LEC-8 CL 601 Modelling Soil Behaviour.pptx

Constitutive modelling of Soil;
Constitutive modelling;
Modelling soil behaviour;
Continuum approach;
Winkler Model;
Coefficient of Subgrade Reaction;
Filanenko Borodich Model;
Two Parameter Elastic Models;
Hetenyi’s Model;
Pasternak Model;
Kerr Model;
Elasto-Plastic Model (Rhines);
Modelling of Reinforced Granular bed;
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 : 8 : Modelling of Soil behaviour

2. TWO APPROACHES 2 CONTINUUM APPROAH - Elastic, Elastoplastic, Hypoplastic, Non- homogeneous, anisotropic, layered soils --- Complex Mathematics MOELLING APPROACH - Simple, Determining Model Parameters is a problem --- Simple Mathematics Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India

3. The Winkler Model -Winkler (1867) P( x,y ) = k w( x,y ) Discrete, independent, linear elastic springs Simple to use Lacks continuity amongst springs Soil behaviour is linear in general 3 Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India

4. W inkler Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 4

5. W inkler Model Winkle r ’ s i dealization represents t he soil medium as a system of identical but mutually independent, closely spaced, discrete, linearly elastic springs. According to this idealization, deformation of foundation due to applied load is confined to loaded regions only. Figure shows the physical representation of the Winkler foundation. The pressure–deflection relation at any point is given by p = kw , where k = modulus of subgrade reaction. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 5

6. W inkler Model  Winkler, assumed the foundation model to consist of closely spaced independent linear springs .  If such a foundation is subjected to a partially distributed surface loading, q, the springs will not be affected beyond the loaded region. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 6

7. W inkler Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 7 For such a situation, an actual foundation is observed to have the surface deformation as shown in Figure . Hence by comparing the behaviour of theoretical model and actual foundation , it can be seen that this model essentially suffers from a complete lack of continuity in the supporting medium. The load deflection equation for this case can be written as p = kw

8. W inkler Models Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 8

9. Limitation s o f W inkle r Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 9 According to this idealization, deformation of foundation due to applied load is confined to loaded regions only . A number of studies in the area of soil–structure interaction have been conducted on the basis of Winkler hypothesis for its simplicity . The fundamental problem with the use of this model is to determine the stiffness of elastic springs used to replace the soil below foundation .

10. Limitation s o f W inkle r Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 10 A number of studies in the area of soil– structure interaction have been conducted on the basis of Winkler hypothesis for its simplicity . The fundamental problem with the use of this model is to determine the stiffness of elastic springs used to replace the soil below foundation . The problem becomes two-fold since the numerical value of the coefficient of subgrade reaction not only depends on the nature of the subgrade , but also on the dimensions of the loaded area as well.

11. Limitation s o f W inkle r Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 11 Since the subgrade stiffness is the only parameter in the Winkler model to idealize the physical behaviour of the subgrade , care must be taken to determine it numerically to use in a practical problem . Modulus of subgrade reaction or the coefficient of subgrade reaction k is the ratio between the pressure p at any given point of the surface of contact and the settlement y produced by the load at that point:

12. Terzaghi (1955) introduced the Coefficient or Modulus of Subgrade Reaction kg/m W idth o f Footing Shap e o f Footing E mbedmen t Dept h o f Footing y  q k s Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 12

13. Limitation s o f W inkle r Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 13 The value of subgrade modulus may be obtained in the following alternative approaches:

14. Coefficient of Subgrade Reaction Plate load test for coefficient of subgrade reaction. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 14

15. Coefficient of Subgrade Reaction Definition of Coefficient of subgrade Reaction. K s = q/ δ K s = coefficient of subgrade reaction. Unit of force/ length 3 . q = bearing pressure δ = settlement Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 15

16. Application of coefficient of subgrade reaction to larger mats. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 16 Coefficient of Subgrade Reaction

17. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 17 Portions of the mat that experience more settlement produce more settlement produce more compression in the springs. Sum of these springs must equal the applied structural loads plus the weight of the mat. Coefficient of Subgrade Reaction

18. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 18 Non-Linear Characteristics of Soil Deformation

19. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 19 Determining the Co-efficient of Subgrade Reaction Not a straight forward process due to: Width of the loaded area; wide mat will settle more then a narrow one because more soil is mobilized by a wide mat

20. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 20 Determining the Co-efficient of Subgrade Reaction Not a straight forward process due to: Depth of the loaded area below the ground surface. Change is stress in the soil due to q is a smaller percentage of the initial stress at shallow depth.

