained using the OpenSees element recorder facility Mazzoni et al 2006 The dilatancy liquefaction parameters include Phase Transformation PT Angle The transformation angle degrees of the cohesionless soil Contraction Parameter c1 A non negative constant defining the rate of shear induced volume decrease contraction or pore pressure buildup A larger value corresponds to faster contraction rate Table 4 2 The contraction rule is defined by p 1 7 7 py 3 c 4 10 Laina where 7 is the stress ratio and 7 is the stress ratio along the PT surface Yang et al 2003 Dilation Parameters d1 amp d2 Non negative constants defining the rate of shear induced volume increase dilation Larger values correspond to stronger dilation rate Table 4 2 The dilation rule is defined by 1 7 Mer y P d exp d 4 11 Gm Si where y is the octahedral shear strain accumulated during a dilation phase Yang et al 2003 Liquefaction Parameters l and l Parameters Table 4 2 controlling the mechanism of liquefaction induced perfectly plastic shear strain accumulation 1 e cyclic mobility Set 7 0 to deactivate this mechanism altogether Post liquefaction y
113. sandy soil PressureDependMultiYield02 U Sand2A can be defined as shown in Figure 4 17 PressureDependMultiYield02 material is modified from PressureDependMultiYield material with 1 additional parameters Contraction parameter 3 and Dilation parameter 3 as shown in Figure 4 17 to account for Ko effect 2 a parameter to account for the influence of previous dilation history on subsequent contraction phase and 3 modified logic related to permanent shear strain accumulation 4 2 3 6 User Defined Sand2B U Sand2B The third type of user defined sandy soil PressureDependMultiYield02 U Sand2B can be defined as shown in Figure 4 18 39 U Clay1 PressurelndependMultiYield for Soil Layer 4 1 Soil Elastic Properties Saturated 18 Mass Density ton m3 Reference 100 Pressure hoo kPa Pressure Dependence o Coefficient Gmax 160000 kPa Bmax 500000 kPa Soil Nonlinear Properties Peak Shear Strain Friction Angle 0 degree 75 kPa Cohesion Fluid Properties Fluid Mass Density I Pace Combined Bulk 2200000 Modulus kPs i e 009 m s 1e 009 m s Horizontal Permeability Vertical Permeability Defining Curve Shear Strain 0 0001 0 0003 0 001 0 003 i ANAL 0 0 0 03 LT o Modulus Reduction Curve Number of Points l G Gmax 0 999 0 995 bl 0 99 0 96 0 8 0 64 0 37 0 18 0 0 0 03 0 01 Ca
114. ser defined cohesionless and cohesive soil materials U Sand1A U Sand1B U Clay1 U Clay2 U Sand2A and U Sand2B are also available to choose If an elastic isotropic material is selected the user is requested to specify Young s Modulus Poisson s Ratio Mass Density Permeability of the material used for the pile soil interfacing layer 4 2 6 Outermost Zone Properties The material for the outermost zone Figure 4 21 can be selected from an available menu of cohesionless and cohesive soil materials including the elastic isotropic material In addition user defined cohesionless and cohesive soil materials U Sand1A U Sand1B U Clay1 U Clay2 U Sand2A and U Sand2B are also available to choose If an elastic isotropic material is selected the user is requested to specify Young s Modulus Poisson s Ratio Mass Density Permeability of the material used for the pile soil interfacing layer 44 Column Soil Interfacing Layer Material for Pile Soil Interfacing Layer Residual Shear Strength for Very Loose Material Only 2 kPa Soil Modulus Variation with Depth P CL OC Youngs Poissons M Modulus kPa Pati fa 3 Mass Permeabili Density f 5 ton m3 m s h f1e 005 Notes P L and C represents parabolic linear and constant variation of soil modulus with depth respectively Figure 4 20 Pile soil interfacing layer material Outermost Zone Material Material for Outermost
115. ss seteps2U 0 01 strain at ultimate stress set lambda 0 1 ratio between unloading slope at eps2 and initial slope Ec tensile strength properties set ftC expr 0 14 fc1C tensile strength tension set ftU expr 0 14 fc 1U tensile strength tension set Ets expr ftU 0 002 tension softening stiffness set Fy expr 66 8 ksi STEEL yield stress set Es expr 29000 ksi modulus of steel set Bs 0 01 strain hardening ratio set RO 18 control the transition from elastic to plastic branches set cR1 0 925 control the transition from elastic to plastic branches set cR2 0 15 control the transition from elastic to plastic branches uniaxialMaterial Concrete01 IDconcCore fclC eps1C fc2C eps2C build core concrete confined uniaxialMaterial Concrete01 IDconcCover fclU eps1U fc2U eps2U build cover concrete unconfined uniaxialMaterial Steel01 IDreinf Fy Es Bs build reinforcement material puts Ec Ec puts uniaxialMaterial Concrete01 IDconcCore fc1C eps1C fc2C eps2C build core concrete confined puts uniaxialMaterial Concrete01 IDconcCover fc1U eps1U fc2U eps2U build cover concrete unconfined puts uniaxialMaterial Steel01 IDreinf Fy Es Bs build reinforcement material uniaxialMaterial Concrete02 IDconcCore fc1C eps1C fc2C eps2C lambda ftC Ets build core concrete confined uniaxialMaterial Concrete02 SIDconcCov
