Filters in Embankment Dams:
Design Example
Noah Vroman, P.E.
USACE Vicksburg District
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Introduction
• Example filter design for a large embankment dam
– The example is based on an actual dam with excellent seepage
performance
– The example includes design of a chimney filter, blanket drain,
and drain collection system
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General Dam Information
Surcharge Pool = 447.5’
Top of Dam = El. 453.0’
Embankment
Weathered Rock
Dam Height = 243.0 ft
Design Head = 237.5 ft……5.5 ft of ‘freeboard’
Dam will serve mainly flood control purposes.
Dam will store a maximum of ~1.4 million acre-feet of water.
Failure of the dam will impact a population of 13,500
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El. 210.0’
Actual Embankment Cross Section
Core trench needs a downstream filter
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Embankment and Foundation Information
• Embankment
– Rolled earthfill
– Core materials will consist of impervious sandy clays/clay
gravels from terrace deposits within local borrow pits at the dam
site
• Foundation
– Composed mainly of sandstone and shale
– Strike favorable to the dam orientation (parallel to dam axis)
– Joints/fractures up to 1/4in widths
• Mainly caused by stress relief in the valley
– Upper zone of the formation is more permeable than lower zone
– A major fault runs perpendicular to the dam near the left
abutment
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Cross Valley Profile
• Overhangs likely encountered in the abutments
• Depth of physical weathering is not significantly deep
• Average slope of abutments are 1H:2V
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General Failure Modes to Consider
Surcharge Pool = 447.5’
Top of Dam = El. 453.0’
El. 210.0’
Embankment Seepage:
- Stability of the Embankment
- Internal Erosion – hydraulic fracturing and cracking
Foundation Seepage:
- Stability of the Embankment Slope
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240
320
380
44
0
Seepage Analysis
Embankment Permeability = 1e-7 ft/min
- Based on lab test on compacted samples
Foundation Permeability = 0.005 ft/min
- Based on field pressure test in borings
- Four orders of magnitude higher than the embankment
Values considered conservative based on data collected
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Embankment Seepage
• Initial Analysis Kh/Kv = 1.0
– Additional analysis was conducted at Kh/Kv =10 and 100 to
account for construction practices
Kh/Ky = 100.0
Kh/Ky = 10.0
240
320
380
44
0
Kh/Ky = 1.0
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Embankment Seepage
• Estimated seepage quantities extremely low
– 2e-4 to 2e-3 gpm
– 20 to 2 gpm per 1,000 ft of dam
• Stability analysis based on seepage analysis
– Kh/Kv = 1.0; FOS = 1.5
– Kh/Kv = 100; FOS = 1.3
– Stability is marginal
• EM 1110-2-1902 requires Factor of Safety of 1.5
• Major concern is internal erosion
– Design will consider chimney filter
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Step 1: Plot Gradation Curves of Core
Embankment Filter Design
Average
Core Material Gradation
Based 179 samples
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Step 2: Re grade Core on #4 Sieve
Average
Core material not considered to be dispersive
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Step 3: Determine Base Soil Category
% Finer than No. 200
Low = 58%
Avg =
65%
High = 78%
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Step 4: Particle Retention Criteria
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Step 5: Permeability Requirements
Max D15B = < 0.075 mm….hydrometer test unavailable
At 0.075 mm
Min D15F = 5 * 0.075 mm = 0.375 mm
Permeability requirements are not essential in this case
Max D15F/MinD15F =5; Max D15F = 0.7 mm
Min D15F = 0.7 mm / 5 = 0.14 mm…>0.1mm GOOD!
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Step 6: Limit filter band width (gap gradedness)
Step 6:
0.7 mm 0.14 mm
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Step 6: Limit filter band width (gap gradedness) (cont’d)
• Max D10
– MaxD15 * 0.7 = 0.7 mm * 0.7 = 0.49 mm – Point C
• Min D10
– MinD15 * 0.7 = 0.14 mm * 0.7 = ~0.1 mm – Point D
• Max D60
– Max D10 * 6 = 0.49 mm * 6 = 2.94 mm – Point E
• Min D60
– Min D10 * 2 = 0.1 mm * 2 = 0.2 mm – Point F
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Step 6: Limit filter band width (gap gradedness)
E
F
0.7 mm 0.14 mm
C
D
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Step 7: Determine Min D5F and Max D100F
H
E
F
C
D
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G
Step 8: Determine Max D90F
H
I
E
F
Max Filter Limit
C D
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G
Step 9: Band Limit Control….Ratio of 5 less than D60
H
I
F
E
Max Filter Limit
Bandwidth = Max D60/5
=2.95 mm/5 = 0.588 mm
D
C
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G
Step 10: Check commercially available materials
H
I
F
C33 – Concrete Sand
E
Max Filter Limit
OK
D
G
C
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Step 10: Alternatively check vertical limits
H
I
F
C33 – Concrete Sand
E
35 Points
OK
Vertical Limit
D
G
C
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Alternate source located 10 miles from site
H
I
E
F
35 Points
OK
Vertical Limit
D
C
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G
Chimney Filter
Chimney Filter
Floodside
Core
Shell
Shell
Weathered Rock
Design:
-
Due to availability of core materials, upstream and downstream shell
zones were added.
-
Vertical 10-foot wide chimney filter.
-
Width of chimney filter selected due to construction equipment and
importance of the filter.
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Design of Drainage Blanket
• Gravel Drainage blanket will be used.
–
–
–
–
Importance to collect foundation seepage.
No particle retention criteria required due to rock formation
Filter and provide drainage for the chimney filter
Sand layer will be placed above the gravel to protect against
shell
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Drainage Blanket
Drainage Blanket
Floodside
Core
Shell
Weathered Rock
Blanket:
Assume gravel blanket is 10 ft thick for trial
Assume permeability is alteast 100 times greater than chimney filter
….will check filter requirements later..
