Modeling of Cyclic Load-Deformation Behavior of Shallow Foundations Supporting Rocking Shear Walls. Sivapalan Gajan. Advisor: Bruce Kutter

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1 Modeling of Cyclic Load-Deformation Behavior of Shallow Foundations Supporting Rocking Shear Walls Sivapalan Gajan Advisor: Bruce Kutter Seminar

2 Overview of Presentation Background Experimental Findings Footing-Soil Interface Modeling Implementation in OpenSEES

3 Shallow Foundations Supporting Rocking Shear Walls Material and geometrical nonlinearities soil yielding and footing uplift Nonlinear bearing pressure distribution Nonlinear moment-rotation behavior Shear wall and frame structure (after ATC, 1997) Energy dissipation beneath the footing and associated permanent deformations

4 Soil-Foundation-Structure Interaction Small displacements protect frame from damage High forces cause shear wall damage, small Foundation yielding and rocking protects shear wall Large displacements cause frame damage,large Stiff and Strong Foundation Flexible and Weak Foundation (ATC )

5 Foundation rocking and mobilization of ultimate capacity reduce seismic demands on the structure (FEMA 1997 and ATC 1997) Issues Analytical challenges to reliable modeling of soil-foundation behavior Uncertainty in soil properties Lack of interaction between Structural and Geotechnical Engineers/Researchers

6 Purposes of Research To further the understanding of footing-soil interface behavior under realistic confining pressures. To investigate the effects of static vertical factor of safety (FS V ) on energy dissipation and permanent deformations To model the nonlinear cyclic load-displacement behavior of footing-soil interface for combined vertical, shear and moment loading - allowing soil yielding and footing uplift.

7 What Have We Done? Centrifuge Experiments Understanding Footing-Soil Interface Behavior Macro-Element Modeling Modeling Footing-Soil Interface Behavior Outcome Interface Model in OpenSEES

8 Centrifuge Experiments Rosebrook (KRR01, KRR02, KRR03) Gajan and Phalen (SSG02, SSG03) Gajan and Thomas (SSG04) Thomas and Gajan (JMT01, JMT02)

9 Single-Wall Double-Wall Frame-Wall

10 Parameters varied Soil properties Soil type (sand and clay) Dr (80% and 60%) Structure properties Shear wall weight (FS = 2 to 15) Footing geometry (rectangular and square) Footing embedment (D = 0 to 3B) Loading types Pure vertical loading Lateral slow cyclic loading Controlling moment to shear ratio (one actuator) Controlling rotation and sliding (two actuators) Dynamic base shaking

11 Forces and Displacements at the Interface

12 Load-Displacement Behavior at Interface FS = 5.0, D = 0.0 m, L = 2.8 m, h = 4.9 m

13 Effect of Soil Type - Clay FS = 3.0, D = 0.0 m, L = 2.7 m, h = 4.6 m

14 Load Paths in V-H-M Space M M V H Vertical Load Ratio Moment-to-Shear Ratio VMAX M FSV = = h V H

15 Effect of Vertical Factor of Safety

16 Effect of Vertical Factor of Safety same Vult, different V same V, different Vult

17 Effect of Load Height (M/H = 1.2 m) FS = 5.0, D = 0.0 m, L = 2.8 m, h = 1.2 m

18 Dynamic Base Shaking FS = 5.0, D = 0.0 m, L = 2.8 m, a_max = 0.5 g

19 Energy Dissipation Vs Permanent Deformation 40 M A θ θ Energy Dissipation per Cycle (knm) s Settlement per Cycle (mm) FS = 2 ~ 4 FS = 5 ~ 8 FS = 10 ~ Half Amplitude Cyclic Rotation (Rad.)

20 Energy Dissipation Vs Permanent Deformation M 0.6 A1 A2 θ Energy Dissipation Ratio EDR = A2 / A1 Uv = s / L Normalized Settlement FS = 2 ~ 4 FS = 5 ~ 8 FS = 10 ~ Half Amplitude Cyclic Rotation (Rad.)

