01_Richiami_di_meccanica_dei_terreni

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Verona 16 aprile 2010 COMPLEM COMP LEMENT ENTII DI GEOT GEOTECN ECNICA ICA Sign up to vote on this title

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RICH RI CHIA IAMI MI DI ME MECCA CCANI NICA CA

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TERRA (ROCCIA SCIOLTA):

Materiale, naturale naturale o no, formato da granuli non legati fra di loro o che possono essere separati applicando applicando modeste  Sign up to vote on this title sollecitazioni o per mezzo di contatto con l’acqua 

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TERRA (ROCCIA SCIOLTA):

Materiale, naturale naturale o no, formato da granuli non legati fra di loro o che possono essere separati applicando applicando modeste  Sign up to vote on this title sollecitazioni o per mezzo di contatto con l’acqua 

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PROPRIETA’ INDICI GAS

V g

P V PT

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Aggregazione naturale o artificiale di tre fasi : SOLI SO LIDA DA - LI LIQU QUID IDA A - GA

V v ACQUA


Sign up to vote on this title

V a V T

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PROPRIETA’ INDICI Valori caratteristici terreno

ghiaia

n (%)

e

25-40

0,30-0,67

w (%) -

γ d


γ 

3 (kN m 3 ) (kN m  Useful  )Not useful

14-21

18-23

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CARATTERISTICHE DELLA FRAZIONE SOLIDA Ciottoli Terre a grana grossa rilevanza: granulometria

>76,20 mm


Ghiaia  Sabbia

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76,20÷2,00 mm Not useful  2,00 ÷0,06 mm

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PROPRIETA’ INDICI DELLA FRAZIONE SOLIDA : GRANULOMETR DISTRIBUZIONE PERCENTUALE DEI GRANI SECONDO LE DIMENSIONI

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TERRE GRANULARI :  vagliatura meccanica Sign up to vote on this title attraverso setacci

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TERRE COESIVE :

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FATTORI DAI QUALI DIPENDE IL COMPORTAMENTO DEI TERRENI INCOERENTI

D r

forma e dimensione dei grani;

=

e max

e max

−e

− e min


distribuzione granulometrica;



stato di addensamento; più

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Più

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TERRE A GRANA FINE Si distinguono :

LIMI




ARGILLE

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COMPORTAMENTO DELLE ARGILLE Sheet Music

La capacità di adsorbire l’acqua nell’interstrato strutturale dà luogo alla caratteristica tipica delle argille, la plasticità, e cioè la capacità di variare consistenza in relazione al contenuto d’acqua. Sign up to vote on this title

LIMITI DI ATTERBERG Miscela fluida Terra acqua

--------------------Stato liquido

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Limite liquido w (c ~1,5 kPa)

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COMPORTAMENTO DELLE ARGILLE I valori dei limiti di dipendono dal tipo di mineral e dal tipo e dalla concentrazio eventualmente disciolti.


Useful  Not useful  L’indice di plasticità

l’ampiezza

dell’interval

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INDICE DI CONSISTENZA Ic

w L − w I c = I P

<0 0 - 0,25 0,25 -0,5 0,5 - 0,75 0,75 - 1,0 >1 0

Consistenza fluida fluido-plastica Sign up to voteplastica on this title molle Useful  Not useful plastica solido plastica i lid

Cu (kP 0 1,5 - 2  20 - 4 40 - 7 75 - 1 > 150

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SISTEMI DI CLASSIFICAZIONE DELLE TERRE

Criteri per suddividere le terre e le miscele di terre diverse in accordoal loro Sign up to vote on this title comportamento facendo uso di semplici test identificativi: 

•

distribuzione distribuzione granulometrica;

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PRINCIPIO DELLE

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STATO TENSIONALE TOTALE NEL TERRENO


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PRESSIONI INTERSTIZIALI NEL TERRENO Sign up to vote on this title

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PRINCIPIO DELLE TENSIONI EFFICACI Terzaghi, 1936 Sign up to vote on this title



