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L. CALLISTO Terreni argillosi poco consistenti
terreni a grana fine poco consistenti
Luigi CALLISTO
summer school – Cagliari22-23 giugno 2015
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L. CALLISTO Terreni argillosi poco consistenti
1. osservazioni sperimentali
2. modelli costitutivi
3. aspetti applicativi
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L. CALLISTO Terreni argillosi poco consistenti
terreni argillosipoco consistentiin Italia(Calabresi e Manfredini 1976)
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L. CALLISTO Terreni argillosi poco consistenti
terra → mezzo particellare
le deformazioni sono prodotte dallo spostamentorelativo fra i granuli
• interazione tra le particelle• volume occupato dalle particelle → stato del materiale
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L. CALLISTO Terreni argillosi poco consistenti
Scott (1963)
struttura dei terreni argillosi
struttura dispersa(acqua dolce)
struttura flocculata(acqua salmastra)
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L. CALLISTO Terreni argillosi poco consistenti
struttura dei terreni argillosi
Collins e Mc Gown (1974)
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L. CALLISTO Terreni argillosi poco consistenti
pseudo-preconsolidazione
Leonards e Altshaeffl (1964) Bjerrum (1967)
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L. CALLISTO Terreni argillosi poco consistenti
relazione univoca fra stato tensionale e volume specifico(State Boundary Surface o superficie di stato)
Henkel (1960)
ln p'
eNCL
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L. CALLISTO Terreni argillosi poco consistenti
alogσ′
void
rat
io e
kσ′ pσ′
e0
v0σ′
NCL
CC
CS elastic unloading-reloading
ε
σ′
Pσ′
Pσ′
plastic loading
elastic unloading-reloading
ε
σ′
Pσ′
Pσ′
plastic loading A
A
B
Pε
tensione di preconsolidazione → soglia di plasticizzazione
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L. CALLISTO Terreni argillosi poco consistenti
Roscoe et al (1958)
superficie di stato→ evoluzione della condizione di plasticizzazione
Roscoe et al (1963)
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L. CALLISTO Terreni argillosi poco consistenti
terreno come mezzo elasto-plasticocon incrudimento: legge di flusso
Roscoe et al (1963)
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L. CALLISTO Terreni argillosi poco consistenti
ricerche sul potenziale plastico (Lewin, 1973)
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L. CALLISTO Terreni argillosi poco consistenti
Roscoe et al (1958)
superficie di stato e stato critico
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L. CALLISTO Terreni argillosi poco consistenti
Roscoe et al (1958) Roscoe et al (1958)
superficie di stato e stato critico
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L. CALLISTO Terreni argillosi poco consistenti
normalizzazione e pressione equivalente
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L. CALLISTO Terreni argillosi poco consistenti
modelli a plasticità diffusa
Al Tabaa & Muir Wood (1989)Dafalias & Hermann (1982)
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L. CALLISTO Terreni argillosi poco consistenti
snervamento di argille naturali
Mitchell (1976) – Leda clay
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L. CALLISTO Terreni argillosi poco consistenti
snervamento di argille naturali
Tavenas et al. (1979) – argille di Saint-Louis e di Saint-Alban
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L. CALLISTO Terreni argillosi poco consistenti
superficie di stato nelle condizioni naturali
Tavenas e Leroueil (1979), argilla di Saint-Alban
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L. CALLISTO Terreni argillosi poco consistenti
superficie di stato nelle condizioni naturali
Graham et al. (1988), argilla del lago Agassiz
