Download - KUAT GESER TANAH(6).pdf
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KUAT GESER TANAH
Vienti Hadsari, ST.,M.Eng
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KUAT GESER TANAH
Kuat geser tanah : Gaya perlawanan butir-butir
tanah terhadap desakan atau tarikan.
Contoh sederhana : keruntuhan lereng
W
F
N
T
Lereng runtuh jika
tegangan geser yang
menahan < gaya dorong
T = gaya dorong
F = gaya yang menahan
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Embankment
Strip footing
KERUNTUHAN GESER PADA TANAH
Tanah biasanya mengalami keruntuhan geser
Saat terjadi keruntuhan, tegangan geser mancapai kuat geser maksimum.
Permukaan keruntuhan
Pertahanan terhadap
keruntuhan geser
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Retaining
wall
KERUNTUHAN GESER PADA TANAH
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Retaining
wall
Permukaan
keruntuhan
Pertahanan
terhadap geser
Saat terjadi keruntuhan, tegangan geser mancapai kuat geser maksimum.
KERUNTUHAN GESER PADA TANAH
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MEKANISME KERUNTUHAN PADA TANAH
Saat keruntuhan, tegangan geser di seluruh permukaan () mencapai kekuatan geser maksimum (f).
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Faktor pengaruh lapangan
Keadaan tanah : angka pori, ukuran, dan bentuk butiran
Jenis tanah : pasir, berpasir, lempung, dsb
Kadar air (terutama lempung)
Jenis beban dan tingkatnya
Kondisi anisotropis
Laboratorium
Metode pengujian
Kadar air
Tingkat regangan
KUAT GESER TANAH
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APLIKASI
Parameter kuat geser tanah yang menahan keruntuhan ialah :
1. Sudut geser dalam (φ) : sudut geser yang terbentuk saat pergeseran dus atau lebih partikel tanah
2. Lekatan / kohesi tanah (c) : gaya tarik menarik antar 2 atau lebih partikel tanah
Tanah Kohesif
Mempunyai nilai kohesi (c) : lempung, lanau
Tanah cohesionless
Mempunyai nilai φ; c = 0 : pasir, kerikil
Parameter kuat geser digunakan untuk menghitung :
daya dukung tanah dasar
Stabilitas lereng
Tegangan lateral
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PARAMETER KUAT GESER TANAH
Gesekan pada tanah berbutir kasar (non-kohesif)
T
N
F
Bidang kasar
Saat T > F massa bergerak
T = F kondisi kritis
F = N.f = N.tg φ + c.A
Untuk satuan luas bid.kontak :
F/A = N/A . tg φ + c
Konsep keruntuhan menurut
Coulomb :
σ = tegangan normal
τ = tegangan geser
φ = kemiringan grafik
C = perpotongan dengan sumbu τ
τ
c
σ
φ
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KONDISI
• Total (c dan φ)
• Efektif (c’ dan φ’)
Konsep dasar Terzaghi : tegangan geser tanah hanya ditahan oleh butir-
butir saja. Tegangan geser : fungsi tegangan normal efektif
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KRITERIA KERUNTUHAN GESER
BERDASAR MOHR-COULOMB
(TEKANAN TOTAL)
f adalah tegangan geser maksimum yang dapat dipikul
dalam tanah tanpa failure, setelah pembebanan sebesar
tan cf
c
Kohesi Sudut geser
dalam
f
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f adalah tegangan geser maksimum yang dapat dipikul
dalam tanah tanpa failure, setelah pembebanan sebesar ’.
’
'tan'' cf
c’
’
Kohesi efektif Sudut geser
dalam efektif f
’
u '
u = tekanan air
pori
KRITERIA KERUNTUHAN GESER BERDASAR MOHR-COULOMB
(TEKANAN EFEKTIF)
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'tan'' ff c
Kuat geser terdiri dari dua komponen :
kohesi dan komponen geser
’f
f
’
'
c’ c’
’f tan ’ frictional component
KRITERIA KERUNTUHAN GESER
BERDASAR MOHR-COULOMB
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c dan merupakan parameter pengukuran kuat geser.
Semakin tinggi nilainya, semakin tinggi pula kuat gesernya.