Tutti gli effetti misurabili di una variazione dello stato di tensione, Not useful  Useful come la compressione, la distorsione e la variazione di resistenza al

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PRINCIPIO DELLE TENSIONI EFFICACI Rappresentazione dello stato tensionale totale ed efficace mediante i cerchi di Mohr Per ko < 1 Acqua presente u> 0 Pressioni efficaci

σ '1

= σ 1 − u = σ v − u

σ '3

= k ⋅ σ 1' = k ⋅ σ '


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Principio delle tensioni efficaci

PRINCIPIO DELLE TENSIONI EFFICACI Forma incrementale




∆σ ' = ∆σ − ∆u

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STATO TENSIONALE IN CONDIZIONI IDRODINAMICHE Stato tensionale in un punto a profondità z

z σ ' = γ 'z ± γ w h h 2


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STORIA TENSIONALE DEL TERRENO Documents

SEDIMENTAZIONE Sheet Music

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wo


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STORIA TENSIONALE DEL TERRENO Linea di compressione normale

 Sign up e to vote e on this C title log σ '

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Permeabilita’del terreno Legge di D’Arcy:

La velocità di flusso (v) è proporzionale al gradiente idraulico Sign up to vote on this title

v = k ⋅i

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VALORI CARATTERISTICI DEL COEFFICIENTE D PERMEABILITA’ Sign up to vote on this title

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TEORIA DELLA FILTRAZIONE BIDIMENSIONA PORTATA IN ENTRATA

Qin = k x dove :

∂h

∂h ∂h +vote k y on this A ytitle SignA upx to ∂ ∂ x y  Useful  Not useful

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Per la conti continui nuità tà del flusso flusso deve deve risultar risultaree :

Qin

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USO DEL RETICOLO DI FILTRAZIONE

La pressione neutra in un punto  qualsiasi quals de l reticolo ret icolo Sign iasi up to del vote on this titleè pari a :

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 Not useful  h  ua =  h + h z − n  γ w Na   Useful

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VERIFICA AL SIFONAMENTO Asportazione Asportazi one di granuli granuli del terreno terreno in prossimi prossimità tà dell della a superficie superficie di uscit uscit dell’acqua e formazione di canalicoli che accelerano il fenomeno.

σ ' = γ '⋅ z

± γ w ⋅ i ⋅ z = 0


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VERIFICA AL SOLLEVAMENTO ∆W’ W'

∆U

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⋅D⋅γ'

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CONSOLIDAZIONE: Processo transitorio accoppiato di deform e filtrazione, indotto da una variazione delle condizioni al contorno.

•La risposta deformativa è somma di una risposta istantanea, di breve ter (“non drenata”) e di una risposta ritardata, di consolidazione, che  evolv Sign up to vote on this title tempo. Useful Not useful 



•La variazione dello stato deformativo dello scheletro solido fa evolver

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CONSOLIDAZIONE PRIMARIA

Diminuzione dell’indice dei vuoti (variazione di volume) del terreno causata dall’aumento della pressione efficace  Sign up to vote on this title

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L’entità della diminuzione dell’indice dei vuoti dipende da:

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Il decorso temporale della consolidazione primaria dipende da:

• caratteristiche di permeabilità del terreno; Sheet Music

•

esistenza o meno di terreni più permeabili ai confini dello strat Sign up to vote on this title

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Misura sperimentale delle caratteristiche di compressibilità e di consolidazione dei terre Sign up to vote on this title

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PROVA DI COMPRESSIONE EDOMETRICA Rappresentazione dei risultati in scala naturale Per ogni valore di σ’ si riporta il valore dell’indice dei vuoti relativo alla fasefinale Sign up to vote on this title della deformazione:  Useful  Not useful

ei = e o − εi ⋅ (1 + e o )

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PROVA DI COMPRESSIONE EDOMETRICA Sheet Music

Rappresentazione dei risultati in scala logaritmica  di Sign upeto vote on this Indice title

