Video lecture for mca ! Edhole
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This document provides an overview of the non-linear Hardening Soil (HS) model and its parameters for computational geotechnics simulations. It describes the HS model's hyperbolic stress-strain curve, stiffness modulus definitions, yield surfaces, plasticity formulations, and the additional cap hardening model. It also shows comparisons of simulated and measured oedometer and triaxial tests on loose and dense sands, demonstrating the HS model's capabilities.
![Plasticity
Flow rule
with
·
· =sinym
·
=sinygp
=sinjm
C [kPa] j’ [o] y [o] E50 [Mpa]
0 30-40 0-10 40
Eur = 3 E50 Vur = 0.2 Rf = 0.9 m = 0.5 Pref = 100 kPa
ev
p
gp
Þp
v
e·
sinym
-sinjcv
1-sinjm
sinjcv
jcv=jp
-yp
Primary soil parameters and standard PLAXIS settings
Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection](https://image.slidesharecdn.com/videolectureformca-140926072622-phpapp01/85/Video-lecture-for-mca-Edhole-13-320.jpg)
Video lecture for mca ! Edhole
- 1. Video Lecture for MCA By: video.edhole.com
- 2. Non-Linear Hyperbolic Model & Parameter Selection Short Course on Computational Geotechnics + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder video.edhole.com
- 3. Contents Introduction Stiffness Modulus Triaxial Data Plasticity HS-Cap-Model Simulation of Oedometer and Triaxial Tests on Loose and Dense Sands Summary Computational Geotechnics Non-Linear Hyperbolic Model video.edhole.com & Parameter Selection
- 4. Introduction Hardening Soils Most soils behave in a nonlinear behavior soon after application of shear stress. Elastic-plastic hardening is a common technique, also used in PLAXIS. Usage of the Soft Soil model with creep Creep is usually of greater significance in soft soils. Rf = qf qa Eur=3E50 Hyperbolic stress strain response curve of Hardening Soil model Computational Geotechnics Non-Linear Hyperbolic Model video.edhole.com & Parameter Selection
- 5. Stiffness Modulus Elastic unloading and reloading (Ohde, 1939) We use the two elastic parameters nur and Eur Definition of E50 in a standard drained triaxial experiment æ è ref ccotj -s3 æ è ref s3 ç E50 =E50 m ' +ccotj pref +ccotj ç m ö ÷ ø æ è ref s3 =E50 ' sinj +ccosj pref sinj +ccosj ç ö ø m ÷ Eur ' ccotj + pref ö ÷ ø Gur = 1 2(1+n) Eur pref=100kPa Initial (primary) loading Computational Geotechnics Non-Linear Hyperbolic Model video.edhole.com & Parameter Selection
- 6. Stiffness Modulus Definition of the normalized oedometric stiffness Values for m from oedometer test versus initial porosity n0 Normalized oedometer modulus versus initial porosity n0 Oedometer tests ref Eoed Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 7. Stiffness Modulus Normalized oedometric stiffness for various soil classed (von Soos, 1991) Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 8. Stiffness Modulus Values for m obtained from triaxial test versus initial porosity n0 Normalized triaxial modulus versus initial porosity n0 ref E50 Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 9. Stiffness Modulus Summary of data for sand: Vermeer & Schanz (1997) Comparison of normalized stiffness moduli from oedometer and Triaxial test ref s y Eoed = Eoed ' pref ref s x E50 = E50 ' pref Engineering practice: mostly data on Eoed Test data: ref »E50 Eoed ref Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 10. Triaxial Data on gp » 2e1 p Equi-g lines (Tatsuoka, 1972) for dense Toyoura Sand Yield and failure surfaces for the Hardening Soil model = qa E50 2e1 q qa-q æ è ref s3 E50=E50 m ' sinj+ccosj pref sinj+ccosj ç ö ÷ ø qf qa= Rf -1 =M(p+ccotj)Rf M= 6sinj 3-sinj Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 11. Plasticity Yield and hardening functions gp =e1 p-e2 p-e3 p »2e1 p =2e1 e = qa -2e1 E50 q qa-q -2q Eur f = qa E50 q qa-q -2q Eur -gp =0 3D extension In order to extent the model to general 3D states in terms of stress, we use a modified expression for in terms of and the mobilized angle of internal friction q q˜ jm ˜ q =s1'+(a-1)s2 3 '-a' sa=3+sinjm 3-sinjm ˜ = 6sinjm f=q˜ -M˜ (p+ccotj) M3-sinjm where Compvutiadtioenaol Gseo.teechdnichs ole.com Non-Linear Hyperbolic Model & Parameter Selection