116. t load levels red color shows yielded soil elements 103 Appendix D I Comparison with LPILE In the LPILE run a p y modulus of 90 psi is employed p y multiplier 1 0 All other properties are the same as described earlier of AA SI T Depth ft nr 20 F 25l l OpenSees Nonlinear Soil LPILE O Experimental 30 i 0 2 0 0 2 0 4 0 6 0 8 Pile deflection in a H 21 kips 0 5 y 10 E S 6 15 oO A 20 25l OpenSees Nonlinear Soil LPILE O Experimental 30 0 5 0 0 5 1 1 5 Pile deflection in b H 31 5 kips Figure D 6 Comparison of the pile deflection profiles for the linear and nonlinear runs 104 rere ear A s gene AT E a 10 oo gt 7 E lt a als AA A EEE as bE AEE owt amp Boe wie nls acl oO A 20 A e a o De MAE STAM o o a OURS ts el 25l l l OpenSees Nonlinear Soil LPILE gt Experimental 0 5 0 0 5 1 1 5 2 2 5 Pile deflection in c H 43 kips Figure D 6 continued Depth ft Y UI 40t OpenSees Linear Soil J OpenSees Nonlinear Soil LPLE 50 Experimental i J 20 0 20 40 60 80 100 120 Bending moment kip ft a H 21 kips Figure D 7 Comparison of the pile bending moment profiles for the linear and nonlinear runs 105 Depth ft Y UI Raney DELE EAST OpenSees Linear Soil 4
117. t of the mesh are activated and nonlinear if specified properties are activated as well The static solver is used and Kmatrix1 is used for convergence A convergence tolerance of 0 0001 is used displacement norm The boundary conditions for this step remain those of BC1 3 Including the beam column elements and their own weight A new mass and stiffness matrix is built based on the latest tangent soil stress strain state and the linear properties of the beam column elements A convergence tolerance of 0 0001 is used displacement norm The load is applied in 20 steps by default the user can modify this value in the OpeSees Parameters section from Analysis Options The stiffness matrix is not updated The boundary conditions for this step remain those of BC1 4 Solution phase Solution is started with a stiffness matrix based on the latest soil and beam column stress strain state Four different analysis scenarios are possible Static Push over analysis The static solver is used with a convergence tolerance of 0 0001 that the user can modify in the OpeSees Parameters section from Analysis Options displacement norm Boundary conditions for this case are Default is fixed boundaries everywhere but the user can change that to Shear Beam or Periodic Boundary Dynamic push over analysis In this case a dynamic solver is used modified Newton Raphson with the time integration parameters y 0 6 and B 0 3025 and the actual
118. ts of the University of California hae f Acknowledgements This research was funded by Pacific Earthquake Engineering Research PEER Center under the National Science Foundation Award Number EEC 9701568 and by the National Science Foundation Grants No CMS0084616 and CMS0200510 This software is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE OpenSeesPL was developed by Dr Jinchi Lu jinlu ucsd edu Dr Ahmed Elgamal elgamal ucsd edu and Dr Zhaohui Yang yangaas qmail com OpenSees currently ver 2 1 0 is employed is a software framework for developing applications to simulate the performance of structural and geotechnical systems subjected to earthquakes For more infomation visit http opensees berkeley edu The OpenSees geotechnical simulation capabilities were developed by Dr Zhaohui Yang and Dr Ahmed Elgamal For more information please visit http cyclic ucsd edu opensees For questions or remarks please send email to Dr Jinchi Lu jinlu ucsd edu Dr Ahmed Elgamal elgamal Sucsd edu or Dr Zhaohui Yang yangasa 2gmail com Figure 2 3 OpenSeesPL copyright message 2 2 2 Model Input Window The model input window controls definitions of the model and analysis options which are organized into four regions Figure 2 1 e Model Definition Controls definitions of pile and soil strata
119. ults for the linear and nonlinear runs H 31 5 kips H 63 kips H 94 5 kips Linear Nonlinear Linear Nonlinear Linear Nonlinear Pile head deflection in 0 039 0 07 0 078 0 23 0 12 0 48 Maximum moment Moray Kip ft 30 48 2 60 124 3 90 215 5 Depth where Mias 2 9 3 8 2 9 4 7 2 9 4 7 occurs ft a First step b H 31 5 kips c H 63 kips d H 94 5 kips Figure C 9 Stress ratio contour fill of the nonlinear run at different load levels red color shows yielded soil elements Appendix D Finite Element Analysis of Arkansas Test Series Pile 2 Using Opensees with LPILE Comparison Introduction In this study we conduct a finite element simulation of Pile No 2 of the Arkansas test series Alizadeh and Davisson 1970 using the OpenSeesPL interface This pipe pile is subjected to lateral loads Comparison with LPILE is also included in Appendix D I please see the end of Appendix D Laterally Loaded Pile Pile Data The pile employed in the OpenSees simulation is circular with a diameter of 16 radius a 8 while the one for the experimental test is a cylindrical pipe pile of the same radius and a wall thickness h 0 312 The cross sectional moment of inertia of the pipe pile 7 838 2 inf Bowles 1988 pages 777 778 which will be used for the circular pile in the OpenSees simulation The geometric and elastic material properties of the pile are listed below Bowles 1988
