1. LINTON UNIVERSITY COLLEGE SCHOOL OF CIVIL ENGINEERING
SOIL MECHANICS (BCE 3303)
Seepage and Flownet
Lecture
Mdm Nur Syazwani

2. INTRODUCTION Two-dimensional flow Water DAM Water PERMEABLE SOIL
Seepage
Water Vx Vz
PERMEABLE SOIL Vx Vz
Two-dimensional flow

3. INTRODUCTION
Pore spaces between soil particles are interconnected and water is free to flow within the soil mass
Flow of water through soils is called seepage.
Seepage takes place when there is difference in water levels on the two sides of the structure
The vertical and horizontal velocity components vary from point to point within the cross-section of the soil mass

7. To address all these, let’s look at some fundamentals in flow……
If we know the permeability of the soil, how do we compute the discharge through the soil?
How do we compute the pore water pressures at various locations in the flow region or assess the uplift loading on the bottom of the concrete dam?
Is there any problem with hydraulic gradient being too high within the soil?
To address all these, let’s look at some fundamentals in flow……

8. FLOW THROUGH SOILS Total head = Total head =
Bernoulli’s equation for steady flow of non-viscous incompressible flow:
Total head =
When water flow through soil, the seepage velocity is often very small and negligible, Bernoulli’s equation becomes:
Elevation Head
Pressure Head
Velocity Head
Total head =

9. DARCY’S LAW
In saturated condition, 1-D flow is governed by Darcy’s Law:
The quantity flowing is therefore given by:
Hydraulic Gradient
Permeability of Soil
Difference in Total Head
Flow Velocity
Flow Path Length
Area through which flow is taking place

10. TWO-DIMENSIONAL FLOW
Seepage taking place around water retaining structure (sheet pile, dams etc.) and embankments is 2-D i.e. vx & vz vary from point to point
A Flow Net is a graphical solution to the Laplace equation for two-dimensional flow in a homogenous and isotropic (kh = kv) soil mass
Two sets of derived orthogonal curves :
Equipotential Lines
Flow Lines

11. FLOW NET (GRAPHICAL PROPERTIES)

12. FLOW NET (GRAPHICAL PROPERTIES)
Flow lines and Equipotential lines are perpendicular
Grids are curvilinear squares, where diagonals cross at right angles
Impermeable boundary is a flow line
The quantity of seepage,
(flow interval)
(equipotential drop)
At any point,
Total head = Elevation Head + Pressure Head

13. FLOW NET (CONSTRUCTION RULES)
Draw to scale the cross sections of the structure, water elevations, and aquifer profiles
Establish boundary conditions, and draw one or two flow lines and equipotential lines near the boundaries
Sketch intermediate flow lines and equipotential lines by smooth curves adhering to right-angle intersections and square grids. Where flow direction is a straight line, flow lines are an equal distance apart and parallel

14. FLOW NET (CONSTRUCTION RULES)
Continue sketching until a problem develops. Each problem will indicate changes to be made in the entire net. Successive trials will result in a reasonably consistent flow net
In most cases, 5 to 10 flow lines are usually sufficient. Depending on the number of flow lines selected, the number of equipotential lines will automatically be fixed by geometry and grid layout

15. INSTABILITY (‘PIPING’)
‘Piping’ effect – an unstable condition cause by the vertical component of seepage pressure (upward direction) exceeds the weight of the soil (downward direction)
Piping failure can lead to the collapse of a water-retaining structure
Factor of safety against piping =
Downward Weight
Upward Seepage Force

16. Example 1 Water Level 3.5m 0.5m k = 6.5 x 10-4 m/s e = 0.68 8m
Impermeable Stratum
Sand 8m
3.5m
0.5m
Water Level
k = 6.5 x 10-4 m/s
e = 0.68
G = 2.62
14m

17. Example 1 Water Level 3.5m 0.5m 8m k = 6.5 x 10-4 m/s e = 0.68
Impermeable Stratum 8m
3.5m
0.5m
Water Level
k = 6.5 x 10-4 m/s
e = 0.68
G = 2.62
14m

18. Example 1 – Sheet Piles Impermeable Stratum 8m 3.5m 0.5m Water Level
k = 6.5 x 10-4 m/s
e = 0.68
G = 2.62
14m
Impermeable Stratum

19. Equipotential Drop, Nd = 11
Solution 1a:
Flow Interval, Nf = 4.3
Equipotential Drop, Nd = 11
The quantity of seepage beneath the sheet pile,
= l/h per m

20. Solution 1b: Taking the impermeable stratum as datum,
upstream = 17.5m
downstream = 14.5m
hT loss = m (per square)
Point
ht (m) he hp
u (kPa) A
17.5 B
(2 x 0.273) = 10
6.954
68.22
C(TOE)
(5 x 0.273) = 6
10.135
99.42 D
(8 x 0.273) = 8
7.316
71.77 E
(10 x 0.273) = 14.77 12
2.77
27.17

21. Solution 1c: Check again piping: 19.27 kN/m3 Effective weight of soil,
Effective weight of soil,
kN/m run
Upward seepage force,
kN/m run
 Piping failure will occur due to the upward seepage force is ( kN/m) larger than the effective weight of the soil ( kN/m)

22. Increase the sheet pile to a depth of 11m
Example 1 (continued)
Impermeable Stratum
11m
3.5m
0.5m
Water Level
k = 6.5 x 10-4 m/s
e = 0.68
G = 2.62
Increase the sheet pile to a depth of 11m
14m

23. Equipotential Drop, Nd = 16 Flow Interval, Nf = 4.5
l/h per m
l/h per m
hT loss = (per square)

24. Point
ht (m) he hp
u (kPa)
Point
ht (m) he hp
u (kPa)

25. Example 2
A river has a water depth of 3m above the clayey sand base. The clayey sand layer is 14m thick which in turn overlies impermeable rock. Laboratory tests indicate that the average permeability of the clayey sand is 4 x 10-3 m/s. The void ratio of the clayey sand is 0.6 and the specific gravity of the grains is It is required to excavate a 35m long, 5m wide and 6m deep trench across the river. To facilitate this work, a cofferdam is to be constructed by driving 2 lines of sheet piles to a depth of 10m below the clayey sand.

26. Example 2 – Cofferdam

31. Example 3 – Concrete Dam

34. Example Water Level 5.0m 1.0m 12m k = 1 x 10-4 m/s 21m
Impermeable Stratum
Sand
12m
5.0m
1.0m
Water Level
k = 1 x 10-4 m/s
21m
γsat = 16.5 kN/m3

35. Example Water Level 5.0m 1.0m k = 1 x 10-4 m/s 12m γsat = 16.5 kN/m3
Impermeable Stratum
12m
5.0m
1.0m
Water Level
k = 1 x 10-4 m/s
γsat = 16.5 kN/m3
21m

36. Example Water Level 5.0m 1.0m k = 1 x 10-4 m/s 12m γsat = 16.5 kN/m3
Impermeable Stratum
12m
5.0m
1.0m
Water Level
k = 1 x 10-4 m/s
γsat = 16.5 kN/m3
21m