Permeability and Seepage
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Transcript of Permeability and Seepage
![Page 1: Permeability and Seepage](https://reader035.fdocuments.in/reader035/viewer/2022081506/5571fb5c497959916994aa8b/html5/thumbnails/1.jpg)
Water flow in saturated soilPermeability and Seepage
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1. Energi Kinetik
datum
z
fluid particle
Energi dari partikel cair terdiri dari :
2. Energi Regangan
3. Energi Potensial
- Akibat Kecepatan (Velocity)
- Akibat Tekanan (Pressure)
- Akibat Elevasi (Elevation) (z) dari datum
Persamaan Bernoulli
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Persamaan Bernoulli
Total head =
datum
z
fluid particleVelocity head
+
Pressure head
+
Elevation head
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Persamaan Bernoulli
Total head =
datum
z
fluid particle
Untuk aliran air yang melalui partikel tanah, maka kecepatannya sangat rendah, bisa diabaikan
Velocity head
+
Pressure head
+
Elevation head
0
Total head = Pressure head + Elevation head
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SEEPAGE – Aliran Air
Air mengalir dari titik dengan TOTAL head yang tinggi ke titik dengan TOTAl head yang rendah
Total head = Pressure head + Elevation head
h = u/w + z
Pressure head = pore water pressure/w
Elevation head = height above the selected datum
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SEEPAGE – Aliran Air
• Aliran air bisa berupa aliran konstan (steady) ataupun tidak konstan (unsteady) yang tergantung pada waktu
• Aliran air bisa berupa aliran laminar (pararel) atau turbulen (mixing) atau transisi keduanya
• Gradien hidrolik (i) = head loss (h) dibagi dengan panjang aliran (l)
i = h/l• Aliran dalam partikel tanah sangat kecil, bisa
dianggap aliran laminar• v = k . i
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Head Loss
A
B
u B/
w
ZA
h A
ZB
h B
h
L
u A/
w
Flow, q
C
C’
Potongan C-C’
Luas, A
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Darcy’s Law
q = v.A = k.i.A
Dimana
q = rate of flow (m3/s)
i = hydraulic gradient
A = area normal to flow direction (m2)
k = hydraulic conductivity (m/s)
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Hydraulic Conductivity
• Disebut juga “Coefficient of permeability” atau
“permeability”
• SATURATED soil permeability
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Apa yang dimaksud dengan Permeabilitas?
Suatu nilai yang menunjukkan tingkat kemudahan cairan (misalnya air) melalui suatu medium yang porous (misalnya tanah)
Tanah lepas
- Mudah dilalui
- Permeablilitas tinggi
Tanah padat
- Sulit dilalui
- Permeabilitas rendah
air
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TIPIKAL NILAI PERMEABILITAS
Clean gravels > 10-1 m/s
Clean sands, sand-gravel 10-4 to 10-2 m/s
Fine sands, silts 10-7 to 10-4 m/s
Intact clays, clay-silts 10-10 to 10-7 m/s
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METODE MENENTUKAN NILAI k
[A] Uji laboratorium• Constant head test• Falling head test• Other
[A] Pertanyaan?
Seberapa baik kualitas sampel?
[B] Uji lapangan
• Pumping tests• Borehole infiltration
tests
• Field constant/Falling head test
[B] Pertanyaan?
Perlu diketahui kondisi profil tanah, muka air tanah, dan kondisi batas lainnya
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Lab Test 1: Constant head test
• Sebuah silinder yang berisi tanah butir kasar
dengan saturasi 100%
• Air dimasukkan ke dalam tangki air yang memiliki
lubang untuk overflow, sehingga tekanan air
konstan, tinggi air dijaga agar tetap konstan
• Volume air dalam waktu tertentu yang keluar diukur
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1. Constant head permeameter
hpB hpC
h
he
Saturated coarse grained soil
q
Water tank - moveable
B
C
D
A
l
Water inOver flow
Datum
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• hC = hpC + ZC
datum di C, sehingga ZC = 0hc = hpc
• hB = hpB + ZB
Datum di C, sehingga he = ZB –ZC = ZB
• Head loss = h = hC – hB = hpC – (hpB + he)• i = h /l• Volume air, V diukur• Waktu, t, dicatat q = V/t• Luas cross section sampel, A, diketahui• q = k . i . A k = q/(i.A) = V.l / (A.h.t)
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Constant head test
Cocok untuk pasir bersih dan kerikil
Contoh:• Sebuah sampel tanah dengan luas cross
4500 mm2,
• Jarak vertikal antara kedua standpipe adalah 100 mm
h sebesar 75 mm
• Outflow sebesar 1 liter setiap menit
Tentukan nilai permeabilitas tanahnya?