120. user specified time step Note that the user can also modify the Rayleigh mass and stiffness proportional viscous damping parameters which are set by default to 2 at the frequencies of 1 Hz and 6 Hz 78 After the dynamic load has been applied analysis can proceed for a user specified number of seconds so that the free vibration response can be assessed if so desired Boundary conditions for this case are Default is fixed boundaries everywhere but the user can change that to Shear Beam or Periodic Boundary Dynamic Base earthquake excitation In this case a dynamic solver is used modified Newton Raphson with the time integration parameters y 0 6 and B 0 3025 and the actual user specified time step The convergence tolerance of 0 0001 is the default but the user can modify this value in the OpeSees Parameters section from Analysis Options displacement norm Note that the user can also modify the Rayleigh mass and stiffness proportional viscous damping parameters which are set by default to 2 at the frequencies of 1 Hz and 6 Hz After the dynamic load has been applied analysis can proceed for a user specified number of seconds so that the free vibration response can be assessed if so desired Boundary conditions for this case are Default is fixed boundaries everywhere with the base moving according to the applied base excitation The user might wish to activate alternate boundary conditions along the lateral b
121. y based 3D ground seismic response with capabilities for 3D excitation and multi layered soil strata Multi yield surface cohesionless Drucker Prager cone model and Mises or J2 soil models are available The coupled solid fluid analysis option allows for conducting liquefaction studies Inclusion of a pile or shaft in the above 3D ground mesh circular or square pile in a soil island The pile can extend above ground and can support a bridge deck or a point mass at the pile top The bridge deck can be specified to only translate laterally or to undergo both lateral translation and rotation In addition to the seismic excitation option the pile system may be subjected to monotonic or cyclic lateral push over loading in prescribed displacement or prescribed force modes Soil within the zone occupied by the pile as specified by pile diameter for instance can be specified independently allowing for a variety of useful modeling scenarios Various Ground Modification scenarios may be studied by appropriate specification of the material within the pile zone For instance liquefaction countermeasures in the form of gravel drains stone columns and solidification cementation may all be analyzed Of particular importance and significance in these scenarios is the ability to include the effect of mild infinite slope inclination i e allowing estimates of accumulated ground deformation effect of liquefaction countermeasures pile pinning eff
122. ypes available for the pile are elasticBeamColumn which represents elastic beam column element and nonlinearBeamColumn which represents a nonlinear beam column element based on based on the non iterative or iterative force formulation Detail information can be found in the OpenSees User Manual Mazzoni et al 2006 3 2 1 Linear Beam Element The material properties of the pile for the linear beam element elasticBeamColumn are defined by the following parameters Figure 3 2 Young s Modulus E Young s Modulus of the pile Mass Density The Mass Density of the pile Moment of Inertia I The Moment of Inertia of the pile This can be specified directly or calculated based on the pile diameter Linear Beam Properties Young s Modulus 30000000 kPa Mass Density 0 ton m3 Moment of Inertia 0 0490873 m4 Re Calculate Figure 3 2 Definition of linear pile properties 3 2 2 Nonlinear Beam Element OpenSees uses the Section command to define the nonlinear beam column element a section defines the stress resultant force deformation response at a cross section of a beam column element Two types of sections are available in OpenSeesPL for the nonlinear beam element nonlinearBeamColumn Aggregator Section or Fiber Section Detail information can be found in the OpenSees User Manual Mazzoni et al 2006 3 2 2 1 Aggregator Section The Aggregator Section is defined by the following parameters in OpenSeesPL Figure 3 3 F

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