∆

Cr = Useful  Not useful ricompression ∆ log σ '

(0,015÷0,035)

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Cedimento edometrico


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Caso generale

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Cedimento edometrico Caso generale, terreno NC e terreno OC caso generale

'

σ vo

+ ∆σ v' > σ c' 

Sign up σto'cvote on this title σ 'vo + H  s logUseful +Not C useful = ⋅ log  C ⋅ ed om 1 + e  r c σ 'vo σ o

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CEDIMENTO EDOMETRICO carico su un’area con dimensioni fi Sheet Music

σ p'


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Determinazione sperimentale del coefficiente di consolidazione Metodo di Casagrande

(H50 / 2)2 ⋅ Tv cv = t 50

per U = 50% Tv = 0.197  H/2 = lunghezza drenaggio Sign up topercorso vote on thisdi title

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CEDIMENTO SECONDARIO S s = C αε ⋅ H ⋅ log

t t100


H =spessore dello strato Cαε =

∆εv/∆ logt

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coefficiente di consolidazione secondaria

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RESISTENZA AL

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RESISTENZA AL TAGLIO DEL TERRENO

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VALORI DI RESISTENZA AL TAGLIO

IN CONDIZIONI DRENATE DEI TERRENI SATURI


I valori di resistenza al taglio dipendono:  Useful  Not useful

• dallo stato iniziale del terreno (NC o OC);

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Criterio di rottura di Mohr – Coulomb (tensioni totali)

τ

τ f

= c + σ tan φ


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r a

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Criterio di rottura di Mohr - Coulomb - Terzaghi Tensioni efficaci

τ’

τ 'f = c '+ (σ − u) tan φ ' Sign up to vote on this title

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CRITERIO DI ROTTURA DI MOHR – COULOMB TENSIONI PRINCIPALI 1.

Il criterio di rottura di Coulomb viene applicato in congiunzione con il p delle tensioni efficaci

2.

L’inviluppo è rappresentato da una curva tangente ai cerchi di  Moh Sign up to vote on this title rappresentano stati di sollecitazione a rottura.  Useful  Not useful In un ambito tensionale ristretto la curva può essere approssimata con un inclinata di un angolo φ sull’orizzontale chiamato angolo di resistenza al taglio.

3.

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Tensioni principali a rottura σ '+ σ ' ⋅ (σ1 '− σ3 ') =  1 3 + c '⋅ cot gϕ '  sen ϕ 2  2 

1 Sheet Music


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(σ

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MISURA DELLA RESISTENZA AL TAGLIO IN LABORATORIO Documents

Strumento

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Tipo di terreno Sabbia

Prova di compressione triassiale

Parametro misurato

Φ‘ E

argilla

c’

Φ’ E’

angolo d’attrito modulo di deformazione Sign up to vote on this title

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coesione efficace Not useful  Useful angolo d’attrito efficace modulo di deformazione efficace

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Resistenza al taglio dei terreni granulari

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Resistenza di picco

Resistenza allo stato critico

Variazioni d volume  assen


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Resistenza al taglio dei terreni granulari Rappresentazione nel piano di Mohr

Resistenza al taglio di picco

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τ ' = σ '⋅ tan ϕ '


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 τ    σ 

tan Φ ' = 

 Not useful (σ 1 σ 3 ) sin Φ ' =

(σ 1

σ 3 )

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Resistenza al taglio dei terreni granulari INDICE DI DILATANZA

Φ ' = Φcv + mDI Bolton(1986) m = 3 per condizioni di assialsimmetria


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DIPENDENZA DELL’ANGOLO D’ATTRITO DALLA DENSITA’ RELATIVA E DALLA GRANULOMETRIA


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RESISTENZA AL TAGLIO DELLE ARGILLE IN CONDIZIO DRENATE


Resistenza di picco

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Resistenza al

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RESISTENZA AL TAGLIO DELLE IN CONDIZIONI DRENA


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VALORI DELL’ANGOLO DI RESISTENZA AL TAGLIO PER ALCUNE ARGILLE ITALIANE