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L. CALLISTO Terreni argillosi poco consistenti
condizioni edometriche – destrutturazionetransizione dallo stato sedimentario a uno stato intrinseco
Smith et al. (1992), argilla di Bothkennar
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L. CALLISTO Terreni argillosi poco consistenti
Callisto & Rampello (2004)
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L. CALLISTO Terreni argillosi poco consistenti
evoluzione della superficie di stato e destrutturazione
Smith et al. (1992), argilla di Bothkennar
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L. CALLISTO Terreni argillosi poco consistenti
Argilla di Pisa, definizione dello stato sedimentario(Skempton 1970)
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L. CALLISTO Terreni argillosi poco consistenti
definizione normalizzata dello stato sedimentario(Burland 1970)
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L. CALLISTO Terreni argillosi poco consistenti
10 100 1000σ'a: kPa
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
e
in situ statesnatural clayreconstituted clay
SCC
ICL
condizioni edometriche – destrutturazione dell’argilla di PisaCallisto (1996), Callisto & Calabresi (1998)
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L. CALLISTO Terreni argillosi poco consistenti
O
AB
A0,R0
A30,R30
A60,R60A90,R90
A135
A180
A280
A315,R315
ω
0 40 80 120 160 p' : kPa
-40
0
40
80q : k
Pa
AUC
AUE
argilla di Pisa – programma sperimentaleCallisto (1996), Callisto & Calabresi (1998)
prove in cella triassiale
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L. CALLISTO Terreni argillosi poco consistenti
-6 -4 -2 0ε (%)
-100
-50
0
50
(kPa
)
s
q
0 5 10 15(kJ/m )
0
80
160
(kPa
)
W
LSP
3
A315
50 100 150 200 (kPa)
0.0
4.0
8.0
ε (%
)
50 100 150 200 (kPa)
0
5
10
15
(kP
a)v
p'
p'
uΔ
ricerca delle condizioni di snervamento
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L. CALLISTO Terreni argillosi poco consistenti
(kPa),
-100
0
100
(kPa
),
0 100 200(kPa)
1.6
1.8
e200
q
Ko
0.1
0.51.02.0
W = 4.0 kJ/m3
Cs = 0.15
p'
δεp' pv
δεp s
(strain energy)direction of the plasticstrain increment vectors
ricerca delle condizioni di snervamento
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L. CALLISTO Terreni argillosi poco consistenti
A180 A135
A90
A30
A280
A60
A0
A315
10 100
p' (kPa)
1.4
1.5
1.6
1.7
1.8
1.9
e
SCC
ICL
deformazioni volumetriche in prove triassiali
O
AB
A0,R0
A30,R30
A60,R60A90,R90
A135
A180
A280
A315,R315
ω
0 40 80 120 160 p' : kPa
-40
0
40
80q : k
Pa
AUC
AUE
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L. CALLISTO Terreni argillosi poco consistenti
Callisto & Rampello (2004)
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L. CALLISTO Terreni argillosi poco consistenti
normalizzazione dei percorsi tensionali
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L. CALLISTO Terreni argillosi poco consistenti
Callisto & Rampello (2004) Muir Wood (1995)
normalizzazione dei percorsi tensionali tenendo conto della destrutturazione
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L. CALLISTO Terreni argillosi poco consistenti
normalizzazione dei percorsi tensionali tenendo conto della destrutturazione
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L. CALLISTO Terreni argillosi poco consistenti
modelli costitutivi di Rouania & Muir Wood (2000) e di Gajo & Muir Wood (2001)
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L. CALLISTO Terreni argillosi poco consistenti
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L. CALLISTO Terreni argillosi poco consistenti
Callisto, Gajo & Muir Wood (2002)
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L. CALLISTO Terreni argillosi poco consistenti
0 50 100 150 200 250p': kPa
-100
-50
0
50
100
q: k
Pa
0.5%
1.0%
2.0%3.0%
4.0%5.0%
7.0%
-0.5%
-1.0%
-2.0%
-5.0%
