comparison of current design methods for granular...

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Kansas City Geotechnical Conference - 2013

Comparison of Current Design Methods for Granular & Grouted Inclusions

Brandon BUSCHMEIER


GROUND IMPROVEMENT TECHNIQUES

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Rapid Impact CompactionVibro-Densification

Dynamic Compaction

DENSIFY

Rapid Impact CompactionVibro-Densification

Dynamic Compaction

DENSIFY

Vacuum ConsolidationWick Drains + Surcharge

CONSOLIDATE

Vacuum ConsolidationWick Drains + Surcharge

CONSOLIDATE

Soil Mixing / Jet GroutingRigid Inclusions / CMC / VCC

Stone Columns / Aggregate Piers / DR

STIFFEN

Soil Mixing / Jet GroutingRigid Inclusions / CMC / VCC

Stone Columns / Aggregate Piers / DR

STIFFEN

Differences in Design Methodology between Granular & Grouted Inclusions

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Kansas City Geotechnical Conference - 2013 3

Stone ColumnsAggregate Piers ( Geopiers / VibroPiers )

Dynamic Replacement

GRANULAR

Stone ColumnsAggregate Piers ( Geopiers / VibroPiers )

Dynamic Replacement

GRANULAR

Deep Soil MixingJet Grouting

Vibro-Concrete ColumnsControlled Modulus Columns

GROUTED

Deep Soil MixingJet Grouting

Vibro-Concrete ColumnsControlled Modulus Columns

GROUTED



GROUND IMPROVEMENT CHALLENGES &

MITIGATIONS

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DifferentialTotal

SETTLEMENT

DifferentialTotal

SETTLEMENT

SandSilts / Clays

LIQUEFACTION

SandSilts / Clays

LIQUEFACTION


EmbankmentsFooting

Local / Global

BEARING CAPACITY

EmbankmentsFooting

Local / Global

BEARING CAPACITY

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EmbankmentsFooting

Local / Global

BEARING CAPACITY

EmbankmentsFooting

Local / Global

BEARING CAPACITY

THE PRESSURE THAT A STRUCTURE / FOUNDATION /

EMBANKMENT CAN APPLY ON THE SOIL WITHOUT CAUSING

OVERSTRESSING (SHEAR FAILURE )


Internal Stability of the Inclusions:

Failure by Lateral Expansion (Bulging)Failure by ShearingFailure by Punching

GRANULAR INCLUSIONS


GRANULAR INCLUSIONS


RIGID INCLUSIONS


RIGID INCLUSIONS


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Bearing Capacity of Footings:

BEARING CAPACITY UNDER FOOTINGS – GRANULAR COLUMNSBEARING CAPACITY UNDER FOOTINGS – GRANULAR COLUMNS


Terzaghi (1943) showed that :

Strip : Qult = c Nc + Df.Ng + 0.5B..N

Square : Qult = 1.2 c Nc + Df.Ng + 0.4B..N

Circular : Qult = 1.2 c Nc + Df.Ng + 0.3B..N

With:

Nq = e tan tan2 ( 45 + /2 )

Nc = ( Nq-1) cot

Several expressions proposed for N

Meyerhoff : N Nq-1) tan ( 1.4



Shear Strain CompatibilityHomogenized Soil Characteristics

GRANULAR INCLUSIONS


GRANULAR INCLUSIONS

The inclusions carry a large part of the load and are internally stable.

The soil is “unloaded” as compared to the same footing without

improvement.

RIGID INCLUSIONS

The inclusions carry a large part of the load and are internally stable.


improvement.

RIGID INCLUSIONS


with

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Simplified Approach : Verify that the load on the footing is less than the combination of :

1. Bearing capacity of the soilAND

2.The reaction from the Rigid inclusion at the top of the rigid inclusions

The rigid inclusions are “unloading” the soil

BEARING CAPACITY UNDER FOOTINGS – RIGID INCLUSIONS

Simplified Approach : Verify that the load on the footing is less than the combination of :

1. Bearing capacity of the soilAND

2.The reaction from the Rigid inclusion at the top of the rigid inclusions

The rigid inclusions are “unloading” the soil

BEARING CAPACITY UNDER FOOTINGS – RIGID INCLUSIONS


Load on Footing < bearing capacity of soil + reaction from rigid inclusion


Embankment Stability:

EMBANKMENT STABILITY- REMINDEREMBANKMENT STABILITY- REMINDER


F = Driving Forces / Resisting Forces

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GRANULAR INCLUSIONS


GRANULAR INCLUSIONS

The inclusions carry a large part of the load and are internally stable


improvement

RIGID INCLUSIONS

The inclusions carry a large part of the load and are internally stable


improvement

RIGID INCLUSIONS


with



EMBANKMENT STABILITY– GRANULAR INCLUSIONSEMBANKMENT STABILITY– GRANULAR INCLUSIONS


Each granular inclusion intercepting the failure surface provides additional shear resistance because of :- Higher friction angle- Higher vertical load in the column

The problem is simplified by assuming equivalent characteristics

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EMBANKMENT STABILITY– GRANULAR INCLUSIONSEMBANKMENT STABILITY– GRANULAR INCLUSIONS


The block of equivalent improved soil is here seen in light blue



EMBANKMENT STABILITY – RIGID INCLUSIONSEMBANKMENT STABILITY – RIGID INCLUSIONS


Same principle as under footing :- The rigid inclusion provide three effects :

1. “Unloading” of the soils between the inclusions2. Increased shear resistance along the failure plane3. Vertical force across the failure plane similar to soil nailing

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In the absence of easy analytical methods, FEM analysis is therefore widely used to model embankments on rigid inclusions

1. Axisymmetric model not feasible

2. 2D Plane strain possible but need to adapt model:

• Rigid Inclusions = “Thin wall” => need to change EI and EA for equivalent wall • “Thin wall” surface area is larger => need to change interface





2D plane strain gives a good approximation of deformations- Tends to over-estimate the load transfer to the rigid inclusions

Limitations of FEM Modeling- Not easy to obtain the factor of safety against failure - C-Phi analysis can be done but it has limitations

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Settlement

Equal Settlement Planes / Strain compatibilityLateral expansion of column

Load transfer function of area replacement ratio

GRANULAR INCLUSIONS

Equal Settlement Planes / Strain compatibilityLateral expansion of column

Load transfer function of area replacement ratio

GRANULAR INCLUSIONS

Equal plane strainLoad transfer through arching

Load transfer through negative skin friction

RIGID INCLUSIONS



RIGID INCLUSIONS


up us

Equal settlement planes

bulging


Settlement

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GRANULAR INCLUSIONSGRANULAR INCLUSIONS


Several methods of calculation have been proposed but they all rely on the principle that the modulus of deformation of the aggregate inclusions and the surrounding soil are “compatible” • 5 < Ec / Es / 10• The settlement are

equal between the column and the soil

• Horizontal planes remain horizontal while the settlement occurs

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Settlement

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From Conservation of Load :

The ratio of stresses “n” is a fundamental parameter in all the calculation methods

Typically : 3 < n < 10


Settlement

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All the methods define the settlement reduction factor as :

The factor is the best indication of the effectiveness of the design

Typically : 2 < < 5

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Settlement

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PURELY ELASTIC METHODS :

HOMOGENEIZATION METHOD

In the case of a purely elastic model, writing Hook’s law together with the conservation of load and the hypothesis of strain compatibility leads to :



Settlement

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PURELY ELASTIC METHODS :

HOMOGENEIZATION METHOD

This solution is simplistic:• Elastic, no bulging –

lateral expansion• Gives a first

approximation of the settlements…

Nevertheless, there are some limitations :• Overestimates the load in inclusions• Overestimates and underestimates settlement• Not traditionally applicable under footings

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Settlement

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ELASTO-PLASTIC METHODS :

PRIEBE (1995)

Priebe derives his formula from several simplifying assumptions :- The deformations in the soil are linear elastic and are assimilated to the deformation

of a thick hollow pipe with an internal pressure equal to the difference of the horizontal stress in the column and in the soil

- Oedometric conditions of the unit cell- The deformations of the column are “following” the deformations of the soil and are

plastic (Mohr-Coulomb)- The aggregate is incompressible (deformations at constant volume)- He also assumes that all horizontal sections remain plane i.e. the vertical deformation

(settlement) of the soil and the columns are always equal (strain compatibility)- Priebe assume that the soil is in hydrostatic conditions i.e. K=1



Settlement

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ELASTO-PLASTIC METHODS :

PRIEBE (1995)- Priebe Charts are an easy way to find the settlement reduction factor