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RESISTENZA AL TAGLIO DELLE ARGILLE NC IN PROVE TRIASSIALI UU

Si misurano: Deformazione assiale media: Sforzo deviatorico medio:

εa = ∆H/Ho

σa – σr = N/A


 Tensione totale radiale media (costante durante la prova): σ =σ

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RESISTENZA AL TAGLIO DELLE ARGILLE NC IN CONDIZIONI NON DRENATE 1)

L’inviluppo a rottura in termini di tensioni efficaci è rappresentato d unico cerchio di Mohr e quindi è impossibile definire i valori di c’ e Sign up to vote on this title



2)

L’inviluppo a rottura in termini di tensioni totali è rappresentato d  Useful  Not useful cerchi di Mohr con lo stesso diametro

3)

I t

i i di tensioni totali, l’invil

rottura è

etta parallela

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RESISTENZA AL TAGLIO RESIDUA

Se la deformazione per taglio raggiunge valori molto elevati (>5 nei terreni argillosi molto plastici si osserva una riduzione resistenza al di sotto del valore allo stato critico.  Sign up to vote on this title 

Useful

Questa resistenza viene chiamata resistenza

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residua di tagli

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Dipendenza della resistenza residua dal contento in argilla (%< 2µm)


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PARAMETRI DI DEFORMAZIONE Documents Sheet Music

Fattori dai quali dipendono (da M.Battaglio e M. Jamiolkowsi, 1987) IMPORTANZA PER TIPO  DI Sign up to vote on TERRENO this title

GRUPPO

FATTORE

Materiale

 a. granulometria b. composizione mineralogica c. forma dei grani

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PARAMETRI DI DEFORMAZIONE - Modulo di Youn

Il comportamento è marcatament non lineare Sign up to vote on this title



La rigidezza dipende dallo stato  Useful  Not useful tensionale

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PARAMETRI DI DEFORMAZIONE – Modulo di Young

E = Eo

E o pa

per ε < (10-4 ÷ 10-3 )%

 p'  = K E ⋅ F ( e) ⋅    pa 

n


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Variazione del modulo secante con il livello di deformazione


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PARAMETRI DI DEFORMAZIONE Variazione del modulo di deformazione

(Janbu,1963 ; Rowe, 1971)

 σ  ' 3

n E

Sign up to vote on this title E = K E p a    p a   Useful  Not useful

K E , n E =

valori sperimentali che dipendono dallo stato tensionale

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PARAMETRI DI DEFORMAZIONE - Relazione di tipo iperbolico trasformata

L’andamento della curva sforzi-deformazion può essere approssimata con una funzione di  iperbolico :Sign up to vote on this title



(σ 1 − σ 3 ) =

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ε

a + b ε

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PARAMETRI DI DEFORMAZIONE - Relazione di tipo iperbolico trasformata Perciò si avrà :

E t =

1 E i

1 


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ε

 

2

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PARAMETRI DI DEFORMAZIONE - Relazione di tipo iperbolico trasformata Quindi, sostituendo nella precedente si ha :

 (σ 1 − σ 3 ) E t = E i 1 −  (σ 1 − σ 3 )ult fattore di correlazione

  

2

 (σ 1 − σ 3Sign )  up to vote on this title E s = E i 1 −  Useful   Not useful − σ σ ( ) 1 3 ult    grado di mobilitazione dello sforzo deviatorico

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Variazione dei moduli in relazione al grado di mobilitazione dello sforzo deviatorico


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Valore operativo del modulo di deformazione

E s Eo

 q  = 1 − R ⋅   q  max 

qmax = carico a rottura q = livello tensionale agente


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MODULO DI DEFORMAZIONE PER TAGLIO




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γ = − lim

δ z →0

δ z

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MODULO DI DEFORMAZIONE PER TAGLIO

Go pa Go

n

 p'  = ⋅   ⋅ OCR m  pa  γ

= ⋅V s2 g


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