21. T wo Paramete r Elastic Models Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 21

22. Filanenko Borodic h Model This model requires continuity between the individual spring elements in the Winkler's model by connecting them to a thin elastic membranes under a constant tension T. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 22

23. Filanenko Borodic h Model This model requires continuity between the individual spring elements in the Winkler's model by connecting them to a thin elastic membranes under a constant tension T. Concentrate d Load Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 23

24. Filanenko Borodic h Model This model requires continuity between the individual spring elements in the Winkler's model by connecting them to a thin elastic membranes under a constant tension T. Rigi d Load Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 24

25. Filanenko Borodic h Model This model requires continuity between the individual spring elements in the Winkler's model by connecting them to a thin elastic membranes under a constant tension T. Unifor m Flexible Load Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 25

26. Filanenko Borodic h Model Hence, the interaction of the spring elements is characterized by the intensity of the tension T in the membrane. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 26 The response of the model can be expressed mathematically as follows:

27. Hetenyi ’ s Model This model suggested in the literature can be regarded as a fair compromise between two extreme approaches (viz., Winkler foundation and isotropic continuum). In this model, the interaction among the discrete springs is accomplished by incorporating an elastic beam or an elastic plate, which undergoes flexural deformation only Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 27

28. Hetenyi ’ s Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 28

29. Pasterna k Model In this model, existence of shear interaction among the spring elements is assumed which is accomplished by connecting the ends of the springs to a beam or plate that only undergoes transverse shear deformation. The load–deflection relationship is obtained by considering the vertical equilibrium of a shear layer. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 29

30. Pasterna k Model The pressure–deflectio n relationshi p i s give n by

31. Pasterna k Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 31 The continuity in this model is characterized by the consideration of the shear layer. A comparison of this model with that of Filonenko – Borodich implies their physical equivalency (‘‘T’’ has been replaced by ‘‘G’’).

32. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 33

33. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 34

34. Ker r Model A shear layer is introduced in the Winkler foundation and the spring constants above and below this layer is assumed to be different as per this formulation. The following figure shows the physical representation of this mechanical model. The governing differential Fig. 4. Hetenyi foundation [30]. equation for this model may be expressed as follows. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 34

35. Ker r Model The governing differential equation for this model may be expressed as follows.

36. Elasto-Plastic Model (Rhines, 1969) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 37

37. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 38

38. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 39

39. Modelling of Reinforced Granular Beds Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 39

40. Differen t type o f reinforcements Geotextiles (GT) • Geogrid s (GG) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 41 • V er y v ersatile in thei r primary f unction Focuses entirely on reinforcement applications, e.g., walls, steep slopes, base and foundation reinforcement

41. • Geonet s (GN) • Geomembr anes (GM) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 42 Function is al w a ys in d r ainage Function is al w a ys containment R ep r esent s a barrier to liquids and gases

42. Major Functions of Geosynthetics R einforcement S eparation F iltration D rainage Moistur e barrier Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 42

43. Applications Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India Foundation for motorways, airports, railroads, sports fields, parking lots, storage capacities Slope stability Confinement Environmental Concerns Dams and Embankments Low cost housing 43

44. Application s o f Geosynthetics Improved subgrad e or roadbase performance Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 44

45. Application s o f Geosynthetics Reinforcemen t o f soil s b y Geotextiles Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 45

46. Application s o f Geosynthetics Railroad stabilization b y Geogrids Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 46

47. 3/12/2014 Interfacial shear mobilization effects Membrane effect of the reinforcement C onfinement effect of the reinforcement R einforcement effect of the fill S eparation effect of the fill and the soft soil Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India Load Transfer Mechanism of Geosynthetic- Reinforced Soil 47

48. A - Soft Soil B - Granular fill R - Failure planes H - Deformed profile M - Soil cracking Q - Stress distribution G1 Tensar grid G2 - Geomembrane Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 48

49. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 49

50. Use of Geotextiles for foundation Bangkok Highway project Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 50

51. Modelling of reinforced Granular Beds Prof. Samirsinh P Parmar , CL-DDU, Gujarat, India 51

52. A ssumptions Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India Geosynthetic reinforcement is linearly elastic, rough enough to prevent slippage at the soil interface and has no shear resistance, and thickness of reinforcement is neglected Spring constant has constant value irrespective of depth and time The rotation of reinforcement is small 52

53. Madhav an d Poorooshasb (1988) Definitio n S k etch P r oposed Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 54

54. F r e e B ody Diag r a m Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 55

55. Equations for the proposed model: Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 56

56. Boundary conditions: For an upstretched membrane at x=L: T=0 and the shear stress = 0. For uniform load of intensity q, from symmetry, at x = 0, dw /dx = 0. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 57

57. Settlement Response of a Reinforced Shallow earth bed by C. Ghosh and M.R. Madhav (1994)- Membrane effect of Reinforced layer, Non-linear response of the granular layer and soft soil, plane strain condition. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 58

58. Reinforced Granular Fill-Soft Soil system: Confinement Effect by C. Ghosh & M.R. Madhav (1994) -Quantified in terms of average increase in confining pressure due to modified shear stiffness of the granular soil surrounding the reinforcement. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 59

59. Madhav and Poorooshasb (1989) Modifications: To study the influence of the membrane in increasing the lateral stress in the former model some modifications have been made. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 59

60. Effect of compaction of the Granular layer Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 61 Interlocking of stresses on compaction - similar to over consolidated clay behavior

61. Shukla an d Chandr a (1995) Defin i tio n S k etch Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 62 Pretensioning the Reinforcement Layer

62. Compressibility of Granular fill Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 63 Pasternak Shear layer for Granular material

63. P r oposed Model Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 64 T ime dependent behaviour of soft clay

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