0.3%
experimentsmodel
0 50 100 150 200 250p': kPa
-100
-50
0
50
100
q: k
Pa
0.5%
1.0%
2.0%
3.0%4.0%
5.0%
-0.5%-1.0%
experimentsmodel
Callisto, Gajo & Muir Wood (2002)
deformazioni deviatoriche deformazioni volumetriche
argilla naturale
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L. CALLISTO Terreni argillosi poco consistenti
Callisto, Gajo & Muir Wood (2002)
condizioni non drenate
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L. CALLISTO Terreni argillosi poco consistenti
Callisto, Gajo & Muir Wood (2002)
deformazioni deviatoriche deformazioni volumetriche
argilla ricostituita
0 50 100 150 200 250p'
-100
-50
0
50
100
150
q: k
Pa
0.5%1.0%
2.0%
3.0%
4.0%
5.0%
0.3%O
experimentsmodel
0 50 100 150 200 250 300p': kPa
0.5%
1.0%
2.0%
3.0%
4.0%
5.0%
O
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L. CALLISTO Terreni argillosi poco consistenti
O
AB
A0,R0
A30,R30
A60,R60A90,R90
A135
A180
A280
A315,R315
ω
0 40 80 120 160 p' : kPa
-40
0
40
80q : k
Pa
AUC
AUE
argilla di Pisa – programma sperimentaleCallisto (1996), Callisto & Calabresi (1998)
prove in cella triassiale
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L. CALLISTO Terreni argillosi poco consistenti
telaio in ottone
pareti in perspexmembrana
spillo per lamisura deglispostamenti
fori di drenaggiointercapedine inpressione
provino
T0T30
T60
T180
T90
T120
T150
T*30
T*60
T*90
T*120
T*150
α
σ'h1 σ'h2
σ'a
O
prove in cella triassiale cubica
argilla di Pisa – programma sperimentaleCallisto (1996), Callisto & Calabresi (1998)
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L. CALLISTO Terreni argillosi poco consistenti
O
σ'h1 σ'h2
-120 -40 40 120
xσ : kPa
-100
-20
60
140
σ'a , yσ : kPa
4 3 21%
T0T30
T60
T90
T120
T150strength envelope
isolinee delladeformazione deviatorica
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L. CALLISTO Terreni argillosi poco consistenti
0 2 4 6 8 10 12 14εs (%)
0
20
40
60
80
100
120q
(kPa
)true triaxial
triaxial (axisymmetric)
0.001 0.01 0.1 1 10εs: %
0
20
40
60
80
100
120
q: k
Pa
true triaxial
triaxial (axisymmetric)
0 2 4 6 8 10 12 14 16εs (%)
0
20
40
60
80
100
120
q (k
Pa)
1:1 sample
standard sample
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L. CALLISTO Terreni argillosi poco consistenti
O
σ'h1 σ'h2
T0
T180
T60
T90
T120
T150
-60 -20 20 60xσ : kPa
-40
0
40
80σ'a , yσ : kPa
1.0 0.3 0.2 0.1%
α
0 60 120 180
α °
0
3000
6000
9000
12000
15000
18000
G (k
Pa)
LSP 5 kPa10 kPa20 kPa
isolinee delladeformazione deviatorica
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L. CALLISTO Terreni argillosi poco consistenti
0 30 60 90 120 150 180
α °
0
3000
6000
9000
12000
15000
18000
G (k
Pa)
LSP = 5 kPa
mezzo elastico conanisotropia trasversale
σ'a
σ'h2σ'h1
O
m = 1.0m = 0.9m = 0.8
T0 T30
T60
T180
T90
T120
T150
α
σh2'
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L. CALLISTO Terreni argillosi poco consistenti
O
σ'h1 σ'h2
T0
T180
T60
T90
T120
T150
-60 -20 20 60 xσ : kPa
-40
0
40
80
σ'a , yσ : kPa
0.1%0.20.31.0
modelexperiments
O
σ'h1 σ'h2
T0
T180
T60
T90
T120
T150
-60 -20 20 60 xσ : kPa
-40
0
40
80
σ'a , yσ : kPa
0.1%0.20.31.0
modelexperiments
previsione calibrazione indipendente
Callisto, Gajo & Muir Wood (2002)
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L. CALLISTO Terreni argillosi poco consistenti
un caso di interesse applicativo
evoluzione nel tempo del comportamento di uno scavo
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L. CALLISTO Terreni argillosi poco consistenti
terreni a grana fine – condizioni di drenaggio
scavo → riduzione delletensioni totaliΔσ < 0
Δσ
σ
σ = σ' + u
riduzione della resistenza disponibile
tempo
tempo
tempo
tensioni totali
pressioni interstiziali
tensioni efficaci
σ
u
σ'
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L. CALLISTO Terreni argillosi poco consistenti
σ'v
σ'h
K0Ka
Kp
B
σ'v0
A
A'
B'
O
Δu
σ'v +σ'h =cost.
