OPENSEES Soil-Pile Interaction Study under Lateral Spread Loading

Transcription

1 OPENSEES Soil-Pile Interaction Study under Lateral Spread Loading Po-Lam - EarthMechanics Pedro Arduino UW Peter Mackenzie-Helnwein UW Overview Introduction Background & Common Practice 3D Analysis of Soil-Pile Interaction Beam-Solid Approach Contact Formulation & Implementation Practical Applications Summary and Conclusions 9/11/28 Kinematic Analysis of Piles using OpenSees 2 California, Berkeley 1

2 Problem Description Kinematic loading on the pile from the upper unliquefied soil mass displacing relative to the underlying stable lower soil mass Slippage displacement concentrated on a usually thin liquefied soil layer between the two stiffer soil masses 9/11/28 Kinematic Analysis of Piles using OpenSees 3 Common Solution strategies Fixed-fixed beam Uncoupled free-field displacement Uncoupled displacement considering pile pinning 2-D FEM analysis 3-D FEM analysis 9/11/28 Kinematic Analysis of Piles using OpenSees 4 California, Berkeley 2

3 Fixed-fixed approach Soil Displacement, Penetration Distance, Lp Non Liq. Zone Deflection, Fixed-Fixed Beam Moment, M = 2 EI/L + +M Shear, F = Fixed-Fixed Beam ( = 6 ) Fixed-Fixed Beam ( = 12 ) +F 3 EI/L Max. Pile Moment Line of Symmetry Thickness of Liq. Zone Max. Pile Moment Effective fixed-fixed Beam Length, Leff Distance, x Non Liq. Zone 9/11/28 Kinematic Analysis of Piles using OpenSees 5 Uncoupled free-field field displacement (with and without pinning effect) 9/11/28 Kinematic Analysis of Piles using OpenSees 6 California, Berkeley 3

4 2-D FEM analysis 9/11/28 Kinematic Analysis of Piles using OpenSees 7 3D FEM Analysis Solid-Solid Model 9/11/28 Kinematic Analysis of Piles using OpenSees 8 California, Berkeley 4

5 New approach: Beam-Solid Contact Element Soil: solid elements Pile: beam elements Pile-Soil Interface: Beam-Solid Contact Element 9/11/28 Kinematic Analysis of Piles using OpenSees 9 Laterally Loaded Piles (comparison with LPILE) Perform numerical load test Compare results 3x Magnification 9/11/28 Kinematic Analysis of Piles using OpenSees 1 California, Berkeley 5

6 Laterally Loaded Piles Numerical p-y curves: Obtained by differentiation of pile bending moments 2 Beam Solid pile: d M dv M = z Ai y i i Obtained directly from p = contact = element force σ 2 output dz dz z f(z,θ) y i p i p y θ Discretized beam Deformed beam with interface forces, f (z,θ) Deformed beam with interface forces, p i = Σf (z,θ)r dθ and displacement, y i p-y curves 9/11/28 Kinematic Analysis of Piles using OpenSees 11 Laterally Loaded Piles Normal interface stresses and radial soil stresses 9/11/28 Kinematic Analysis of Piles using OpenSees 12 California, Berkeley 6

7 Laterally Loaded Piles Evaluation Numerical p-y of beam curvesresponse 9/11/28 Kinematic Analysis of Piles using OpenSees 13 Laterally Loaded Piles GiD Visualization of pile and soil deformation with interface forces 9/11/28 Kinematic Analysis of Piles using OpenSees 14 California, Berkeley 7

8 Back to our problem Undeformed mesh 9/11/28 Kinematic Analysis of Piles using OpenSees 15 Base Soil & Pile Properties Soil profile E [kpa] Poisson s ratio Unit weight [kn/m 3 ] Top strong layer (brown) 25, Middle soft layer (white) 2, Bottom strong layer (brown) Elastic isotropic soil properties 25, Elasto-plastic (Drucker Prager) soil properties Soil profile Top strong layer (brown) Middle soft layer (white) Bottom strong layer (brown) K [kpa] G [kpa] Friction angle φ [degrees] Cohesion c [kpa] Unit weight [kn/m 3 ] /11/28 Kinematic Analysis of Piles using OpenSees 16 California, Berkeley 8

