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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
Andrea GalliAussois, October 4th, 2010
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
Andrea GalliAussois, October 4th, 2010
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
Andrea GalliAussois, October 4th, 2010
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
Andrea GalliAussois, October 4th, 2010
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
Andrea GalliAussois, October 4th, 2010
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
Andrea GalliAussois, October 4th, 2010
72. Small scale tests - experimental
20 cm20 cm
4 cm
20 cm20 cm
4 cm
Dry Ticino sand
Andrea GalliAussois, October 4th, 2010
82. Small scale tests - experimental
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
Andrea GalliAussois, October 4th, 2010
92. Small scale tests - experimental
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
Andrea GalliAussois, October 4th, 2010
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
Andrea GalliAussois, October 4th, 2010
112. Small scale tests - 3D numerical analyses (FLAC3D)
v
hKσσ=
B1
Geotextile 1Non-woven
Geotextile 2Non-woven+ knitted net
Andrea GalliAussois, October 4th, 2010
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
Andrea GalliAussois, October 4th, 2010
133. Simplified constitutive model for a GEC slice and validation
• 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:
Andrea GalliAussois, October 4th, 2010
143. Simplified constitutive model for a GEC slice and validation
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%.
Andrea GalliAussois, October 4th, 2010
153. Simplified constitutive model for a GEC slice and validation
Experimental data from Wu and Hong (2009)
Andrea GalliAussois, October 4th, 2010
163. Simplified constitutive model for a GEC slice and validation
Experimental data from Wu and Hong (2009)
Andrea GalliAussois, October 4th, 2010
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
4. Numerical examples on small scale tests
The small scale prototype was modelled by means of five slices, each one governed by the simplified constitutive rule.
Geotextile 1Non-woven
Geotextile 2Non-woven+knitted net
Andrea GalliAussois, October 4th, 2010
184. Numerical examples on small scale tests
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
Andrea GalliAussois, October 4th, 2010
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
4. Numerical examples on small scale tests
The small scale prototype was modelled by means of five slices, each one governed by the simplified constitutive rule.
Geotextile 1Non-woven
Geotextile 2Non-woven+knitted net
Andrea GalliAussois, October 4th, 2010
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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