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.
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In this project, quintic polynomials were used to perform platooning in nonholonomic robots. Both hardware and simulations results have been presented.
Sachpazis: Strip Foundation Analysis and Design example (EN1997-1:2004)Dr.Costas Sachpazis
Strip Foundation Analysis and Design example, in accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values
Platoon Control of Nonholonomic Robots using Quintic Bezier SplinesKaustav Mondal
In this project, quintic polynomials were used to perform platooning in nonholonomic robots. Both hardware and simulations results have been presented.
Sachpazis: Strip Foundation Analysis and Design example (EN1997-1:2004)Dr.Costas Sachpazis
Strip Foundation Analysis and Design example, in accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values
PROPAN - Potential Flow Code for Foils and Rotors: PROPAN is short for Propeller Panel Method. PROPAN is a panel code for the calculation of steady and unsteady potential flow around foils, open and ducted propellers, and wind and marine current turbines. PROPAN was developed by MARETEC (Marine and Environmental Technology Research Centre) at Instituto Superior Técnico (IST) which belongs to Lisbon University.
Determination Of Geometric Stress Intensity Factor For A Photoelastic Compac...Anupam Dhyani
Experimental and analytical studies with finite elements was done on a polycarbonate transparent material as a forerunner to a similar study on transparent glass -epoxy composites
International Conference of Fracture 2017: A procedure to determine the fracture properties of nuclear cladding from ring compression tests. A parametric study
Transient three dimensional cfd modelling of ceilng fanLahiru Dilshan
Ceiling fans are used to get thermal comfort, especially in tropical countries. With the increment of the usage of air conditioners, the emission of CO2 is increased. But ceiling fans are a limited solution, that saves much energy compared to air conditioners. Ceiling fans generate a non-uniform velocity profile, so that, there is a non-uniform thermal environment. That non-uniform environment does not imply lower thermal comfort, that will give enough thermal comfort with low energy cost by air velocity. Hence, there will be difficulties of analysing with simple modelling techniques in that environment. So, to predict the performance of the ceiling fan required more accurate models.
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Apresentação de Victor Manuel Salazar Araque, da Computer Modelling Group, durante o evento promovido pelo Sistema FIEB, Fundamentos da Exploração e Produção de Não Convencionais: a Experiência Canadense.
Increasing life of spur gears with the help of finite element analysisijmech
The Focus of this research is on mathematical analysis of life of gears and reducing noise frequency of gears due to change of material from C-45 to 19mncr5. Calculations for gears life was done with the help of Lewis equation and Buckingham formula. Basically life of a gear is depending upon the stress, more the stress on gear lesser life of gear will be. In this paper some major condition to perform a gear without failure is achieved i.e. tangential force should be less than tangential load to sustain static load, dynamic
load should be less than endurance load to sustain dynamic load and wear load should be less than static
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Pullout Behavior of Geotextiles: Numerical PredictionIJERA Editor
The mechanism of soil-geosynthetic interaction is usually complex and depends on the nature of the reinforcement, as well as on the characteristics of the surrounding soil. The strength parameters of the interface are the key for the design of reinforced soil slopes. Usually, these parameters are defined from laboratory pullout tests. The absence of test results implies on conservative assumptions and higher costs. The possibility of using computer programs for analyzing the load transfer mechanism arises as an attractive design tool. This paper presents the numerical simulation of pullout tests, conducted in large equipments. The numerical predictions of the load and displacement distribution along the geosynthetic length were compared to instrumented test results, available in the literature. The analyses revealed to be satisfactory and consistent with the experimental results. Thus, it becomes possible to reduce the uncertainties in the design of the anchorage length for the reinforcement by previously performing studies with computer programs that simulates stress x strain behavior of geotechnical problems.
Introduction to Hypo plasticity, Modelling Approach, What is Hypo-plasticity, ?Why Hypo-plasticity?, Constitutive Equations, Applications of Hypo-plasticity, Influence parameters, Research Trends in Hypo-plasticity, Constitutive methods- GTE, IIT Kanpur- Geo tech, Term Paper
A Numerical Study on the Application of BEM to Steady Cavitating Potential Fl...João Baltazar
This study addresses some numerical aspects of the implementation of a low-order Boundary Element Method (BEM) for three-dimensional steady potential flow calculations on lifting surfaces with partial cavitation.
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The study focuses on the efficiency improvement due to an alternative iterative procedure to solve the linear system of equations resulting from the formulation of the cavitating flow problem. Usually, the solution of the problem for a given cavitation number is to iterate on the cavity length. For each iteration step a new linear system of equations is solved for the unknown source strengths on the cavity and the unknown potentials on the wetted part. The solution is obtained for given potentials on the cavity, known from the dynamic boundary condition and for given sources on the wetted part, known from the kinematical boundary condition. This implies the solution of a large system of equations (at least one matrix inversion) for each iteration step on the cavity length.
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Numerical studies were carried out for the MARIN S-Propeller and results compared with other methods [1]. The procedure converged for all cases to the solution of the original coupled system. A large reduction in computational time is achieved with the alternative procedure for the cavity potential flow solution.
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Biological screening of herbal drugs: Introduction and Need for
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for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
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Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
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Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
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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