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Seepage Analysis with Blanket Drain
• Seepage collected in drain
360
400
320
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220
240
280
440
– 10 ft thick blanket; Q = 0.1101 ft^3/min….69 gpm per 100 ft
Flow capacity of the seepage blanket
• Cedergren: Seepage, Drainage, and Flow Nets; 1967
– Estimate required thickness from Darcy’s Law (assumes laminar
flow and may under estimate the head loss)
• Q = kiA …….k = permeability, i = gradient, A = area
• Q = 0.1101 ft^3/min
• k = 6 ft/min
• i = H/L …… L = length of drainage blanket = 840 ft
• A = 10 ft thick …. Assume per foot of dam
H = 0.1101 ft^3/min * 840 ft / (6 ft/min) / 10 ft
H = 1.5 ft …. Blanket thicker than required for seepage
TRY a 4 ft thick blanket
H
L
GOAL: H < BLANKET THICKNESS
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Flow capacity of the seepage blanket
•
•
•
•
•
Q = kiA …….k = permeability, i = gradient, A = area
Q = 0.1101 ft^3/min
k = 6 ft/min
i = H/L …… L = length of drainage blanket = 840 ft
A = 4 ft thick …. Assume per foot of dam
H = 0.1101 ft^3/min * 840 ft / (6 ft/min) / 4 ft
H = 3.85 ft…..USE A 5ft THICK BLANKET TO ACCOUNT FOR
UNKNOWNS
Other consideration: 50’ deep grout curtain installed beneath
the core centerline and will reduce foundation seepage.
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Step 1: Plot Gradation Curves of Chimney Filter
Chimney Filter Gradation
Based 164 samples
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Step 2: Re grade Chimney Filter on #4 Sieve
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Step 3: Determine Base Soil Category
% Finer than No. 200
Low = 0%
Avg =
2.5%
High = 5%
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Step 4: Particle Retention Criteria
D85B:
Low =1.84 mm
(Fine Side
Boundary)
D15F =7.36 mm
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Step 5: Permeability Requirements
Max D15B = 0.411 mm
Min D15F = 5 * 0.411 mm = 2.055 mm
Permeability requirements are essential in this case!
Seepage analysis assumed 6 ft/min.
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7.36 mm
2.05 mm
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Step 6: Limit filter band width (gap gradedness)
Step 6:
B
0.14 mm
A 0.7 mm
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Step 6: Limit filter band width (gap gradedness) (cont’d)
• Max D10
– MaxD15 * 0.7 = 7.35 mm * 0.7 = 5.152 mm – Point C
• Min D10
– MinD15 * 0.7 = 2.055 mm * 0.7 = 1.439 mm – Point D
• Max D60
– Max D10 * 6 = 5.152 mm * 6 = 30.912 mm – Point E
• Min D60
– Min D10 * 2 = 1.44 mm * 2 = 2.877 mm – Point F
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Step 6: Limit filter band width (gap gradedness)
E
F
A
C
B
D
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Step 7: Determine Min D5F and Max D100F
H
E
F
C
D
G
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Step 8: Determine Max D90F
H
I
Min D10 = 1.43
mm
E
F
Max Filter Limit
C
D
G
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Step 9: Band Limit Control….Ratio of 5 less than D60
H
Bandwidth = Max D60/5
I
=30.91 mm/5 = 6.18 mm
E
F
Max Filter Limit
C
D
G
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Step 10: Check source located 10 miles from site
H
I
E
F
X CLOSE!
Max Filter Limit
C
D
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Step 10: Check source located 18 miles from site
H
I
E
F
OK
Check Max and
Segregation
Max Filter Limit
C
D
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Step 10:Check source located 18 miles from site
• Maximum Particle:
– Source: 3 in
– USACE guidelines allows 3 in
• Segregation:
–
–
–
–
D10 = 5.15 mm (coarse side)
Max D90 from criteria = 50 mm
Source Max D90 =52 mm
Segregation is OK!
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Step 10: Alternatively check vertical limits
H
I
E
F
35 Points
OK
Vertical Limit
C
D
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Check Blanket Permeability
• Seepage Analysis: 6 ft/min
• Estimate permeability based on gravel material selected
– D15 Max = 7.36 mm………..k = 0.35 (7.36 mm)^2 = 18.9 cm/sec
k = 37.5 ft/min
– D15 Min = 3.5 mm………….k = 0.35 (3.5 mm)^2 = 4.28 cm/sec
k = 8.42 ft/min
• Good!
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Embankment Design
Drainage Blanket
Floodside
Core
Shell
Weathered Rock
• Shell composed of 35% fines, 40% sand, and 25%
gravel
• Shell is graded from fine to coarse in direction away from
the core.
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Embankment Design
Drainage Blanket
Floodside
Core
Shell
Weathered Rock
• Protective filter is needed above the gravel drainage
blanket…….will use 1 ft thick sand layer above drainage
blanket.
• Will need a collection system in the drainage blanket
– Use perforated pipe
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Check Stability
• Stability analysis based without chimney and drainage
blanket
– FOS = 1.3
• Stability analysis with chimney and drainage blanket
– FOS = 1.68
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Perforated Pipe Requirements
• Max Perforation Size = Min D50 of the Blanket
– D50 = 9.5 mm or 3/8 inch
• Pipe required to handle 0.11 ft^3/min per foot of dam
– Dam is 1,500 ft long.
• Collection pipe diameter should be oversized for
potential biofouling which would clog the perforations.
– Capacity of the pipe to collect seepage related to the pipe
diameter.
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