Calculate settlement without improvement and apply Priebe reduction factor to get the improved settlement

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Settlement

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MANY OTHER METHODS EXIST :

- Elastic- Balaam & Booker (1981)

- Elasto-Plastic- Ghionna & Jamiolkowski (1981)- Goughnour & Bayuk (1979)

- Empirical - Thorburn- GreenWood

- All are based on n, , and Es / Ec and give a factor β

- Trend:- FEM analysis particularly for more complex geometries



Settlement

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COMPARISON ELASTIC / ELASTO-PLASTIC METHODS:

• Elastic Methods• Increase of load on

system has marginal effect

• Elasto-Plastic Methods• Load is critical• Progressive

plasticization of the column with depth

• Priebe • Popular but not

conservative

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Settlement

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SETTLEMENT UNDER FOOTINGS :

All previous methods assume infinite number of columns under an infinite spread load…

Under footings, two (2) factors :

1. Limited loaded area => decrease of vertical stress with depth2. At the outer edge of the footing, less confinement (radial stress)



Settlement

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SETTLEMENT UNDER FOOTINGS :

Priebe developed a semi-empirical method to calculate the settlement of a footing on granular inclusions

Method:• Calculate the settlement for an

infinite, uniformly loaded area on granular inclusion improved soil

• Apply an additional settlement reduction factor

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Settlement

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RIGID INCLUSIONS



RIGID INCLUSIONS


The calculation of settlements for a structure supported by a network of rigid inclusions is not as straight-forward as the case of granular inclusion

WHY?The ratio of moduli is such (several orders of magnitude) that there is no strain compatibility => Complex soil-structure interaction


Settlement

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SETTLEMENT UNDER A SLAB

RIGID INCLUSIONS


RIGID INCLUSIONS


4 Main Components that interact with each other :

- The structure / slab- The Load Transfer Platform- The rigid inclusion- The surrounding soils

The design of a rigid inclusion solution must incorporate all components

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Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


The Load Transfer Platform

- Made of granular compacted material- Can also be made of cement or lime

treatment sands and silts- Can have layers of geo-grid or

geotextile depending on the design method

- Generally 2 to 4 feet thick

- Main Purpose : Transfer the load from structure to rigid inclusions


Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


The Load Transfer Platform

Several design approaches are possible :

- FHWA : Collin Method : Beam Method- British Standard : Membrane Method- France ASIRI: Arching Method

qs

All methods have the same goal : Evaluate Qp and qs as function of…

• H (Thickness)• (Friction angle)• E (Modulus)

H

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Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


Some methods include at least one layer of geotextile:

NEVERTHELESS:• Geotextile layers are

deemed too deformable• Require large deformation

to mobilize full tensile strength

• For Slabs• Tight Settlement

Criteria• For Embankments

• Lateral Restraint • Confinement


Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


ASIRI proposes Method of Diffusion Cone

• The angle of diffusion is assumed to be the peak friction angle of the material in the LTP

• From the proposed geometry, the load in the rigid inclusion Qp and the stress in the soil qs can be estimated and used for settlement calculation

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Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


Additional Load Transfer Mechanism :

• Negative skin friction

=> as it compresses, the soil grabs onto the rigid inclusion and transfers load to it


Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


Full view of the load transfer mechanism below the LTP

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Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


To take all these interactions into account :- Load transfer in LTP- Load transfer along rigid inclusion- Differential settlement between soil and inclusion

USE OF FEM


Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


Axisymmetric models are commonly used under slabs• Symmetry• Simplification• Comparable to more

complex models

=> Unit Cell Analysis

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Settlement

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SETTLEMENT UNDER FOOTINGS

RIGID INCLUSIONS


RIGID INCLUSIONS


Under footings, since the thickness of the LTP is usually thinner and the rigidity of the footing forces the neutral plane to be at the bottom of footing, an analytical approach is feasible

• The problem is decomposed into two domains : • Soil in between the inclusions• Rigid inclusions

• Interaction between two domains is described by the shear friction along the rigid inclusion


Settlement

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RIGID INCLUSIONS


RIGID INCLUSIONS


3D FEM ANALYSIS CAN ALSO BE USED FOR FOOTING WITH RIGID INCLUSIONS

2D PLANE STRAIN NOT FEASIBLE

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LIQUEFACTIONLIQUEFACTION


Liquefaction occurs from:• Shaking• Pore water pressure rises• Effective stress is reduced to

zero which corresponds to acomplete loss of shear strength

• Typically observed in saturatedloose sand and sandy silts

• Loose sands have a tendency tocontract under shear stress whiledense sand dilate under shearstress


