fluid transport in soils iii: piping and boiling...so far, soil particles have been assumed stable...
TRANSCRIPT
Lecture No.6
Fluid transport in soils III: Piping and Boiling
（土中の流体移動 III：パイピングとボイリング）
So far, soil particles have been assumed stable (do not move).
How far can a pot go up, without causing piping and boiling?
Pot
■ Instability by Seepage （浸透による不安定現象） 1
Force by water
pressure
H1
H2
L
Cross-section
area, A
DH
Reaction（反力）
from bottom, P
Force by water
pressure
Soil’s
weight
If the pot is lifted, P becomes 0 at some point (soil starts floating)
Pot
■ Force equilibrium under seepage （浸透下の力の釣り合い） 2
Force by water
pressure
H1
H2
gwH2A
L
Cross-section
area, A
gt LA
DH
Reaction（反力）
from bottom, P
Force by water
pressure
Soil’s
weight
gwH2A + gtLA - gwH1A – P = 0
Hydraulic gradient when P = 0:
gwH1A
Pot
■ Force equilibrium under seepage （浸透下の力の釣り合い） 3
P = 0
The net force exerted by water in flow direction, F
■ Seepage force （浸透力） 4
Force by
water pressure
gwH2A
gt LA
Reaction（反力）
from bottom, P
Force by water
pressure
Soil’s
weight
gwH1A
Per area (i.e. pressure) L
gwH2
Pressures
gwH1
gwL gwiL
Hydrostatic
Boiling ≈ Quicksand （クイックサンド）
Instability (complete loss of strength)
by upward seepage;
inter-particle contact is lost and
soil behaves as mud. （流体の開放面向きの浸透により、
土粒子が浮いた状態になり、強度を
失う不安定現象。泥水のようになる） Boiling!
■ Boiling and piping （ボイリングとパイピング） 5
Piping
Formation of localised seepage
channel by loss of soil particles. （流れの局所化により水みちが形成）
How much is the critical hydraulic gradient, ic?
Example:
Assuming Gs = 2.7, e = 0.8 …
H2
H1
L
Cross-
section
area, A
DH
■ Critical hydraulic gradient, ic （限界動水勾配） 6
However, in reality, boiling occurs with much smaller value
of ic than the theory predicts (such as 0.6~0.8).
Consider equilibrium of force just inside the sheet-pile. Why?
a i
a
i
Pressure distribution （圧力分布）
Pore water pressure （間隙水圧） u
D
H
■ Stability of excavated base （掘削底面の安定性） 7
Application of the theory to 2D flow
Impervious layer
H
D
①
②
③
④
⑤
① ② ③ ④ ⑤
Pressure
Head
(Pressure)
0
(0)
H
(gwH) 0
Potential
Head H+D D 0 D 0
Piezometric
Head H+D H+D D
Base of the potential head （位置水頭の基準）
Pore water pressure
at different points
■ Stability of excavated base （掘削底面の安定性） 8
Equilibrium of force
(for D/2×D block)
a i
a
i
Pressure distribution （圧力分布）
Hwg2
1
DwgD2
1D
H
D2
1
■ Stability of excavated base （掘削底面の安定性） 9
At the critical equilibrium,
avwhg
2
2
1DtgTotal weight
of soil
(including water)
Total water
pressure
Submerged
weight of soil:
Total weight minus
buoyant force （浮力）
Excess pore water pressure （過剰間隙水圧）
At the critical equilibrium,
( )DγhγD wavw +×2
1
■ Submerged unit weight, g ' （水中単位体積重量） 10
Subtract
buoyant
force （浮力）
Subtract
hydrostatic
pressure
■ Factor of safety against boiling （ボイリングに対する安全率） 11
Submerged weight of soil:
Total weight minus
buoyant force （浮力）
Excess pore water pressure （過剰間隙水圧） avwhγD
2
1
( 22
2
1
2
1DDwt ggg W
U
The critical hydraulic gradient
ic increases by p/gwD
Surcharge
(pressure), p
D
H
( )DγhγD wavw +×2
1
2
2
1Dtg
pD2
1
( 02
1-
2
1
2
1 2 DhDDpD wavwt ggg
Dγ
p
γ
γγ
D
hi
ww
wtav
c +==
D2
1
■ Effect of surcharge （上載圧の効果） 12