9 Base Soil & Pile properties Beam material Diam Area [m2] Pile elastic properties I [m4] E [kpa] G [kpa] RC Concrete beam 2.5m ,, 12,5, RC Concrete beam ,, 12,5, RC Concrete beam ,, 12,5, Interface Contact element material properties Friction coefficient (µ= µ=tan(φ)) Stiffness (for sticking) [kpa] Beam-solid contact.1 1 9/11/28 Kinematic Analysis of Piles using OpenSees 17 GiD post processing Self Weight - Vertical and Horizontal stresses due to self weight (notice near isotropic condition in liquefied layer) Notice horizontal and vertical stresses are similar (fluid) in the liquefiable layer Vertical Stress Horizontal Stress 9/11/28 Kinematic Analysis of Piles using OpenSees 18 California, Berkeley 9

10 GiD post processing Initial Conditions OpenSees Vertical stresses Contact Forces 9/11/28 Kinematic Analysis of Piles using OpenSees 19 Push-over deformation pattern 9/11/28 Kinematic Analysis of Piles using OpenSees 2 California, Berkeley 1

11 GiD post processing σ xx stresses after displacement 9/11/28 Kinematic Analysis of Piles using OpenSees 21 GiD post processing Contact Forces at the end of displacement Perspective View XZ Plane View 9/11/28 Kinematic Analysis of Piles using OpenSees 22 California, Berkeley 11

12 GiD post processing Contours of Contact Forces at the end of Displacement 9/11/28 Kinematic Analysis of Piles using OpenSees 23 GiD post processing Forces in the Beam at the End of Displacement Perspective View XZ Plane View 9/11/28 Kinematic Analysis of Piles using OpenSees 24 California, Berkeley 12

13 GiD GiD post processing (a) Contact forces at soil-pile interface and (b) Horizontal pile forces at the end of loading 9/11/28 Kinematic Analysis of Piles using OpenSees 25 GiD GiD Diagrams Shear diagram Bending moment diagram 9/11/28 Kinematic Analysis of Piles using OpenSees 26 California, Berkeley 13

14 Parametric Study Pile diameters D1=2.5 m, D2=54in., and D3=24in. Soft Layer Thicknesses T1=1D, T2 = 2D, and T4=4D. Piles stiffness, EI (scale factors for base EI values E-3 =.125, E-2 =.25, E-1 =.5, E =1., E1 =2., E2 =4., and E3 =8.. Total cases = 84 cases 9/11/28 Kinematic Analysis of Piles using OpenSees 27 Final OpenSees Meshes Finite element meshes for different soft layer thickness. (a)t=1d, (b)t=2d, and (c)t=4d 9/11/28 Kinematic Analysis of Piles using OpenSees 28 California, Berkeley 14

15 Characteristic Results of Parametric study Effect of soil displacement Shear diagrams Bending Moment diagrams Shear force distribution V for EI= 239. MNm 2 Moment distribution M for EI= 239. MNm Height above base in (m) 15 1 Height above base in (m) Shear force in (kn) Moment in (knm) x 1 Location and value of maxv and maxm changes with soil displacement 9/11/28 Kinematic Analysis of Piles using OpenSees 29 Characteristic Results of Parametric study Effect of pile stiffness EI Shear force distribution V for EI= MNm 2 Moment distribution M for EI= MNm EI 1 less stiff Height above base in (m) 15 1 Height above base in (m) Shear force in (kn) Shear force distribution V for EI= 478. MNm Moment in (knm) x 1 4 Moment distribution M for EI= 478. MNm EI 2 stiffer Height above base in (m) Height above base in (m) Location and value of maxv and maxm varies for different EI Shear force in (kn) Moment in (knm) x 1 4 9/11/28 Kinematic Analysis of Piles using OpenSees 3 California, Berkeley 15

