SCHEDE APPLICATIVE DI GEOTECNICA

Argomento Tensioni Totali e Tensioni efficaci Redattore Dott. Ing. Simone Caffè Riferimento ENV 1997 – 1 – 1

SCHEDE APPLICATIVE DI GEOTECNICA

Scheda 1 Pagina 1di 3

STRATIGRAFIA DEL TERRENO

La potenza del primo strato è pari a 5 [m], mentre quella del secondo strato è pari a 10 [m]. La falda è alta 5 [m].

CALCOLO DELLE TENSIONI TOTALI VERTICALI [ ]1 1

yy=γdry⋅y σ

(

^y1 ⁰

)

⁰

yy = =

σ [kPa]

(

^{y 5}

)

^{[ ]}1 ^h1 ^{17 5 85} 1 dry

yy = =γ ⋅ = ⋅ =

σ [kPa]

[ ] [ ]

2 2 dry 1 1

dry

yy =γ ⋅h +γ ⋅y σ

(

^{y 0}

)

^{[ ]}1 ^h1 ^{17 5 85} 2 dry

yy = =γ ⋅ = ⋅ =

σ [kPa]

(

^{y 5}

)

^{[ ] h [ ]}2 ^h2 ^{17 5 16 5 165}

dry 1 1

dry 2

yy = =γ ⋅ +γ ⋅ = ⋅ + ⋅ =

σ [kPa]

[ ] [ ]2 2

(

[ ]wet^{2 water}

)

^{3 water 3}

1 dry dry1

yy=γ ⋅h +γ ⋅h + γ −γ ⋅y +γ ⋅y

σ

(

^{y 0}

)

^{[ ] h [ ]}2 ^h2 ^{17 5 16 5 165}

dry 1 1

dry 3

yy = =γ ⋅ +γ ⋅ = ⋅ + ⋅ =

σ [kPa]

( )

^{[ ] [ ]}

(

^{[ ]}

)

(

^{y 5}

)

^{17 5 16 5}

(

^{21 10}

)

^{5 10 5 270}

y y

h h

5 y

3 yy

3 water 3 water wet2 2 2

1 dry dry1 3

yy

=

⋅ +

⋅

− +

⋅ +

⋅

=

= σ

⋅ γ +

⋅ γ

− γ +

⋅ γ +

⋅ γ

=

=

σ [kPa]

CALCOLO DELLE TENSIONI EFFICACI VERTICALI [ ]1 1

yy =γdry⋅y σ′

(

^y1 ⁰

)

⁰

yy = =

σ′ [kPa]

(

^{y 5}

)

^{[ ]}1 ^h1 ^{17 5 85} 1 dry

yy = =γ ⋅ = ⋅ =

σ′ [kPa]

[ ] [ ]

2 2 1 dry dry1

yy =γ ⋅h +γ ⋅y σ′

(

^{y 0}

)

^{[ ]}1 ^h1 ^{17 5 85} dry

2

yy = =γ ⋅ = ⋅ =

σ′ [kPa]

(

^{y 5}

)

^{[ ] h [ ]}2 ^h2 ^{17 5 16 5 165}

1 dry dry1 2

yy = =γ ⋅ +γ ⋅ = ⋅ + ⋅ =

σ′ [kPa]

[ ] [ ]

(

[ ]2 water

)

3

wet 2 2

dry 1 1

dry

yy=γ ⋅h +γ ⋅h + γ −γ ⋅y

σ′

(

^{y 0}

)

^{[ ] h [ ]}2 ^h2 ^{17 5 16 5 165}

1 dry dry1 3

yy = =γ ⋅ +γ ⋅ = ⋅ + ⋅ =

σ′ [kPa]

( )

^{[ ] [ ]}

(

^{[ ]}

)

(

^yy3 ⁵⁵

)

^{17 5h16 5}

(

^{h21 10}

)

^{5 220 y}

yy

3 water wet2 2 2

dry 1 1

dry 3

yy

=

⋅

− +

⋅ +

⋅

=

= σ′

⋅ γ

− γ +

⋅ γ +

⋅ γ

=

=

σ′ [kPa]

[ ]

[ ]

[ ]

[ ]

[ ]= ° φ

= γ

= γ

30 m kN 20

m kN 17

1

3 wet1

3 dry1

Falda

y1

y2

y3

y

x

[

³

]

water =10kNm γ

[ ]

[ ]

[ ]

[ ]

[ ]= ° φ

= γ

= γ

26 m kN 21

m kN 16

2

3 wet2

3 dry2

Argomento Tensioni Totali e Tensioni efficaci Redattore Dott. Ing. Simone Caffè Riferimento ENV 1997 – 1 – 1

SCHEDE APPLICATIVE DI GEOTECNICA

Scheda 1 Pagina 2di 3

CALCOLO DELLE TENSIONI TOTALI ORIZZONTALI

Calcolo del coefficiente di spinta a riposo:

[ ] [ ]

( )

[ ]^{==1−−senφφ}[ ]^==1−−sen

( )

^26==0.5616

k

50 . 0 30 sen 1 sen 1 k

2 02

1 01

[-]