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Jawab
• Outflow, q = 1000 cm3/min = 1000 cm3/60 sec
atau q = 16.7 cm3/sec = 16.7x10-6 m3/sec
• i = h/l = 75/100 = 0.75
• k = q/(iA)
= (16.7x10-6)/(0.75x4500x10-6) m/sec
k = 5 x 10-3 m/sec
Bandingkan nilainya dengan tabel tipikal nilai k !!
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Test 2: Falling head permeameter
Untuk pasir halus, lanau, bisa juga
untuk lempung
• Sebuah tabung silinder (feeder, penghantar)
• Penetrasi air kedalam sampel silinder akibat
head loas dalam tabung feeder
• Harus diperhatikan:
− Tidak ada penguapan tes lambat
− Jumlah air yang cukup
− Sebuah prosedur yang lambat
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2. Falling Head Permeameter
Level pada waktu, t1
h1
Level of cell outflow
ke permeameter cell
Tabung dengan luas ‘a'
h2
Level pada, t2
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Falling head test
2
1
12 h
hln
)t(t
L
A
ak
• Sampel tanah dengan paljang L, dan luas A
• Aliran dalam tabung = aliran dalam sampel
tanah
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3. Field testing – Pumping Test
Impermeable boundary
Sumur Pompaq, air dipompa keluar
Dalam t tertentu r2
r1
Water table
Drawdown –phreatic or flow line
h1h2
Check WellPompa
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Pumping test
Data yang dibutuhkan
1. Muka air tanah
2. Profil tanah, termasuk kedalaman lapisan impermeable
Harus mampu
1. Menurunkan m.a.t
2. Menciptakan aliran, phreatic line
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Solution
Axi-symmetric problem
By integration of Darcy’s Law,
1
221
22 r
rln
)h(hπ
qk
Modifikasi rumus, akan tergantung pada kondisi profil tanah (confined/unconfined aquifer)
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FLOW NET
Jejaring aliran
Terdiri atas :• Flow lines• Equipotential lines
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Flow Net
concrete dam
impervious strata
soil
Aliran laminar
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Flow Lines Jarak terdekat/terkecil untuk air keluar
Elevation head reference line/datum
Flow Lines
Phreatic surface
l
h
Equipotential lines
he2
hp1
1he1
hp2
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FLOW LINES
• Bergerak pararel dengan lapisan impermeable
(impervious boundaries)
• Bergerak pararel dengan permukaan air
• Dasar dari bangunan air/struktur lain adalah flow
line
• Lapisan impervious adalah flow line
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Impervious boundary
5 Flow LinesTentukan!!!
h
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EQUIPOTENTIAL LINES• Garis yang menunjukkan titik-titik dengan total head
yang sama
• Equipotential line menghubungkan antara
struktur/bangunan air dengan lapisan impervious
• Berpotongan dengan flowline dan permukaan tanah
dengan membentuk sudut 900
• Equipotential line berpotongan dengan lapisan
impervious dan struktur, membentuk sudut 900
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concrete dam
impervious strata
soil
datum
hL
TH = 0TH = hL
TH=0.8 hL
EQUIPOTENTIAL LINES
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EQUIPOTENTIAL LINES
Impervious boundary
10 Eqipotential linesTentukan!!
h
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FLOW NET
Air mengalir mengikuti jarak yang
terpendek, dengan gradien hirolik
terbesar, imax
Perpotongan antara garis aliran
(flow line) dan Eqipotential line,
harus tegak lurus (900), Mengapa?
Ingat, aliran harus laminar
min
imax b
hi
900
EL
FL
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FLOW NET
Flownet adalah sebuah metode grafis yang
menggambarkan bagaimana head atau hilangnya energi
saat air mengalir melalui sebuah medium yang porous
Pada tanah yang isotropi (isotropic) maka air harus melalui
bagian dengan gradien hidrolik terbesar
Isotropic : kondisi tanah dengan nilai permeabilitas vertikal
sama dengan permeabilitas horizontal, Anisotropic ? (akan
dipelajari nanti)
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hi
ab
Flowq
mper ab
hkq i
qFL 1 FL 2
EL 1
EL 2
Konstan
h1
h2
h2 – h1 = hi
i = hi /l = hi /b q = k.i.A A = a x 1 m = a m2 plane strain
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ab
Flowq
mper ab
hkq i
Agar konstan maka a = b
Harus bujur sangkar, atau lingkaran
q = konstan jika a dan b konstant
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Impervious boundary
h
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Flownet Construction
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Equipotential Lines
Flow lines
Discharge in flow direction,
= q per “flow tube”
l
h1
h2
h3
90º
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Number of Drops dan Number of Flow
Flow Channel/Flow Tube/Tabung Aliran : Tabung atau
Saluran diantara 2 garis aliran
Number of flow (Nf) : jumlah total dari flow channel atau
secara sederhana Nf = (jumlah flow line – 1)
Equipotential drop : menggambarkan penurunan head dari
satu garis equipotential ke garis equipotential berikutnya,
terletak diantara 2 garis equipotetial
Number of drop (Nd) : jumlah total dari equipotential drop atau
secara sederhana Nd = (jumlah equipotential line – 1)
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Number of Drops dan Number of Flow
Impervious Boundary
Eqipotential lines : 10
h
Flow lines : 5
Nd : 9
Nf : 4
h = (9/9)h
(8/9) h
(7/9) h
(6/9) h (5/9) h
(4/9) h
(3/9) h (2/9) h
(1/9) h
(0/9) h = 0
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Flow Net Calculations
Nd adalah nilai penurunan equipotential sepanjang garis
aliran, maka head loss (hilangnya energi) dari satu gari
equipotential ke garis equipotential berikutnya adalah :
h1-2 = (h) = h / Nd
dari hukum Darcy, rata-rata aliran adalah :
b
a
N
ΔhkΔq
atau
1ab
ΔhkkiAΔq
d
i
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Flow Net Calculations
tapi a = b
dan jumlah channel total adalah Nf,
Maka debit air per satuan lebar adalah :
ΔhN
Nkq
d
f
INGAT !! Persamaan ini hanya untuk “persegi” (a = b)
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Contoh Soal : Jika k = 10-7 m/sec, berapa debit perhari yang melalui dam selebar 100 m?
