MEKANIKA TANAH 1 - Spada UNS

MEKANIKA TANAH 1

CONFINED AND UNCONFINED FLOWNETS

(Pertemuan 11)

Disusun oleh:

Tim KBK Geoteknik Prodi Teknik Sipil FT UNS

Lab. Mekanika Tanah FT UNS, Jl Ir Sutami 36 a Surakarta

5. FLOWNETS DAN SEEPAGE

A. FLOWNETS (CONFINED)

• Confined: jika 4 boundary pada flownets diketahui:

– 2 boundary: equipotential lines

– 2 boundary: flow lines

A. FLOWNETS (CONFINED)

- Flow lines: a water particle will travel from upstream to downstream side in permeable soil medium

- Equipotential lines: potential head at all points is equal.

Impervious layer H₁

H₂ Sheet pile

Flow line Equipotential

line k_x  k_z  k

A. FLOWNETS (CONFINED)

- Equipotential lines intersect the flow lines at right angles

- The flow elements formed are approximate squares

H

1 H₂

Impervious layer Sheet pile

b a

c

d e

f g

N_f = 4 N_d = 6

A. FLOWNETS (CONFINED)

- Flownets di bawah dam

H₁

H₂

Impervious layer

k k

k_x  _z  a d

N_f = 4 N_d = 8 H

A. FLOWNETS

• h

₁

, h

₂

, h

₃

, h

_n

= piezometric levels corresponding to the

equipotential lines

• D h : selisih head

• D q: beda flux antara garis aliran

• q: total flux

• N

_d

: jumlah potential drop

• N

_f

: jumlah flow channel

Dq h₁

h₃

h₄

l

2 l

3

l

1 l

2 l

Dq 3

1 Dq

2 Dq

3

q q

q

q Δ Δ ... Δ

Δ ₁  ₂  ₃  

Δ ₃ ....

3 4 3

2 2

3 2

1 1

2

1  



 



 

 



 



 

 



 



   l

l h k h

l l h k h

l l h k h

q

Dh = H

N_d Dq = k H

N_d q = kN_f H N_d

A. FLOWNETS

Dq

Dq h₁

h₂

h₃

h₄ b₁

b₂

b₃ l₁

l₂

l₃

3 ....

3 4 3

2 2

3 2

1 1

2

1  



 



 

 



 



 

 



 



  b

l h k h

l b h k h

l b h k h

l n b l

b l

b   ...

If

3 3 2

2 1

1 



 



  D

Nd

kH n q

N n kH N

q

d f 



 



 

Aliran melalui pias persegi empat:

H₁

H₂

Impervious layer

Sheet pile

Channel-1

Channel-2

Channel-3

1

1 1  b

l

1

2 2  b

l

38 , 0

1

3 3  b

l

 

d d

d

d N

H kH N

H k N

H k N

k

q q

q q

38 , 2 38

, 0

3 2

1









D

 D

 D



15 m

5 m

Impervious layer Sheet pile

I II

III

30 m a

b

c

1 2 3 4 d 5

Example-1

sec / cm 10

5 ^3





 k k k_{x z}

(a)How high (above the ground surface) the water will rise if piezometers are placed at points a, b, c dan d

From the figure : N_f = 3 dan N_d = 6

Potential drop between 2 equipotential lines: H/N_d = 10/6 = 1,667 m

Point a is located on equipotential line 1 Potential drop at a = 1 x 1,667 m

• Water in piezometer at point a will rise to an elevation of (15- 1,667) = 13,333 m above the ground surface.

Similary, the piezometer levels for:

• Point b = (15 - 2 x 1,667) = 11,67 m above the ground surface

• Point c = (15 - 5 x 1,667) = 6,67 m above the ground surface

• Point d = (15 - 5 x 1,667) = 6,67 m above the ground surface

(b) The rate of flow through flow channel II per unit length:

(c) Total rate of flow through all the channels per unit length Dq = k H

N_d

= 5´10^-5 10 6 æ

èç ö

ø÷ = 8, 33´10^-5m³/det/m

q = k H × N_f N_d

= 5´10^-5 10×3 6 æ

èç ö

ø÷ = 2, 5´10^-4m³/det/m

4 m

Impermeable layer Sheet pile

4,8 m

Datum

3. Draw net water pressure distribution at the sheet pile.

4,7 m 2,5 m

Total head at the water table (upstream) = 2,5 m (pressure head = 0; elevation head +2,50 m)

Total heal at the ground surface in front of sheet pile

(downstream equipotential) =0 (pressure head = 4,00 m; elevation head = -4,00m)

N_d = 12

Water pressure at both sides of sheet pile no. 1-7

example, at Surface 4, Total head behind the sheet pile:

Total heat in front of sheet pile:

Elevation heat at the surface 4 = -5,5 m Net pressure behind the sheet pile :

Similar calculation for the other point

m 83 , 12 1

5 , 8 2 ,

8  





 D





d d

d

b N

n H h

n h

m 21 12 0

5

1 2, , N

n H h

n h

d d

d

f  

D

    

kN/m2

9 , 15 )

5 , 5 21 , 0 ( 8 , 9 ) 5 , 5 83 , 1 ( 8 ,

9    



 _f

b u

u

Example 4

q = 0,25 m³/hour per length

N_f = 6,0 N_d = 11

• Hydraulic conductivity of sand:

• Hydraulic gradient below the excavated surface :

Distance (Ds) between 2 last equipotential line = 0,9 m.

d f

N kH N q 

m/det 10

8 2 11 60

50 6 4

25

0 ₅

2

 











 



  ,

,

, N

H N k q

d f

50 9 0

0 11

50 4

, , , s

i h 



 







 D D

B. FLOWNETS (UNCONFINED)

• Jika tidak semua boundary diketahui, biasanya yang tidak diketahui flow lines paling atas, mis:

pada bendungan

DAFTAR PUSTAKA

• Fathani, T.F., Slide kuliah Mekanika Tanah

• Hardiyatmo. 2006. Mekanika Tanah 1. Gadjah

Mada University Press, Yogyakarta

SEKIAN DAN TERIMAKASIH

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Tim KBK Geoteknik Prodi Teknik Sipil UNS