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SEEPAGE PROBLEMS

PART 1: CONFINED FLOW PROBLEMS

CE 162

1st Semester 2013-2014

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OVERVIEW

• Continuity Equation & Laplace’s Equation 

• Flow Nets

•

Seepage calculations from flow nets• Flows nets in anisotropic soils

• Uplift Pressures

• Erosion and Piping

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CONTINUITY EQUATION

CE 216Geotechnical Engineering I

1st Sem. 2013-2014

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Continuity Equation

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Continuity Equation

v = ki = k Ñh = k ¶h

¶ xe x +

¶h

¶ ye y

æ 

è ç ö

 ø÷

D q =Ñ×v = k ¶2h

¶ x2+

¶2h

¶ y2

æ 

è ç ö

 ø÷= 0

Ñ2h = 0 Ñ =¶

¶ xe x +

¶

¶ ye y

æ 

è ç ö

 ø÷

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FLOW NETS IN ISOTROPIC SOILS

CE 216Geotechnical Engineering I

1st Sem. 2013-2014

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• Boundary Types (Drawn in ink)

 – Head (Dirichlet/Essential)

 – Flow (Neuman/Natural)

• Flow Net lines (Drawn in pencil) – Equipotential lines

 – Flow lines

 –Equipotential lines perpendicular to flow lines

• Elements/Cells : region bounded by 2 parallelflow lines and 2 parallel equipotential lines.

Flow Nets

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Flow Net

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Flow Net

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• Limit number of flow channels to 3.

• Rotate problem to check compliance with

square and perpendicular conditions.

• Limit partial drops to 1.

• Subdivide elements in half 

 –

Infinite element (2 sides) – 3-sided irregular element

 – 5-sided irregular element

Flow Net Techniques

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• Draw problem boundaries to scale in ink.

• Draw flow lines.

•

Draw equipotential lines• Repeatedly adjust flow lines and equipotential

lines until flow net are roughly perpendicular

to each other and elements are approximately

square.

Constructing flow nets

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BASIC FLOW NET COMPUTATIONS

CE 216Geotechnical Engineering I

1st Sem. 2013-2014

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Rate of Seepage

q = k D  H n f  

nd 

where

q= flow rate per unit width

k =

 permeabilityD  H = head drop per equipotential line

n f   = number of flow channels

nd  = number of drops

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• Given a point within the flow net, extrapolate

the head and elevation relative to the datum.

• Note prescribed heads and elevation should

be measured to the datum.

• Use definition of hydraulic head to compute

the pore pressure

Computing pore pressures

u = g w h -  z ( )

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• For a given point within the flow net, use thesubdivision technique to create an reducedelement in which the point is roughly in the

center.• Compute the head drop within the subdivided

element.

• Estimate with length of distance along the

direction of flow in the reduced element.• Divide the head drop by the flow distance to

estimate the hydraulic gradient.

Computing hydraulic gradients

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FLOW NETS IN ANISOTROPIC SOILS

CE 216Geotechnical Engineering I

1st Sem. 2013-2014

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Flow nets in anisotropic soils

Ñ×k ×Ñh = 0¶

¶ xk  xx

¶h

¶ x+ k 

 xy

¶h

¶ y

æ 

è ç

 ö

 ø÷

+¶

¶ yk  yx

¶h

¶ x+ k 

 yy

¶h

¶ y

æ 

è ç

 ö

 ø÷

= 0

k  xx¶2h

¶ x2+ k  yy

¶2h

¶ y2= 0

k  xx

k  yy

¶2h

¶ x2+

¶2h

¶ y2= 0

¶2h

¶ x 2 +

¶2h

¶ y2 = 0 x =k  yy

k  xx x = k  x

¶

¶ x =¶

¶ x

¶ x

¶ x = k¶

¶ x

¶2

¶ x2 = k 2 ¶2

¶ x 2

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Flow nets in anisotropic soils

• Scale in the direction of minimum permeabilityneeds to be stretched by the scale factor.

• Computations involving rate of seepage can bedirectly made from the flow net in the “stretchedscale”.

•

Flow net must be redrawn into equal scale inorder to compute pore pressures and hydraulicgradients.

q = k min

k max

D  H n f  

nd 

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Flow nets in anisotropic soils

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Flow nets in anisotropic soils

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UPLIFT PRESSURE ON STRUCTURES

CE 216

Geotechnical Engineering I

1st Sem. 2013-2014

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SEEPAGE FORCES

CE 216

Geotechnical Engineering I

1st Sem. 2013-2014

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EROSION AND PIPING

CE 266

Earth Structures

1st Sem. 2012-2013

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THE END

THANK YOU

CE 162

1st

Semester 2013-2014