application of unsaturated soil mechanics to …不飽和土質力学の地盤工学への適用...
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不飽和土質力学の地盤工学への適用Application of Unsaturated Soil Mechanics to
Geotechnical Engineering
概要
平成22年度 地盤工学会 研究業績賞
東京農工大学大学院 農学研究院向後 雄二
・フィルダムの築堤と貯水時の安定問題
・降雨時の斜面安定問題・地下水位の低下による
地盤沈下・斜面の地震時の安定問題
・不飽和地盤材料の力学特性・不飽和地盤材料の力学挙動
発現メカニズム・弾塑性モデル・水分特性曲線モデル
不飽和土質力学 地盤工学
飽和不飽和圧密解析法
適用
＊不飽和土の典型的な力学的挙動①飽和土と比べて大きなせん断強度を有し，浸水により強度が低下する。②一定荷重下で浸水させると，圧縮（飽和コラプス；地盤が締まる）あるいは膨張（地盤が緩む）を示す。③飽和土と比べて剛性が高い。④同密度，同拘束圧であれば，飽和土よりもより過圧密側の挙動を示す。つまり，せん断時の体積変化は小さく，応力-ひずみ関係はより軟化挙動を示す。⑤降伏応力が飽和土より大きい。
サクションs
s =ua-uw
ua:間隙空気圧uw:間隙水圧
有効応力の増加
降伏応力の増加
不飽和土の力学的挙動＊の発現
不飽和土の力学挙動の発現メカニズムモデルの提案
(a) Insular air saturation (b) Pendular saturation
(c) Fuzzy saturation
Soil particle
Pore water
Pore air
不飽和土の弾塑性モデル
q
p’
降伏面s = s2
降伏面s = s1
s1 < s2
0
水分特性曲線のモデル化
f w f c c r c c
f w f c h c
0
01
r rr
r
rd r
rd rw
S Sr
S S
飽和度 Sr
サク
ショ
ンs
(kP
a)
Srw SrdSr
現在の点再吸水開始点
Srd0
吸水
脱水
共役点
飽和度 Sr
サク
ショ
ンs
(kP
a)
Srw SrdSr
現在の点再吸水開始点
Srd0
吸水
脱水
共役点
再吸水線
e d e c c r c c
e d e c h c
r rw
rd rw
S Sr
S S
再脱水線
有限要素飽和不飽和圧密解析法
水分保持状態
要素実験のシミュレーション
0 1 2 3 4 5 6 7
0
100
200
300
400
500
600
Soaked during shearing (Experimental)
Soaked during shearing (Calculated)
Saturated(Experimental)
Unsaturated(Experimental)
q
(kP
a)
Axial Strain （％）
0 1 2 3 4 5 6 7
-5
-4
-3
-2
-1
0
Soaked during shearing (Experimental)
Soaked during shearing (Calculated)
Saturated(Experimental)
Unsaturated(Experimental)
Volu
metric
Strain
（％
）
Axial Strain （％）0 1 2 3 4 5 6 7
0
100
200
300
400
500
600
Soaked during shearing (Experimental)
Soaked during shearing (Calculated)
Saturated(Experimental)
Unsaturated(Experimental)
q
(kP
a)
Axial Strain （％）
0 1 2 3 4 5 6 7
-5
-4
-3
-2
-1
0
Soaked during shearing (Experimental)
Soaked during shearing (Calculated)
Saturated(Experimental)
Unsaturated(Experimental)
Volu
metric
Strain
（％
）
Axial Strain （％）
(a) ロック材の三軸圧縮試験
(ｃ) 水分特性曲線と繰り返し弾塑性モデルの適用例
(b) ロック材の圧密試験
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Sr0 = 24.7% soaked
Sr0 = 49.2% soaked
Soaking
Soaking
Symbols = Experimental results
Solid lines = Simulation results
Void
rati
o e
0.2
0.3
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Vertical stress ( )kPa
Sr0 = 24.7% soaked
Sr0 = 49.2% soaked
Soaking
Soaking
Symbols = Experimental results
Solid lines = Simulation results
Void
rati
o e
v
v
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
Sr0 = 25.0%
Sr0 = 83.2%
Sr0 = 48.4%
Sr0 = Initial degree of saturation
Void
rati
o e
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
Sr0 = 25.0%
Sr0 = 83.2%
Sr0 = 48.4%
Sr0 = Initial degree of saturation
Void
rati
o e
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
S r0 = 25.0%
S r0 = 83.2%
S r0 = 48.4%
S r0 = Initial degree of saturation
Void
rati
o e
Vertical stress (kPa)v
v
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Sr0 = 24.7% soaked
Sr0 = 49.2% soaked
Soaking
Soaking
Symbols = Experimental results
Solid lines = Simulation results
Void
rati
o e
0.2
0.3
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Vertical stress ( )kPa
Sr0 = 24.7% soaked
Sr0 = 49.2% soaked
Soaking
Soaking
Symbols = Experimental results
Solid lines = Simulation results
Void
rati
o e
v
v
0.2
0.3
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Sr0 = 24.7% soaked
Sr0 = 49.2% soaked
Soaking
Soaking
Symbols = Experimental results
Solid lines = Simulation results
Void
rati
o e
0.2
0.3
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Vertical stress ( )kPaVertical stress ( )kPa
Sr0 = 24.7% soaked
Sr0 = 49.2% soaked
Soaking
Soaking
Symbols = Experimental results