- 12. Plasticity q* =s1 '+(b-1)s2 3 '-b' s b=3+sinym 3-sinym g=-m y(p+ccot) * M* q M*= 6sinym 3-sinym Plastic potential and flow rule with ê ê ê ê ê · = ep · e1 p · ú ú ú ú ú e2 p · e3 p é ë ù =L · û ¶g ¶s12 12 +L · ¶g ¶s13 13 =L · ê ê ê 12 1 2-1 2siny -1 ú ú ú +L · 2-1 2siny 0 é ë ù û ê ê ê 13 1 2-1 2siny 0 -1 ú ú ú 2-1 2siny é ë ù û Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 13. Plasticity Flow rule with · · =sinym · =sinygp =sinjm C [kPa] j’ [o] y [o] E50 [Mpa] 0 30-40 0-10 40 Eur = 3 E50 Vur = 0.2 Rf = 0.9 m = 0.5 Pref = 100 kPa ev p gp Þp v e· sinym -sinjcv 1-sinjm sinjcv jcv=jp -yp Primary soil parameters and standard PLAXIS settings Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 14. Plasticity Hardening soil response in drained triaxial experiments Results of drained loading: stress-strain relation (s3 = 100 kPa) Results of drained loading: axial-volumetric strain relation (s3 = 100 kPa) Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 15. Plasticity Undrained hardening soil analysis Method A: switch to drained Input: c';j';y' Eref 50 ì í ï ï î nur=0.2;Eur=3E50;m=0.5;pref =100kPa Method B: switch to undrained Input: cu;ju ;y ref E50 ì í ï îï nur=0.2;Eur=3E50;m=0.5;pref =100kPa Compvutiadtioenaol Gseo.teechdnichs ole.com Non-Linear Hyperbolic Model & Parameter Selection
- 16. Plasticity Interesting in case you have data on Cu and not no C’ and f’ 2cu m =E50 m =Eur Eu » 1.4 E50 50 =E50 Eref s3 ' sinju +Cucosju pref sinju +Cucosju æ ç è ö ÷ ø ref =const. +Cucosju æ è ref s3 Eur =Eur ' sinju +Cucosju ç pref sinju ö ÷ ø ref =const. Assume E50 = 0.7 Eu and use graph by Duncan & Buchignani (1976) to estimate Eu Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 17. Plasticity Hardening soil response in undrained triaxial tests Results of undrained triaxial loading: stress-strain relations (s3 = 100 kPa) Results of undrained triaxial loading: p-q diagram (s3 = 100 kPa) Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 18. HS-Cap-Model fc=q˜ 2 M2+p2-pc 2 gc=fc · = p · ep v Kc - p · Ks (Associated flow) =1 H p · H= Kc Ks-Kc Ks Cap yield surface Flow rule Hardening law For isotropic compression we assume with Compvutiadtioenaol Gseo.teechdnichs ole.com Non-Linear Hyperbolic Model & Parameter Selection
- 19. HS-Cap-Model For isotropic compression we have q = 0 and it follows from p · =p · ¶g ¶pc · =HL · For the determination of, we have another consistency condition: c p · v =Hep cc =2HL · cp T · c=¶fc f ¶s +¶fc ¶pc s · p · c=0 Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 20. HS-Cap-Model Additional parameters The extra input parameters are K0 (=1-sinf) and Eoed/E50 (=1.0) The two auxiliary material parameter M and Kc/Ks are determined iteratively from the simulation of an oedometer test. There are no direct input parameters. The user should not be too concerned about these parameters. Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 21. HS-Cap-Model 1 Graphical presentation of HS-Cap-Model I: Purely elastic response II: Purely frictional hardening with f III: Material failure according to Mohr-Coulomb IV: Mohr-Coulomb and cap fc V: Combined frictional hardening f and cap fc VI: Purely cap hardening with fc VII: Isotropic compression 2 3 Yield surfaces of the extended HS model in p-q space (left) and in the deviatoric plane (right) Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 22. HS-Cap-Model s1 = s2 = s3 Yield surfaces of the extended HS model in principal stress space Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 23. Simulation of Oedometer and Triaxial Tests on Loose and Dense Sands Comparison of calculated () and measured triaxial tests on loose Hostun Sand Comparison of calculated () and measured oedometer tests on loose Hostun Sand Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 24. Simulation of Oedometer and Triaxial Tests on Loose and Dense Sands Comparison of calculated () and measured triaxial tests on dense Hostun Sand Comparison of calculated () and measured oedometer tests on dense Hostun Sand Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection
- 25. Summary Main characteristics •Pressure dependent stiffness •Isotropic shear hardening •Ultimate Mohr-Coulomb failure condition •Non-associated plastic flow •Additional cap hardening HS-model versus MC-model As in Mohr-Coulomb model Normalized primary loading stiffness Unloading / reloading Poisson’s ratio Normalized unloading / reloading stiffness Power in stiffness laws Failure ratio c,j,y ref E50 nur ref Eur m Rf Computational Geotechnics Non-Linear Hyperbolic Model videos.edhole.com & Parameter Selection