16 Characteristic Results of Parametric study Basic definitions D 1D T (L eff -T)/2D L eff /D 1D 9/11/28 Kinematic Analysis of Piles using OpenSees 31 Characteristic Results of Parametric study maxm and location 3 x 1 4 extreme values for moment M for EI= 239. MNm 2 abs(max M) in top layer abs(max M) in bottom layer 2 Location of extreme moments M for EI= 239. MNm 2 position of maxm in top layer position of maxm in bottom layer L effective Moment M in (knm) 1 Height above base in (m) L eff pseudo time pseudo time 9/11/28 Kinematic Analysis of Piles using OpenSees 32 California, Berkeley 16

17 Characteristic Results of Parametric study Pile deformation 25 2 depth (m) pile displacement (m) 9/11/28 Kinematic Analysis of Piles using OpenSees 33 Non-dimensional characteristic parameter ET s D β = EI 2 2 E s modulus o elasticity of stiff soil layer EI stiffness of pile T thickness of liquefiable layer D outer diameter of pile 9/11/28 Kinematic Analysis of Piles using OpenSees 34 California, Berkeley 17

18 Embedment length in stiff soil layer (approximated as average of top and bottom layer) (Leff - T)/2D Data Fit T=1D (2.5m) T=2D (2.5m) T=4D (2.5m) T=1D (54") T=2D (54") t=4d (54") T=1D (24") T=2D (24") T=4D (24") Es=5 (54") Results Es D^2 encourage T^2 / EI the use of a linear regression for most of the parameter space 9/11/28 Kinematic Analysis of Piles using OpenSees 35 Dimensionless shear force demand. Maximum shear occurs within the liquefied layer maxv T^2 D / EI Delta Data Fit Es=5 (54") T=1D (2.5m) T=2D (2.5m) T=4D (2.5m) T=1D (54") T=2D (54") t=4d (54") T=1D (24") T=2D (24") T=4D (24") Es=5 (54") Es=125 (54") Es=75 (54") Es=25 (54") Es D^2 T^2 / EI 9/11/28 Kinematic Analysis of Piles using OpenSees 36 California, Berkeley 18

19 Dimensionless bending moment (or curvature demand). Max M occurs at from the layer interface within the stiff layer maxm T D / EI Delta Data Fit Es=5 (54") T=1D (2.5m) T=2D (2.5m) T=4D (2.5m) T=1D (54") T=2D (54") t=4d (54") T=1D (24") T=2D (24") T=4D (24") Es=5 (54") Es=125 (54") Es=75 (54") Es=25 (54") Es D^2 T^2 / EI 9/11/28 Kinematic Analysis of Piles using OpenSees 37 Design Procedure EI maxv = γ V 2 T D Maximum shear force in the pile EI max M = γ M T D Maximum moment in the pile L = D Location of maximum moment embed γ L γ L γ V γ M =.5 log 1 β =.17β =.9β Non-dimensional coefficients β = EsT D EI 2 2 Dimensionless characteristic parameter 9/11/28 Kinematic Analysis of Piles using OpenSees 38 California, Berkeley 19

20 Dimensionless shear force demand. Maximum shear occurs within the liquefied layer. maxv T^2 D / EI Delta Data Fit T=2D (2.5m) T=1D (2.5m) T=4D (2.5m) T=1D (54") T=2D (54") t=4d (54") T=1D (24") T=2D (24") T=4D (24") Es=5 (54") Es=125 (54") Es=75 (54") Es=25 (54") Es D^2 T^2 / EI 9/11/28 Kinematic Analysis of Piles using OpenSees 39 Dimensionless bending moment (or curvature demand). Max M occurs at L embed from the layer interface within the stiff layer. maxm T D / EI Delta Data Fit T=2D (2.5m) T=1D (2.5m) T=4D (2.5m) T=1D (54") T=2D (54") t=4d (54") T=1D (24") T=2D (24") T=4D (24") Es=5 (54") Es=125 (54") Es=75 (54") Es=25 (54") Es D^2 T^2 / EI 9/11/28 Kinematic Analysis of Piles using OpenSees 4 California, Berkeley 2

21 Comparison of fixed-fixed vs. OpenSees.14 Moment relative to Fixed-Fixed Beam Cal. Moment to Fixed-Fixed Moment Es D^2 T^2/EI 9/11/28 Kinematic Analysis of Piles using OpenSees 41 Questions? 9/11/28 Kinematic Analysis of Piles using OpenSees 42 California, Berkeley 21