[ ] [ ]

1 1 1 dry xx =k0 ⋅γ ⋅y σ

(

^y1 ⁰

)

⁰

xx = =

σ [kPa]

(

^{y 5}

)

^{k[ ] [ ]}1 ^h1 ^{0.50 17 5 42.50} 1 dry

1 0

xx = = ⋅γ ⋅ = ⋅ ⋅ =

σ [kPa]

[ ]

(

[ ]1 1 [ ]dry^{2 2}

)

2 dry

xx=k0 ⋅γ ⋅h +γ ⋅y σ

(

^{y 0}

)

^{k[ ] [ ]}1 ^h1 ^{0.5616 17 5 47.74} 2 dry

0 2

xx = = ⋅γ ⋅ = ⋅ ⋅ =

σ [kPa]

(

^{y 5}

)

^{k[ ]}

(

^{[ ] h [ ]}2 ^h2

)

^0.5616

(

^{17 5 16 5}

)

^92.664

1 dry dry1 02 2

xx = = ⋅ γ ⋅ +γ ⋅ = ⋅ ⋅ + ⋅ =

σ [kPa]

[ ]

[

[ ] [ ]2 2

(

[ ]wet^{2 water}

)

³

]

^{water 3}

1 dry 1 dry 2

xx=k0 ⋅γ ⋅h +γ ⋅h +γ −γ ⋅y +γ ⋅y

σ

(

^{y 0}

)

^{k[ ]}

[

^{[ ] h [ ]}2 ^h2

]

^0.5616

(

^{17 5 16 5}

)

^92.664

1 dry dry1 02 3

xx = = ⋅γ ⋅ +γ ⋅ = ⋅ ⋅ + ⋅ =

σ [kPa]

( )

^{[ ]}

[

^{[ ] [ ]}

(

^{[ ]}

) ]

(

^yy3 ⁵⁵

)

^k0.5616

[

^{17h5 16 5h}

(

^{21 10}

)

⁵

]

^{10 y5 173.55 y}

xx

3 water 3 water wet2 2 2

1 dry dry1 02 3

xx

=

⋅ +

⋅

− +

⋅ +

⋅

⋅

=

= σ

⋅ γ +

⋅ γ

− γ +

⋅ γ +

⋅ γ

⋅

=

=

σ [kPa]

Argomento Tensioni Totali e Tensioni efficaci Redattore Dott. Ing. Simone Caffè Riferimento ENV 1997 – 1 – 1

SCHEDE APPLICATIVE DI GEOTECNICA

Scheda 1 Pagina 3di 3

CALCOLO DELLE TENSIONI EFFICACI ORIZZONTALI

Calcolo del coefficiente di spinta a riposo:

[ ] [ ]

( )

[ ]^{==1−−senφφ}[ ]^==1−−sen

( )

^26==0.5616

k

50 . 0 30 sen 1 sen 1 k

2 02

1 01

[-]

[ ] [ ]

1 1 1 dry xx =k0 ⋅γ ⋅y σ′

(

^y1 ⁰

)

⁰

xx = =

σ′ [kPa]

(

^{y 5}

)

^{k[ ] [ ]}1 ^h1 ^{0.50 17 5 42.50} 1 dry

1 0

xx = = ⋅γ ⋅ = ⋅ ⋅ =

σ′ [kPa]

[ ]

(

[ ]1 1 [ ]dry^{2 2}

)

2 dry

xx=k0 ⋅γ ⋅h +γ ⋅y σ′

(

^{y 0}

)

^{k[ ] [ ]}1 ^h1 ^{0.561617 5 47.74} 2 dry

0 2

xx = = ⋅γ ⋅ = ⋅ ⋅ =

σ′ [kPa]

(

^{y 5}

)

^{k[ ]}

(

^{[ ] h [ ]}2 ^h2

)

^0.5616

(

^{17 5 16 5}

)

^92.664

1 dry dry1 02 2

xx = = ⋅ γ ⋅ +γ ⋅ = ⋅ ⋅ + ⋅ =

σ′ [kPa]

[ ]

[

[ ] [ ]2 2

(

[ ]wet^{2 water}

)

³

]

1 dry 1 dry 2

xx=k0 ⋅γ ⋅h +γ ⋅h +γ −γ ⋅y σ′

(

^{y3 0}

)

^{k[ ]02}

[

^{[ ]dry1 h1 [ ]dry2 h2}

]

^0.5616

⁽

^{17 5 16 5}

⁾

^92.664

xx = = ⋅γ ⋅ +γ ⋅ = ⋅ ⋅ + ⋅ =

σ′ [kPa]

( )

^{[ ]}

[

^{[ ] [ ]}

(

^{[ ]}

) ]

(

^yy3 ⁵⁵

)

^0k.5616

[

^{17h5 16 5h}

(

^{21 10}

)

⁵

]

^123y.55

xx

3 water wet2 2 2

1 dry dry1 02 3

xx

=

⋅

− +

⋅ +

⋅

⋅

=

= σ′

⋅ γ

− γ +

⋅ γ +

⋅ γ

⋅

=

=

σ′ [kPa]

Discontinuità