B A
percorsi tensioni efficacicomportamento meccanico del terreno
× direzione percorsi tensioni totali
percorsi tensionali - condizioni non drenate
ipotesi: legame elastico(lontano dalle condizioni limite)
11
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L. CALLISTO Terreni argillosi poco consistenti
H
σ'vσv u
condizioni iniziali
andamenti σ, u, σ' nei terreni di fondo scavo
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L. CALLISTO Terreni argillosi poco consistenti
H
σ'vσv u
condizioni inizialiΔu = Δσv Δσ'v = 0
condizioni inizialibreve termine
Δσv
andamenti σ, u, σ' nei terreni di fondo scavo
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L. CALLISTO Terreni argillosi poco consistenti
H
σ'vσv u
condizioni inizialicondizioni inizialibreve termine
Δσv Δu = α Δσv Δσ'v = (1-α) Δσv
andamenti σ, u, σ' nei terreni di fondo scavo
α < 1
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L. CALLISTO Terreni argillosi poco consistenti
H
σ'vσv u
condizioni inizialicondizioni inizialibreve termine
Δσv Δu = α Δσv Δσ'v = (1-α) Δσv
andamenti σ, u, σ' nei terreni di fondo scavo
α < 1
perdita di suzione
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L. CALLISTO Terreni argillosi poco consistenti
H
σ'vσv u
condizioni inizialicondizioni inizialibreve terminelungo termine
Δσv Δu = α Δσv Δσ'v = (1-α) Δσv
andamenti σ, u, σ' nei terreni di fondo scavo
α < 1
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L. CALLISTO Terreni argillosi poco consistenti
effetto del tempo (Callisto et al. 2014)
(3 mesi) (12 mesi)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
DX
(T )
/ DX
∞
dx
Nmax
M
smax/(gH)=0.4
one-D consolidation
smax/(gH)=0.1
t
H
EkT 2
w
refC50,C
γ=time factor
degr
eeof
cons
olid
atio
n
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L. CALLISTO Terreni argillosi poco consistenti
scavo profondo a Bologna -20 -10 0 10 20
u (mm)
5
10
15
20
25
30
35
40
45
Q.A
. (m
s.l.
m.)
letture:26-28/1/2005letture: 5-7/4/2005
34
3 mesi
3
4
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L. CALLISTO Terreni argillosi poco consistenti
modello costitutivo (Rouainia & Muir Wood 2000)
superficie di plasticizzazione
yield
bounding
legame elastico isotropo legge di flusso associata
superficie esterna (bounding)
F. Bertoldo (2014)
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L. CALLISTO Terreni argillosi poco consistenti
F. Bertoldo (2014)
modello costitutivo (Rouainia & Muir Wood 2000) – modulo plastico
0 0.2 0.4 0.6 0.8
0
20
40
60
0.0001 0.001 0.01 0.1
0
2000
4000
6000
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L. CALLISTO Terreni argillosi poco consistenti
integrazione esplicita con controllo dell’errore (Sloan et al. 2001)
sì no
− aggiornamento dello stato tensionale
− aggiornamento dei valori assunti dalle variabili di stato
F. Bertoldo (2014)
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L. CALLISTO Terreni argillosi poco consistenti
simulazione di uno scavo in argilla – descrizione del problema
terreno → elementi rettangolari CPE4P
paratia → elementi beam
no interfaccia paratia-terreno
scavo in cond. drenate (1 metro)
vincolo in testa
prosecuzione dello scavo in cond. non drenate
analisi FEM (Abaqus)
