of engineers us army corps critical state for · 2017. 8. 2. · 4 heartland engineers us army...
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1 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Critical State forProbabilistic Analysis ofLevee Underseepage
Douglas Crum, P. E.
2 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
1. Failure Prediction
2. Reliability
3. Levee Underseepage
4. Surcharge Factor
5. Evidence (Case Histories)
6. Recommendations
3 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Levee Consequences & Damages
• ImpendingFailureMechanism
• Prediction ofLimit(Collapse)State
• Not DesignCriteria
4 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Reliability Criteria• PGL No. 26 (1991)
• Requires reliability approach for levees• Mentions PFP/PNP
••• ETL 1110ETL 1110ETL 1110---222---328 (1993)328 (1993)328 (1993)••• Template MethodTemplate MethodTemplate Method
• ER 1105-2-101 (1996)• Requires risk analysis for flood damage reduction studies
• EM 1110-2-1619 (1996)• Economics
• ETL 1110-2-556 (1999)• Geotechnical risk analysis for planning studies• Appendix B, “Evaluating the Reliability of Existing Levees”
5 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Reliability
• Taylor’s Series (first order – second moment)• Point Estimate• Advanced Method (Hasofer & Lind)• Monte Carlo
Methods
6 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Underseepage (i > icr)
Throughseepage
Overtopping
Medium Consequence = Flood Fight
High Consequence = Breach
Low Consequence = Just Watch
P=.8
P=.1
P=.1
P=.1
P=.2
P=.7
P=.01
P=.02
P=.07
Reliability
7 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
LEVEE FAILURE MODES• Overtopping
•Other (Scour, Trees, etc.)
8 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
LEVEE FAILURE MODESSlides
• End of Construction• Steady State Seepage• Rapid Drawdown
• SeepageThrough-seepageUnder-seepage Pipes/Structures
9 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
gw
blwblsatg
HZZFS
⋅⋅−⋅=
γγγ
blwgw
blsatup
ZHZFS⋅⋅
⋅=+ γγ
γ
At critical state:FSup = FSg = 1
Levee Underseepage:Piping and Heave
10 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
icr = γb/γh20 = (Gs – 1)/(1+e)
Performance Function
Critical state at “quick conditions”is when effectivestress throughout layer is reduced to zero.
FSg = icr/i
11 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
FSg = icr/iCapacity (C) = icr = critical gradient
Demand (D) = i = calculated gradient
22
)()(
DC
DECE
σσβ
+
−=
Normally distributed, uncorrelated:
Unsatisfactory Performance atthe Critical Gradient
12 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
X3L2X1
X3X1 + L2 + X3
mtoe =
Levee Underseepage
13 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Hea
ve
River Water Level
Piez
omet
er le
vel a
t toe
~icr
Flow
, Q (g
pm/lf
)
mtoe
1
Levee Underseepage: ExtrapolatedGradient
14 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
WESTechnicalMemorandum3-424Figure 47(1956)
15 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
CASE 1: Kansas City District, HistoricDesign Criteria for Agricultural Levees
• No past boil activity, FSg = 1• Minor boil or heavy seepage, FSg = 1.25• Major boil activity, FSg = 1.5
The ratio 1:1.5 approximates(Critical State : Failure State).�(icr/if) = 1/1.5 = 0.67 ≅ 0.7
References:Design memorandum no. 1 – underseepage control – levee unit 400-L, 20 Nov. 1953Design memorandum no. 1 – underseepage control – levee unit 406-L, revised 24 mar 1953
16 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
CASE 2: Rock Island District, HistoricDesign Criteria for Agricultural Levees
• “The Rock Island District has a philosophy….. toorganize the necessary men and equipment to put up aflood fight. …they feel justified in allowing majorboils to develop…”
• Design criteria at toe: FSg > 0.7Assuming a necessary flood fight to prevent abreach is tantamount to failure, i = if�(icr/if) = FSg = 0.7
Reference:Rock Island District Levee Practices, MRKED-F Memorandum for Branch File,25 October 1962.
17 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
CASE 3: Kansas City District, BackCalculation from 1952 Flood
�(icr/if) = (.55/.8) = 0.6875 ≅ 0.7
Reference:Meeting at MRD on Underseepage Control on Agricultural Levees, 27 November 1962.
Tolerable Seepage, distributed seepage, pinboils> 0.8
Objectionable seepage, major flood fight,boils requiring sandbagging< 0.55
Seepage Conditions during flood crestComputed FSgat flood crest
18 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
CASE 4: St. Louis District, BackCalculation from 1993 Flood
Bois Brule & Kaskaskia Island levee failures• Both failures were due to underseepage and resulted in
an actual breach of the levee.• Back calculated gradient = 1.35• Assume icr ≅ 0.85
�(icr/if) = (.85/1.35) = 0.63
Reference:Communication with Mr. Edward Demsky, CEMVS, 19 July 2004
19 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
CASE 5: 1993 Flood Calibrations forExisting Projects
L455 Levees
0.00
0.01
0.02
0.03
0.04
0.05
0 10 20 30 40
SectionPr
obab
ility
of
Failu
reR471 Levees
0.00
0.10
0.20
0.30
0.40
0 10 20 30 40
Section
Prob
abili
ty o
f Fa
ilure
20 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
FSg = icr/iCapacity (C) = icr = critical gradient
Demand (D) = i = calculated gradient
22
)()(
DC
DECE
σσβ
+
−=
Normally distributed, uncorrelated:
Unsatisfactory Performance atthe Critical Gradient
21 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
FS = if /iSurcharge Factor = (icr/if) ≅ 0.7
Capacity (C) = if = icr/(icr/if) = “failure” gradient
Demand (D) = i = calculated gradient (extrapolated)
22
)()(
DC
DECE
σσβ
+
−=
Normally distributed, uncorrelated:
Unsatisfactory Performance atImpending Failure
22 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Recommendations
• Rational methods are necessary for derivingthe Limit State from design criteria
• A consistent methodology should beadopted
• Impending Levee Breaches Occur near aSurcharge Factor of (icr/if) = 0.7
23 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Design Criteria Concerns
• Deterioration of Levee from Past SeepageDistress
• Flood Fight Capability• Managing Risk & Consequences
(Urban/Rural/Agricultural)• Affect on B/C ratio
24 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
“The committee recommends that the Corpsundertake statistical ex post studies to comparepredictions of geotechnical levee failureprobabilities made by the reliability modelagainst frequencies of actual levee failuresduring floods.”
From executive summary, “Risk Analysis and Uncertaintyin Flood Damage Reduction Studies”, National AcademyPress, (2000).
25 HEARTLAND ENGINEERS
US Army CorpsUS Army Corpsof Engineersof EngineersKansas City DistrictKansas City District
Doug Crum
816/983-3604
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