Formelsammlung zur Vorlesung Bodenmechanik I - IBF

11. Erddruck SS 2011
• Erddruckbeiwerte – Aktiv
- Fall 1 α = 0 β = 0 δ = 0 a k t i v
⎛ ⎞
= tan ⎜ − ⎟
⎝ 4 2 ⎠
2 π ϕ
K ah
π/4 = 45° !
π ϕ
ϑ a = +
4 2
e = γ ⋅ h + q ⋅ K − 2⋅
c ⋅
ah
[ ] ah K ah
1 2
⎡
Eah = ⎢ ⋅γ
⋅ h
⎣2
⎤
+ q ⋅ h⎥
⋅ K ah − 2 ⋅c
⋅ h ⋅
⎦
= 0 E = E
E av
a ah
- Fall 2 α = 0 β = 0 δ ≠ 0 a k t i v
K ah =
⎡
⎢1
+
⎣
2
cos ϕ
2
sin(
ϕ + δ ) ⋅sinϕ
⎤
⎥
cosδ
⎦
⎡
ϑ
⎢
a = ϕ + arccot tanϕ
+
⎢
⎣
tanδ
1+
⎤
tanϕ
⎥
cosϕ
⎥
⎦
arccot[ L] = 90°
− arctan[
L]
e ah = [ γ ⋅ h + q]
⋅ K ah − 2⋅ c ⋅ K ah ⋅ cosδ
⎡1
2 ⎤
E ah =
⎢
⋅γ
⋅ h + q ⋅ h ⋅ − 2⋅
⋅ ⋅
⎣2
⎥
Kah
c h
⎦
Kah
⋅ cosδ
E av = Eah
⋅ tanδ
Eah
E a =
cosδ
- Fall 3 α ≠ 0 β ≠ 0 δ ≠ 0 a k t i v
2
cos ( ϕ + α )
K ah=
2
⎡ 2 sin(
ϕ + δ ) ⋅sin(
ϕ − β ) ⎤
cos α ⋅ ⎢1
+
⎥
⎣ cos(
α − δ ) ⋅ cos(
α + β ) ⎦
ϑ = ϕ
e
E
E
a
ah
ah
av
( )
( )
( ) ( )
( ) ( ) ⎥ ⎡
1
+ arccot⎢tan
α + ϕ +
⎣
cos α + ϕ
sin ϕ + δ ⋅ cos α + β ⎤
sin ϕ − β ⋅cos
δ −α
⎦
[ γ ⋅ h + q]
⋅ K − ⋅ c ⋅ K ⋅ ( δ −α
)
= ah 2 ah cos
1 2
⎡
=
⎢
⋅γ
⋅ h
⎣2
⎤
+ q ⋅ h
⎥
⋅ Kah
− 2⋅
c ⋅h
⋅
⎦
Kah
⋅ cos −
= ah ⋅ tan δ −α
E
Eah
E
a =
cosδ
−α
K
ah
( δ α )
Formelsammlung Bodenmechanik I 15