21 Failure Envelopes in V-H-M Space Normalized Moment [F M = M/(V ULT.L)] F M /F H = 1.75 F M /F H = 1.25 F M /F H = 0.42 Cremer et al. (2001) Houlsby and Cassidy (2002) Nova and Montrasio (1991) Normalized Shear [F H = H/V ULT ] F M /F H = 1.25 F M /F H = 1.75 F M /F H = Normalized Vertical Load [F V = V/V ULT ]

22 Footing-Soil Interface Modeling Considers foundation and surrounding soil as a single macro-element Constitutive model that relates the forces (V, H, M) and displacements (s, u, θ) acting at the base center point of the footing macro-element

23 Lateral Cyclic Loading - Animation

24 Forces and Displacements at the Interface

25 Modeling of Moment-Rotation Behavior Internal variables Footing location Current soil surface location (soil_min) Maximum past settlement (soil_max) Current bearing pressure Maximum past pressure experienced

26 Cyclic Moment-Rotation Model

27 Model Simulations - Animation

28 Shear Sliding Modeling: Coupling with V 0 p[i] 1 p[i] = q[i] qult = 1 FS node _ i Fh = H Vult Fh = 1 2 Fv [ 1 Fv] 0 p[i] 1 1 Fv = = FS V Vult

29 Effect of Moment-to-Shear Ratio on Ultimate Capacities 0.15 F M /F H = h/l h/l = 1.75 h/l = 1.25 Normalized Moment [M/(V ULT.L)] FS V = FS V = 2 ~ 5 FS V = 5 ~ 10 FS V = 10 ~ 15 h/l = Normalized Shear [H/V ULT ]

30 Moment-Shear Coupling 0.15 F M /F H = 1.75 F M /F H = 1.25 Gradient Flow Direction Normalized Moment [F M = M/(V ULT.L)] FS V = F M /F H = 0.42 FS V = Normalized Shear (F H = H/V ULT )

31 Shear-Sliding Modeling: Global Coupling with M Fm = M Vult L dθ f _ global = d d _ in d du Fh = H Vult When (d d_in) f_global infinite When (d 0) f_global 0 Fm A Fh B 2 2 = 1 dθ du = Fm Fh B A 2 2 = h L B A 2 2

32 Footing geometry width, B length, L Model Parameters Strength parameters ultimate-to-applied vertical load ratio (FS V ) moment-to-shear ratio Stiffness parameters unloading-reloading vertical stiffness, kv initial shear stiffness, kh rebounding ratio, Rv Soil parameters can be specified as a function of depth (settlement)

33 Model Simulations - (FS = 5)

34 Simulation and Experiment (FS = 5)

35 Model Simulations - (FS = 2.5)

36 Simulation and Experiment (FS = 2.5)

37 Model Simulations - (FS = 7.5)

38 Simulation and Experiment (FS = 7.5)

39 OpenSEES Model Builder Node Element Material Load pattern Constraints Etc. Builds the model Domain Model Builder stores everything Analysis performs analysis Recorder gets the force disp. info. Recorder Nodal displacements Element forces Etc. Records everything that happens in Domain Analysis System of equations Solution algorithm Integrator Etc. Performs analysis in Domain

40 Interface Model in OpenSEES Winkler Model Macro-Element Model

41 Class Hierarchy in OpenSEES OpenSEES DomainComponent Material Analysis Classes Node Element Load BeamColumn 8-node Brick Uniaxial Section Integrator Convergence Test ZeroLengthSection FiberSection SectionForceDeformation SoilFootingSection

42 Accessing the model in OpenSEES section SoilFootingSection -secid -Vult -V -L -Kv -Kh <-nosubnodes -tol> element ZeroLengthSection -eleid -inode -jnode -secid <-orientation> -ndm 2 ndf 3 Vult Ultimate vertical load V Self weight of the structure L Length of the footing Kv Initial vertical stiffness Kh Initial horizontal stiffness Node j (0, 0) Free j Element - ZeroLengthSection Node i (0, 0) i Section - SoilFootingSection Fixed

43 OpenSEES Simulations

44 Frame Shear Wall Foundation System

45 Modifications in OpenSEES Model V is a Constant (Original Model) V is NOT a Constant (Improved Model in OpenSEES)

46 Dynamic Analysis in OpenSEES

47 Summary Footing-soil interface behavior depends on Static vertical factor of safety (FS V ) Applied moment-to-shear ratio Larger FS V Increases the moment capacity Decreases the permanent deformation Larger FS V + Rocking allowed Considerable amount of energy can still be dissipated without degradation in moment capacity

48 Footing-Soil Interface-Element Model is based on the physics, geometry and mechanism of the problem and reproduces the loaddisplacement behavior observed in the experiments Captures the coupled force-displacement relationships in (V-H-M) space with only 4 major model parameters No need for external mesh generation and the model is computationally fast Can be used independently as well as with other structural models to analyse soil-foundation-structure interaction problems

49 Further Work Dynamic finite element analysis in OpenSEES with structural, soil and interface elements Uncertainty analysis Effect of uncertainties in soil properties on model predictions Model simulations for I-shape foundations? Make the model work better!

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