LEC-2 CL 601 Constitutive Modelling Introduction.pptx

Constitutive modelling of soil;
Introduction;
Intro. Constitutive modelling;
different types of modelling;
complexities-soil behavior;
Geotechnical Engineering . Problems;
Boundary value problems;
continuum mechanics;
laboratory tests;
response of geomaterials;
reference books;
Lecture notes; M Tech geotechnical Engineering;

1. Constitutive Modelling of Geomaterials Prof. Samirsinh P Parmar Mail: [email protected] Asst. Prof. Department of Civil Engineering, Faculty of Technology, Dharmasinh Desai University, Nadiad , Gujarat, INDIA Lecture: 2 : Constitutive Modelling Introduction

2. 1. Introduction Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 2

3. A model is an appropriate simplification of reality …Engineering is fundamentally concerned with modeling. Engineering is concerned with finding solutions to real problems F we need to be able to see through to the essence of the problem and identify the key features which need to be modeled F which is to say those features of which we need to take account and include in the design . M. Wood, 2004 Why modeling is required ? Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 3

4. Geological modeling Physical modeling Empirical modeling Theoretical modeling Constitutive modeling Numerical modeling Different types of modelling Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 4

5. Complexities of the mechanical behaviour of soils Soils are very complex materials to describe mathematically. They are: Multiphase (consist of solids, liquids and gases); Granular (built of particles of different sizes and shapes); Non-homogeneous (their mechanical properties vary in space); Anisotropic (their mechanical properties vary with loading direction) . 5 Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA

6. Geotechnical Engineering problems Foundations – Bearing capacity and settlement Shallow D ee p Foundations Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 6

7. Geotechnical Engineering problems Retaining structures – Earth pressure and displacement Gravity Cantilever Anchored Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 7

8. Geotechnical Engineering problems Slope and excavation – Stability Slope Open excavation Tunn e l Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 8

9. Geotechnical Engineering problems GeoFenvironmental problems– Weathering and erosion

10. Geotechnical Engineering problems GeoFenvironmental problems– Energy & environment issues Energy Recovery CO 2 Sequestration Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 10

11. Geotechnical Modelling Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 11

12. Boundary value problems ( BVP ) Initial Value Problem (IVP) e.g. y" + y = sin x , y (0) = 1, y' (0) = – 2 Complex systems of differential equations are solved by discretizing with Finite element method (FEM) or Finite difference method (FDM). A Boundary value problem is a system of differential equations with solution and derivative values specified at more than one point. e.g . y" + y = sin x , y (0) = 1, y (1) = – 2 Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 12

13. Continuum mechanics In the study of classical mechanics we make the simplifying assumption, for analysis purposes, that the matter is distributed continuously, without gaps or empty space s (i.e. , we disregar d the molecular structur e o f matter). Suc h a hypothetical continuous matter is termed a continuum . A mathematical study of mechanics of such an idealized continuum is called continuum mechanics . Continuum mechanics deals with deformable bodies, as opposed to rigid bodies. Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 13

14. Continuum mechanics Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 14

15. Boundary value problems ( BVP ) Constitutive relationships are normally derived from the stressFstrain data determined in laboratory tests on material samples. A test is called elementary, if the stresses and strains in the test are the same at any point in the sample. Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 15

16. Laboratory tests Oedometric compression test  r  Drained triaxial compression test  r  Undrained triaxial compression test  v  Hydrostatic compression test  a   r Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 16

17. Issues with geomaterials Typical Examples Soils Rocks Building Stones (e.g., masonry, concrete) Granular Materials (sands, powders, cereals, etc.) Key Features Discrete assemblies of particles, packets or minerals. Heterogeneous grain size (particle size, minerals, etc.). CohesiveFFrictional two contributions for the shearing resistance. Porous voids, cracks, etc. Multiphase mixtures of solids, liquids and gases. Chemically Active chemistry of the fluid; type of mineral. Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 17

18. Issues with geomaterials Geomaterials: Discrete/Heterogeneous Media All materials have a discrete nature, depending on the scale at which they are observed. This discrete connotation is fundamental in determining their engineering properties. Granitic Rock Beach Sand Compacted Clay Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 18

19. Issues with geomaterials Geomaterials: Discrete/Heterogeneous Media http://dutcgeo.ct.tudelft.nl/allersma/ diskvideo6.avi The notion of continuum requires the identification of the size at which microscopic discrete/heterogeneous effects are homogeneously smeared across the volume. Representative Elementary Volume ( REV ) Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 19

20. Geomaterials: Porous/Multiphase Media Issues with geomaterials Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 20

21. Issues with geomaterials The main mechanical implication of the porous/fluidF infiltrated nature of geomaterials is the concept of effective stresses.      u Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 21

22. Mechanical Behaviour of Soil Possesses such features as: Non-linearity ( in initial loading, unloading and reloading ); Irreversibility ( produces residual strains in a closed stress cycle ); Hysteresis of unloading-reloading and memory ( remembers the highest stress before the unloading and follows the initial loading curve after reaching it in reloading ); Stress path dependency ( reaches the same stress at different strains ); Rate dependency ( different stress-strain curves at various strain rates ); Time dependency ( creep, aging, relaxation ). 22 Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA

23. Responses of geomaterials Non linearity (in initial loading, unloading and reloading); Irreversibility (produces residual strains in a closed stress cycle); Hysteresis of unloading reloading and memory (remembers the highest stress before the unloading and follows the initial loading curve after reaching it in reloading); Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 23

24. Stress path dependency (reaches the same stress at different strains); Rate dependency (different stressFstrain curves at various strain rates); Time dependency (creep, aging, relaxation). Responses of geomaterials Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 24

25. Responses of geomaterials Clay Strain hardening Strain Softening Sand Prof. Samirsinh P Parmar / Dept.of Civil Engg ./ DDU Nadiad , INDIA 25

26. References/Books … Prof. Samirsinh P Parmar/Dept.of Civil Engg./ DDU Nadiad, INDIA 26

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