06_Galli

Andrea GalliAussois, October 4th, 2010

1ALERT Workshop 2010 - Session IEngineering geostructures

Mechanical behaviour of geo-encased stone columns: small scale tests and numerical modellingAndrea Galli, Claudio di PriscoPolitecnico di Milano – Dept. of Structural Engineering


2Motivation

Geo-encased stone columns (GEC) are often employed as foundations ofembankments on soft soil strata, in order to

1. Prevent possible local and/or global failure2. Reduce differential settlements3. Fasten the consolidation process

embankment

embankment

embankment

soft soil

soft soil

soft soil

AmburgFinkenwerderAirport


3Motivation

Design criteria are still based on oversimplifiedempirical approaches, and often they disregard

1. the actual soil-geotextile interaction2. the effect of the load history

3. time consuming and not suitable for large parametrical analyses4. based on simplified constitutive models

Or they are based on numerical approaches which are often

Our goal is to define a homogeization process, leading to a simplified constitutive ruleaccounting for the mechanical behaviour of the geo-encased column and of thesurrounding soil


4

1. Definition of the unit cell and of its rheological model

2. Description of small scale tests and their numerical 3D modelling

3. Definition of the simplified constitutive model for a GEC slice and validation

4. Numerical examples on small scale tests

5. Conclusions and perspectives

Outline of the presentation


51. The “unit cell”

embankmentgeotextiles

granular column

encasing membrane

soft soil

• Granular columns behave like a deformable inclusion within the soil; they are a sortof “soft” piles, and they may be subject to bulging

• Our goal is to define an homogenised constitutive rule for a single unit cell,composed by the column and the surrounding soil


61. The “unit cell”A complex system:A. Load on the column topB. Tensile load on geotextilesC. Load on the soft soil surrounding the column

soft soil

soft soil

rigid subgrade

rigid subgrade

The columns and thesurrounding soft soilwork in parallel if andonly if the geotextilereinforcement is rigid.

The stiffness of the two“sister” springs KGECand KS are highlycoupled.

In the present work, weassume ∆σ’vs = 0


72. Small scale tests - experimental

20 cm20 cm

4 cm

20 cm20 cm

4 cm

Dry Ticino sand



Geotextile 1Non-wovenStiffness J = 46 kN/mStrength Tg = 18 kN/m

Equivalent circular shallow foundation • non linear behaviour

• higher and constant stiffness in unloading-reloading

• remarkable bulging effect

Bulging



Geotextile 2Non-woven + knitted netStiffness J = 625 kN/mStrength Tg = 75 kN/m

• locking behaviour

• higher and constant stiffness for unloading-reloading amplitude less than 70% of maximum load

• no bulging effect


102. Small scale tests - 3D numerical analyses (FLAC3D)

n

aa p

ppkE

⋅⋅= '

Dense sand

Loose sand

- elastic perfectly plastic soil model- Mohr-Coulomb failure condition- non associate flow rule.

Elastic parameters were calibrated according to some experimental oedometric tests on sand specimens

Unit weightγ 15.7 kN/m3 15.7 kN/m3

Friction angleφ 40 30

Dilatancy angleψ 20 5

Poisson ratioν 0.3 0.3

Parameter n 0.22 0.4

Parameter k 220 140

Dense sand Loose sand

Interface friction angleδ 30


112. Small scale tests - 3D numerical analyses (FLAC3D)

v

hKσσ=

B1

Geotextile 1Non-woven

Geotextile 2Non-woven+ knitted net


123. Simplified constitutive model for a GEC slice and validation

• The geometry of a unit cell can be thought as axi-symmetric

• Each single slice of a GEC can be thought as a triaxial specimen

• The mechanical behaviour of the external soil can be modelled by an elastic perfectly plastic constitutive rule, with a Mohr-Coulomb failure criterion and a non associate flow rule

• The tensile mechanical behaviour of the geotextile can be roughly assumed to be elastic perfectly plastic

T

δ

Tamm

δamm

E



• Elastoplastic constitutive law with mixed isotropic-kinematik hardening rule

• Non associate plastic flow rule

• Matsuoka-Nakai failure criterion

di Prisco, Nova, Lanier (1993)The soil inside the column can be modelled by:



A validation of the proposed constitutive rule for the slice has been obtained with reference to the experimental data by Wu and Hong (2009), on triaxial sand specimens (140 mm height x 70 mm in diameter), reinforced by means of geotextiles.

The soil employed was a uniformly graded angular quartz sand with a specific gravity Gs of 2.65, effective size D10 of 0.7 mm, uniformity coefficient Cu of 1.23. The maximum and minimum dry unit weights of the soil are 16.48 and 13.73 kN/m3, respectively. The peak friction angle decreases from 46.9 for a confining pressure of 20 kPa to 37.7 for a confining pressure of 500 kPa.

Two relative densitiesDR= 60% and 80%.



Experimental data from Wu and Hong (2009)



Experimental data from Wu and Hong (2009)


17

0500

10001500200025003000350040004500

0.00 0.20 0.40 0.60 0.80u/D

q [k

Pa] q

exp

0

150

300

450

600

750

900

0.00 0.20 0.40 0.60 0.80u/D

q [k

Pa] q

exp


The small scale prototype was modelled by means of five slices, each one governed by the simplified constitutive rule.


Geotextile 2Non-woven+knitted net



The effect of the shear stresses was additionally taken into consideration by introducing vertical elastoplastic springs at nodes between two slices

u1

2

3

4

5 5

4

3

2

1u


19

0500

10001500200025003000350040004500

0.00 0.20 0.40 0.60 0.80u/D

q [k

Pa]

q tot

q

q lat

exp

0

150

300

450

600

750

900

0.00 0.20 0.40 0.60 0.80u/D

q [k

Pa]

q tot

q

q lat

exp


The small scale prototype was modelled by means of five slices, each one governed by the simplified constitutive rule.


Geotextile 2Non-woven+knitted net


205. Conclusions

• A homogenization procedure for GECs under vertical load has been presented

• The proposed constitutive model is able to reproduce the interaction among the granular column, the geotextile and the surrounding soil

• The effect of the shear stresses at soil-geotextile interface has been studied

• The model is able to take into account the loading history, and to reproduce the effect of a pre-load

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