paratia di pali accostati Φ 600 mm interasse 700 mm
F. Bertoldo (2014)
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L. CALLISTO Terreni argillosi poco consistenti
simulazione di uno scavo in argilla – descrizione del problema
0 1 2 3 4 5 0 25000
F. Bertoldo (2014)
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L. CALLISTO Terreni argillosi poco consistenti
simulazioni numeriche di percorsi tensionali tipici di problemi di scavocondizioni non drenate (a controllo di deformazioni)
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
r = 1
-10 -8 -6 -4 -2 0 2 4 6 8 10εv (%)
-50
0
50
(σ'v -
σ'h)
/2(k
Pa)
r = 1
0 50 100 150σ'h (kPa)
0
50
100
150
σ'v
(kP
a)
-10 -8 -6 -4 -2 0 2 4 6 8 10εv (%)
-50
0
50
(σ'v -
σ'h)
/2(k
Pa)
0 50 100 150σ'h (kPa)
0
50
100
150
σ'v
(kP
a)
r = 1.5
r = 1.5
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
stato di deformazione piana
compressione estensione
F. Bertoldo (2014)
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L. CALLISTO Terreni argillosi poco consistenti
12 /19
simulazioni numeriche di percorsi tensionali tipici di problemi di scavocondizioni non drenate (a controllo di tensioni) e consolidazione
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
s'h (kPa) s'h (kPa)
0
50
s'v (kPa)
stato di deformazione piana
r = 1
r = 1
0 50 100 150σ'h (kPa)
0
50
100
150
σ'v
(kP
a)
0 50σ'h (kPa)
0
-2
εh (
%)
0 -2εv (%)
0
50
100
σ'v
(kP
a)
compressione estensione
0 50 100 150σ'h (kPa)
0
50
100
150
σ'v
(kP
a)
0 50σ'h (kPa)
0
-2
εh (
%)
0 -2εv (%)
0
50
100
σ'v
(kP
a)
0 50 100 150σ'h (kPa)
0
50
100
150
σ'v
(kP
a)
0 50σ'h (kPa)
0
-2
εh (
%)
0 -2εv (%)
0
50
100
σ'v
(kP
a)
r = 1.5
r = 1.5
0 50 100 150σ'h (kPa)
0
50
100
150
σ'v
(kP
a)
0 50σ'h (kPa)
0
-2
εh (
%)
0 -2εv (%)
0
50
100
σ'v
(kP
a)
F. Bertoldo (2014)
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L. CALLISTO Terreni argillosi poco consistenti
simulazione di uno scavo in argilla – situazione a fine scavo
sovrapressioni interstiziali indotte spostamenti orizzontali
r0 = 1 r0 = 2
F. Bertoldo (2014)
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L. CALLISTO Terreni argillosi poco consistenti
simulazione di uno scavo in argilla – effetto della consolidazione
spost. piede
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L. CALLISTO Terreni argillosi poco consistenti
simulazione di uno scavo in argilla – destrutturazione
spost. piede
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L. CALLISTO Terreni argillosi poco consistenti
BIBLIOGRAFIA
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Atkinson J.H. e Bransby P.L. (1978). The mechanics of soils: an introduction to criticalstate soil mechanics. London: Mc Graw Hill.
Atkinson J.H. e Sallfors G. (1991). Experimental determination of soil properties. Proc.10th European Conf. Soil Mech. & Found. Engng, Firenze. Roterdam: Balkema,3, 915-956.
Atkinson J.H., Richardson D. e Stallebrass S.E. (1990). Effect of recent stress history onthe stiffness of overconsolidated soil. Géotechnique 40, N.3, 531-540.
Atkinson J.H., Richardson D. e Robinson P.J. (1987). Compression and extension of K0normally consolidated kaolin clay. Journal of Geotechnical Engineering, ASCE,113, N.12, 1468-1482.