Soil Liquefaction Mitigation:

• Compaction with Vibration• Shear Reinforcement

• Draining Effect• Ductile

GRANULAR INCLUSIONS

• Compaction with Vibration• Shear Reinforcement

• Draining Effect• Ductile

GRANULAR INCLUSIONS

• Limited Compaction with Static Displacement

• Shear Reinforcement but no Strain Compatibility

• Brittle

RIGID INCLUSIONS

• Limited Compaction with Static Displacement

• Shear Reinforcement but no Strain Compatibility

• Brittle

RIGID INCLUSIONS


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LIQUEFACTIONLIQUEFACTION


Seed & Idriss Simplified ( 1971 ) –NCEER workshop ( 1996 )

CSR : Cyclic Stress Ratio induced by earthquakeCRR : Cyclic Resistance Ratio of the in-situ soil

F = CRR/CSR

CRR mostly based on historical data of previous earthquakes

CRR increase with (N1)60

The denser the ground, the higher the factor of safety

CS

R



Compaction through VibrationShear Reinforcement

Ductile

GRANULAR INCLUSIONS

Compaction through VibrationShear Reinforcement

Ductile

GRANULAR INCLUSIONS


Baez & Martin ( 1993 )

• Granular inclusions “attract” shear stresses because of higher shear modulus

• Reduce shear stress in surrounding soils

• Define new CSR reduction factor:• Area replacement ratio• Ratio of shear moduli

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Limited compaction through static displacement- Area Replacement ratios are limited to 2 to 10% - Static displacement does not allow significant improvement

unless dense grid ( $$ )

Shear reinforcement but no strain compatibility- Main action of discrete rigid inclusions is to reduce earthquake

induced shear strains, thereby limiting pore pressure generation- Increase composite strength- Provide support for structure in case of liquefaction

- BUT : Research has shown that there is no strain compatibility + brittle behavior

RIGID INCLUSIONS

Limited compaction through static displacement- Area Replacement ratios are limited to 2 to 10% - Static displacement does not allow significant improvement

unless dense grid ( $$ )

Shear reinforcement but no strain compatibility- Main action of discrete rigid inclusions is to reduce earthquake

induced shear strains, thereby limiting pore pressure generation- Increase composite strength- Provide support for structure in case of liquefaction

- BUT : Research has shown that there is no strain compatibility + brittle behavior

RIGID INCLUSIONS




RIGID INCLUSIONSRIGID INCLUSIONS


Olgun & Martin ( 2008 )

While the soil deforms mainly in shear, rigid inclusions deform both in shear and bending ( flexural deformation )

• The column does not follow the deformation of the soil and is therefore less effective in reducing the shear strains and stresses ( soil “flows” around column )

• The more rigid the column, the more predominant the flexural behavior

• Cannot apply Baez & Martin to rigid inclusions

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One development is the use of soil mixing panel to create cells and mitigate liquefaction

The soil-mix panels are constructed using either secant soil mix columns or Cutter-Soil Mixing





Stiff Panels attract a significant amount of shear stress ( Shear Wall ) Reduction of the induced loading on the soil Mitigation of liquefaction Provide support for structure

Results of current research are showing that the soil mix panels are changing the behavior of the ground and therefore reducing the level of ground shaking under a structure

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CONCLUSION

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Slab / Embankment Footing Slab / Embankment Footing

BEARINGCAPACITY

SETTLEMENT

LIQUEFACTION

HOMOGENI--ZATION METHOD

HOMOGENI -ZATION METHOD

RIGID INCLUSIONS AS NAILS OR2D OR 3D FEM / CHECK BENDING

RIGID INCLUSIONS UNLOAD THE SOIL / CHECK INTERNAL STABILITY

HOMOGENI –-ZATION METHODPRIEBE…

MODIFIED PRIEBE METHOD

FEM AXISYMETRICAL

ANALYTICAL ITERATIVE SOLUTION OR3D FEM AXISYMETRICAL

SHEAR HOMOGENIZATION METHOD

NCEER ( 1996 )

???

SHEAR REINFORCEMENT OF PANEL SOLUTION


Questions!?

THANKS!

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