Solid lines = Simulation results
Void
rati
o e
v
v
v
v
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
Sr0 = 25.0%
Sr0 = 83.2%
Sr0 = 48.4%
Sr0 = Initial degree of saturation
Void
rati
o e
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
Sr0 = 25.0%
Sr0 = 83.2%
Sr0 = 48.4%
Sr0 = Initial degree of saturation
Void
rati
o e
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
S r0 = 25.0%
S r0 = 83.2%
S r0 = 48.4%
S r0 = Initial degree of saturation
Void
rati
o e
Vertical stress (kPa)v
v
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
Sr0 = 25.0%
Sr0 = 83.2%
Sr0 = 48.4%
Sr0 = Initial degree of saturation
Void
rati
o e
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
Sr0 = 25.0%
Sr0 = 83.2%
Sr0 = 48.4%
Sr0 = Initial degree of saturation
Void
rati
o e
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 10 100 1000 10000
Symbols = Experimental results
Solid lines = Simulation results
S r0 = 25.0%
S r0 = 83.2%
S r0 = 48.4%
S r0 = Initial degree of saturation
Void
rati
o e
Vertical stress (kPa)v
vVertical stress (kPa)v
v
v
v
0
5
10
15
20
25
30
0 20 40 60 80 100
Degree of saturation Sr (%)
Su
ctio
n s
(
kP
a)
0.80
1.00
1.20
1.40
1.60
1.80
1 10 100 1000
Effective mean stress (kPa)
Void
rat
io
Simulation
Experimental
モデルまたは実構造物の解析
stage 5
stage 3
stage 2
stage 7
stage 8
stage 6
stage 5
stage 3
stage 2
stage 7
stage 8
stage 6
100 200100 200
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
stage 1
stage 4
stage 3
stage 2
stage 5
100 200
00
100 200
00
100 200
0
0
100 200
0
0
100 200
0
0
100 200
0
0
stage 7
stage 8
stage 6
0
10
20
30
40
50
0 100 200 300 400 500 600 700 800
経過時間（日）
水位
（ｍ
）
Measured
Analysis
１
３
２
４
５
６
７
８
Elapsed Time (day)
Upstr
eam
wate
r le
vel (m
)
0
10
20
30
40
50
0 100 200 300 400 500 600 700 800
経過時間（日）
水位
（ｍ
）
Measured
Analysis
１
３
２
４
５
６
７
８
Elapsed Time (day)
Upstr
eam
wate
r le
vel (m
)
100 200100 200
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
stage 1
stage 4
stage 3
stage 2
stage 5
100 200
00
100 200
00
100 200
0
0
100 200
0
0
100 200
0
0
100 200
0
0
stage 7
stage 8
stage 6
100 200100 200
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
100 200
0
stage 1
stage 4
stage 3
stage 2
stage 5
100 200
00
100 200
00
100 200
0
0
100 200
0
0
100 200
0
0
100 200
0
0
stage 7
stage 8
stage 6
100 200
00
100 200
00
100 200
0
0
100 200
0
0
100 200
0
0
100 200
0
0
stage 7
stage 8
stage 6
0
10
20
30
40
50
0 100 200 300 400 500 600 700 800
経過時間（日）
水位
（ｍ
）
Measured
Analysis
１
３
２
４
５
６
７
８
Elapsed Time (day)
Upstr
eam
wate
r le
vel (m
)
0
10
20
30
40
50
0 100 200 300 400 500 600 700 800
経過時間（日）
水位
（ｍ
）
Measured
Analysis
１
３
２
４
５
６
７
８
Elapsed Time (day)
Upstr
eam
wate
r le
vel (m
)
1390
1420
1450
1480
1510
1540
0
60
120
180
240
300
01-Apr-00
01-Aug-00
01-Dec-00
02-Apr-01
02-Aug-01
02-Dec-01
03-Apr-02
03-Aug-02
03-Dec-02
04-Apr-03
04-Aug-03
04-Dec-03
04-Apr-04
04-Aug-04
04-Dec-04
05-Apr-05
05-Aug-05
FL o
r R
WL
（E
L m
）
PW
P o
r V
TE
P
(×10kP
a)
Date
PWP measured
VTEP measured
VTEP estimated
Reservoir water Level
Fill Level
PWP estimated
1390
1415
1440
1465
1490
1515
1540
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
01-Apr-00
01-Aug-00
01-Dec-00
02-Apr-01
02-Aug-01
02-Dec-01
03-Apr-02
03-Aug-02
03-Dec-02
04-Apr-03
04-Aug-03
04-Dec-03
04-Apr-04
04-Aug-04
04-Dec-04
05-Apr-05
05-Aug-05
FL o
r R
WL （
EL m
）
Sett
lem
ent
（
ｍ）
Estimated
Measured
Reservoir Water Level
Fill Level
Date
図-4 各種計測器の配置
1420
1460
1500
1380
1540E.L.(m)
凡例
○：間隙水圧計
●：土圧，間隙水圧計
：層別沈下計
pwp
EP & PWP
Cross Arm
PWP
EP & PWP
Cross arm
飽和不飽和圧密解析法の適用例
フィルダム湛水時の遠心実験解析(a)水平応力(b)変位
実フィルダム湛水時の解析
(a)
(b)