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Modelling of Soil behaviour

Sarvesh Chandra

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TWO APPROACHES

• CONTINUUM APPROAH - Elastic, Elastoplastic, Hypoplastic, Non-homogeneous, anisotropic, layered soils --- Complex Mathematics

• MOELLING APPROACH - Simple, Determining Model Parameters is a problem --- Simple Mathematics

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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

Winkler Model

Winkler Model

Winkler’s idealization represents the soil medium as asystem of identical but mutually independent, closelyspaced, discrete, linearly elastic springs.

According to this idealization, deformation of foundationdue to applied load is confined to loaded regions only.

Figure shows the physical representation of the Winklerfoundation.

The pressure–deflection relation at any point is given by p= kw, where k = modulus of subgrade reaction.

Winkler Model

Winkler, assumed the foundation model toconsist of closely spaced independentlinear springs.If such a foundation is subjected to a

partially distributed surface loading, q, thesprings will not be affected beyond theloaded region.

Winkler Model For such a situation, an

actual foundation isobserved to have thesurface deformation asshown in Figure.

Hence by comparing thebehaviour of theoreticalmodel and actualfoundation, it can be seenthat this model essentiallysuffers from a completelack of continuity in thesupporting medium.

The load deflectionequation for this case canbe written as p = kw

Winkler Models

Limitations of Winkler Model According to this idealization,

deformation of foundationdue to applied load isconfined to loaded regionsonly.

A number of studies in thearea of soil–structureinteraction have beenconducted on the basis ofWinkler hypothesis for itssimplicity.

The fundamental problemwith the use of this model isto determine the stiffness ofelastic springs used toreplace the soil belowfoundation.

Limitations of Winkler Model According to this idealization,

deformation of foundationdue to applied load isconfined to loaded regionsonly.

A number of studies in thearea of soil–structureinteraction have beenconducted on the basis ofWinkler hypothesis for itssimplicity.

The fundamental problemwith the use of this model isto determine the stiffness ofelastic springs used toreplace the soil belowfoundation.

Limitations of Winkler ModelA number of studies in the area of soil–

structure interaction have been conducted onthe basis of Winkler hypothesis for itssimplicity. The fundamental problem with theuse of this model is to determine the stiffnessof elastic springs used to replace the soilbelow foundation.

The problem becomes two-fold since thenumerical value of the coefficient of subgradereaction not only depends on the nature of thesubgrade, but also on the dimensions of theloaded area as well.

Limitations of Winkler ModelSince the subgrade stiffness is the only

parameter in the Winkler model toidealize the physical behaviour of thesubgrade, care must be taken todetermine it numerically to use in apractical problem.Modulus of subgrade reaction or the

coefficient of subgrade reaction k is theratio between the pressure p at anygiven point of the surface of contact andthe settlement y produced by the load atthat point:

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Terzaghi (1955) introduced the Coefficient or Modulus of Subgrade Reaction

kg/m• Width of Footing• Shape of Footing• Embedment Depth of Footing

yqks

Limitations of Winkler Model The value of subgrade modulus may be obtained in the

following alternative approaches:

Two Parameter Elastic Models

Filanenko Borodich ModelThis model requires continuity between the individual spring elements in theWinkler's model by connecting them to a thin elastic membranes under aconstant tension T.

Filanenko Borodich ModelThis model requires continuity between the individual springelements in the Winkler's model by connecting them to a thinelastic membranes under a constant tension T.

Concentrated Load

Filanenko Borodich ModelThis model requires continuity between the individual springelements in the Winkler's model by connecting them to a thinelastic membranes under a constant tension T.

Rigid Load

Filanenko Borodich ModelThis model requires continuity between the individual springelements in the Winkler's model by connecting them to a thinelastic membranes under a constant tension T.

Uniform Flexible Load

Filanenko Borodich ModelThe response of the model can be expressedmathematically as follows:

Hence, the interaction of the spring elements is characterized by the intensity of the tension T

in the membrane.

Hetenyi’s ModelThis model suggested in the literature can be regarded as afair compromise between two extreme approaches (viz.,Winkler foundation and isotropic continuum). In this model,the interaction among the discrete springs is accomplishedby incorporating an elastic beam or an elastic plate, whichundergoes flexural deformation only

Hetenyi’s Model

Pasternak Model• In this model, existence of shear interaction among the

spring elements is assumed which is accomplished byconnecting the ends of the springs to a beam or plate thatonly undergoes transverse shear deformation.

• The load–deflection relationship is obtained byconsidering the vertical equilibrium of a shear layer.

Pasternak Model

The pressure–deflection relationship is given by

Pasternak Model

The continuity in this model ischaracterized by the consideration ofthe shear layer.

A comparison of this model with that ofFilonenko–Borodich implies theirphysical equivalency (‘‘T’’ has beenreplaced by ‘‘G’’).

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Kerr ModelA shear layer is introduced in the Winkler foundation andthe spring constants above and below this layer isassumed to be different as per this formulation.

The following figure shows the physical representation ofthis mechanical model. The governing differential Fig. 4.Hetenyi foundation [30]. equation for this model may beexpressed as follows.

Kerr ModelThe governing differential equation for this model may beexpressed as follows.

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Elasto-Plastic Model (Rhines, 1969)

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Modelling of Reinforced Granular Beds

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Different type of reinforcements• Geotextiles (GT) •Geogrids (GG)

•Very versatile in their primary function • Focuses entirely on reinforcementapplications, e.g., walls, steep slopes,base and foundation reinforcement

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•Geonets (GN) •Geomembranes (GM)

• Function is always in drainage • Function is always containment• Represents a barrier to liquids and gases

Major Functions of Geosynthetics

• Reinforcement• Separation• Filtration• Drainage• Moisture barrier

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Applications

• Foundation for motorways, airports, railroads, sports fields, parking lots, storage capacities

• Slope stability• Confinement• Environmental Concerns• Dams and Embankments• Low cost housing

Applications of Geosynthetics

Improved subgrade or roadbase performance

Applications of Geosynthetics

Reinforcement of soils by Geotextiles

Applications of Geosynthetics

Railroad stabilization by Geogrids

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• Interfacial shear mobilization effects• Membrane effect of the reinforcement• Confinement effect of the reinforcement• Reinforcement effect of the fill• Separation effect of the fill and the soft soil

Load Transfer Mechanism of Geosynthetic-Reinforced Soil

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A - Soft Soil B - Granular fill R - Failure planes H - Deformed profile M - Soil cracking Q - Stress distribution G1 Tensar gridG2 - Geomembrane

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Use of Geotextiles for foundationBangkok Highway project

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Modelling of reinforced Granular Beds

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• Assumptions

– 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

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Madhav and Poorooshasb (1988)

Definition Sketch Proposed Model

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Free Body Diagram

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Equations for the proposed model:

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Boundary conditions:

For an unstretched 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.

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• 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.

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• 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.

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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.

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Effect of compaction of the Granular layer

Interlocking of stresses on compaction - similar to over consolidated clay behaviour

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Shukla and Chandra (1995)

Definition Sketch

Pretensioning the Reinforcement Layer

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Compressibility of Granular fill

Pasternak Shear layer forGranular material

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Time dependent behaviour of soft clay

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Thank You.