Baracos A. (1977). Compositional and structural anisotropy of Winnipeg soils - a studybased on scanning electron microscopy and X-ray diffraction analyses. CanadianGeotechical Journal 14, 125-137.
Bjerrum L. (1967). Engineering geology of Norwegian normally consolidated clays asrelated to settlements of buildings. Géotechnique 17, N.2, 83-117.
Budhu M. e Wu C.S. (1991). Mechanics of sampling disturbances in a soft clay.
Burland J.B. (1990). On the compressibility and shear strength of natural clays.Géotechnique 40, N.3, 329-378.
Calabresi G. e Manfredini G. (1976). Terreni coesivi poco consistenti in Italia. RivistaItaliana di Geotecnica, X, N.1, 49-64.
Callisto, L (1996) Studio sperimentale su un’argilla naturale: il comportamentomeccanico dell’argilla di Pisa. Thesis, Dottorato di ricenrca in ingegneriageotecnica, Universita di Roma ‘La Sapienza’.
Callisto L. (2011). Diaframmi a sostegno di scavi profondi in terreni a grana fine. Attidelle XXIII Conferenze Geotecniche di Torino.
Callisto, L & Calabresi, G (1998) Mechanical behaviour of a natural soft clay.Géotechnique 48 4, 495-513.
Callisto L. e Rampello S. (2004). An interpretation of structural degradation for threenatural clays. Canadian Geotechnical Journal 41, No.4, 392-407. doi:10.1139/T03-099.
Collins K. e Mc Gown A. (1974). The form and function of microfabric features in avariety of natural soils. Géotechnique 24, N.2, 223-254.
Dafalias Y.F. e Hermann L.R. (1982a). Bounding surface formulation of soil plasticity.Soil Mechanics - Transient and Cyclic Loads. G.N. Pande and O.C. Zienkiewicz(eds): Wiley.
Dafalias Y.F. e Hermann L.R. (1982b). A generalised bounding surface constitutivemodel for clays. Application of Plasticity and Generalised Stress-Strain inGeotechnical Engineering. R.N. Yong and E.T. Selig (eds). New York: ASCE,78-95.
Dafalias Y.F. e Popov E.P. (1977). Cyclic loading for materials with a vanishing elasticregion. Nucl. Eng. Design 41, 293-302.
Delage P. e Lefebvre G. (1984). Study of the structure of a sensitive Champlain clayand of its evoution during consolidation. Canadian Geotechical Journal 21, 21-35.
Folkes D.J. e Crooks J.H.A. (1985). Effective stress paths and yielding in soft claysbelow embankments. Canadian Geotechical Journal 22, 357-374.
Gajo, A and Muir Wood, D (2001) A new approach to anisotropic, bounding surfaceplasticity: general formulation and simulations of natural and reconstituted claybehaviour. International Journal for Numerical and Analytical Methods inGeomechanics 25, 3, 207-241.
Gillot J.E. (1970). Fabric of Leda clay investigated by optical, electron-optical, and X-ray diffraction methods. Engineering Geology, 4, 133-153.
Graham J. e Houlsby G.T. (1983). Anisotropic elasticity of a natural clay. Géotechnique33, N.2, 165-180.
Graham J., Noonan M.L. e Lew K.V. (1983). Yield states and stress-strain relationshipsin a natural plastic clay. Canadian Geotechical Journal 20, 502-516.
Henkel D.J e Sowa V.A. (1963). The influence of stress history on stress paths inundrained triaxial tests on clay. Laboratory Shear Testing of Soils. ASTM SpecialTechnical Publication No.361, 280-291.
Henkel D.J. (1959). The relationships between the strength, pore-water pressure, andvolume-change characteristics of saturated clays. Géotechnique 9, 119-135.
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L. CALLISTO Terreni argillosi poco consistenti
Henkel D.J. (1960). The relationships between the effective stresses and water contentin saturated clays. Géotechnique 10, 41-54.
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L. CALLISTO Terreni argillosi poco consistenti
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