Dam
cutoff
Low permeability rock
50 m of water
5 m of water
Dam
cutoff
Low permeability rock
50 m of water
5 m of water
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Jawab
Diketahui
Nf = 5
Nd = 14
h = 45 m
k = 10-7 m/sec
q = 10-7 . (5/14) . 45 . 100 m lebar
q = 0.000161 m3/sec
q = 13.9 m3/day
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Contoh Soal : berapa nilai gradien hidrolik (i) pada titik C?
Dam
cutoff
Low permeability rock
50 m of water
5 m of water
Dam
cutoff
Low permeability rock
50 m of water
5 m of water
Titik C
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Jawab
Average length (l) of flow is about 3 m
h pada titik C
h = (1/14) . 45
h = 3.2 m
i = h/l
i = 3.2/3 = 1.06
i = h/l
icr = (/ w)
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Critical hydraulic gradient, ic
The value of i for which the effective the effective
stressstress in the saturated system becomes
ZERO!
Consequences:
no stress to hold granular soils together
soil may flow
“boiling” or “piping” = EROSION
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z
= satz = total stress
u due to seepage,
= i(z)(w)
(represents proportion of h occurring over length AB)
= - u
= (satz) – (wz + i(z)w)
= z – i(z)w
Seepage Condition – upward flow of water
= 0, when z = i(z)w OR i = (/ w)
A
B
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GRANULAR SOILS chiefly!
When the effective stress becomes zero, no stress is carried by the soil grains
Note: when flow is downwards, the effective stress is increased!
So the erosion problem and ensuing instability is most likely for upward flow,
i.e. water exit points through the foundations of dams and cut-off walls
Likelihood of Erosion
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Minimising the risk of erosionMinimising the risk of erosion
1. Add more weight at exit points
permeable concrete mats?
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Lengthen flow path?
1. Deeper cut-offs
2. Horizontal barriers
3. Impermeable blanket on exit surface
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Simple cut-offs (FESEEP)
Nf = 5Nd =10Nf = 5
Nd =11Nf = 5
Nd =13
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“Impermeable” Clay Blanket
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Summary: Key PointsSummary: Key Points
• Heads in soil• Darcy’s Law• Coefficient of permeability• Measurement of permeability• Flownets• Flownet rules• Seepage from flownets• Piping, boiling or erosion• Critical hydraulic gradient
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Exercises
a) Draw a flow net for seepage under a vertical sheet pile wall penetrating 10 m into a uniform stratum of sand 20 m thick.
b) If the water level on one side of the wall is 11 m above the sand and on the other side 1.5 m above the sand, compute the quantity of seepage per unit width of wall. [k = 3 10-5 m/s]
c) What is the factor of safety against developing the “quick” condition on the outflow side of the wall? [sat= 21 kN/m3]
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Finite Difference spreadsheet solution
and other numerical approaches
Authors: Mahes Rajakaruna (ex UniSA)
& University of Sydney (FESEEP)
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Finite Difference approach to flow nets - flow line set up
ROWCOL
A B C D E F G H I J K L M N O P Q R S T U V W
Soil level
Impermeable boundary
Interior cell value =(H4+I5+H6+G5)/4
Cell H5
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98-99
99-100
100-101
101-102
102-103
Flow lines from finite difference program (spreadsheet)
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Equipotentials from finite difference program (spreadsheet)
113-114
112-113
111-112
110-111
109-110
108-109
107-108
106-107
105-106
104-105
103-104
102-103
101-102
100-101
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FESEEP: University of Sydney
Mesh of foundation soil
cutoff
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FESEEP Output (University of Sydney)
flownet
pore pressures increasing
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Dam
cutoff
Low permeability rock
50 m of water
5 m of water