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Lingkaran MOHR
Element tanah
’1
’1
’3 ’3
q
’
q
q
222
22
'
3
'
1
'
3
'
1'
'
3
'
1
Cos
Sinf
f
Menghasilkan gaya pada and :
2'
3
'
1
2'
3
'
1'2
22
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Mohr Circle of stress
2'
3
'
1
2'
3
'
1'2
22
’
2
'
3
'
1
2
'
3
'
1
'
3 '
1
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Mohr Circle of stress
2'
3
'
1
2'
3
'
1'2
22
’
2
'
3
'
1
2
'
3
'
1
'
3 '
1
PD = Pole w.r.t. plane
q
(’, )
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Element tanah pada lokasi yang
berbeda
Permukaan keruntuhan
Lingkaran MOHR & Failure
Envelope
X X
X ~ failure
Y Y
Y ~ stabil
’
'tan'' cf
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Y
c
c
c
Mula2, lingkaran mohr
adalah suatu titik
c+
Elemen tanah tidak akan
mengalami failure jika
lingkaran Mohr berada dalam
failure envelope
m.t.
Lingkaran MOHR & Failure
Envelope
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Mohr Circles & Failure Envelope
Y
c
c
c
GL
Seiring proses pembebanan
bertambah, lingkaran mohr
menjadi besar…
.. Dan akhirnya, failure
terjadi saat lingkaran mohr
menyentuh envelope
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’
2
'
3
'
1 '
3 '
1
PD = Pole w.r.t. plane
q
(’, f)
Orientasi Bidang Failure
’
’1
’1
’3’3
q
’
’1
’1
’3’3
’
Failure envelope
(90 – q)
Adapun,
90 – q ’ = q
q 45 + ’/2
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Lingkaran MOHR pada tekanan total & effektif
= X
v’
h’ X
u
u
+
v’ h’
Tekanan efektif
u v h
X
v
h
Tekanan total
or ’
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= X
v’
h’ X
u
u
+
v’ h’
Tekanan efektif
u v h
X
v
h
Tekanan total
or ’
Jika X
adalah
saat tjd
failure
c
Failure envelope pada
tekanan total
’
c’
Failure envelope pada
tekanan efektif
Lingkaran MOHR pada tekanan total & effektif
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Kriteria MOHR-Coulomb failure dengan Tekanan
pada Lingkaran MOHR
X
’v = ’1
’h = ’3
X is on failure ’1 ’3
effective stresses
’ ’ c’
Failure envelope in terms
of effective stresses
c’ Cot’ (’1 ’3)/2
(’1 ’3)/2
2'
2''
'
3
'
1
'
3
'
1
SinCotc
Adapun,
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Kritera Mohr Coulomb failure criterion with
tekanan pada lingkaran Mohr
2'
2''
'
3
'
1
'
3
'
1
SinCotc
( ) ( ) ''2''
3
'
1
'
3
'
1 CoscSin
( ) ( ) ''2'1'1 '
3
'
1 CoscSinSin
( )( ) ( )'1
''2
'1
'1'
3
'
1
Sin
Cosc
Sin
Sin
2
'45'2
2
'452'
3
'
1
TancTan
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PENGUJIAN KUAT GESER TANAH
Pengujian Laboratorium
Unconfined Compression Test
Direct Shear Test
Triaxial Test (UU,CU,CD)
Pengujian Lapangan
SPT
Korelasi antar parameter
Nilai tahanan ujunh konus sondir (qc)
Nilai N-SPT
California Bearing Capacity
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Laboratorium Tes
Kondisi lapangan
z vc
vc
hc hc
Sebelum konstruksi ada
sampel tanah
z vc +
hc hc
Setelah dan selama ada
konstruksi
vc +
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TRIAXIAL SHEAR TEST
Sampel tanah
saat failure
Failure plane
Porous
stone
impervious
membrane
Piston (to apply deviatoric stress)
O-ring
pedestal
Perspex
cell
Cell pressure
Back pressure Pore pressure or
volume change
Wate
r
Soil
sample
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TRIAXIAL SHEAR TEST
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TRIAXIAL SHEAR TEST
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3 Jenis :
Unconsolidated Undrained (UU)
Consolidated Undrained (CU)
Consolidated Undrained (CD)
MACAM2 UJI TRIAXIAL
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MACAM2 UJI TRIAXIAL
Apakah katup drainase
terbuka?
yes no
Consolidated
sample Unconsolidated
sample
Apakah katup drainase
terbuka? yes no
Drained
loading
Undrained
loading
Tegangan yg ada : c
c c
c
c Step 1
deviator stress
( = q)
Pembebanan
Step 2
c c
c+ q
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Apakah katup drainase
terbuka?
yes no
Consolidated
sample Unconsolidated
sample
Di bawah tekanan sel c
Step 1
Apakah katup drainase
terbuka? yes no
Drained
loading
Undrained
loading
Geser
(pembebanan)
Step 2
CD test
CU test
UU
test
MACAM2 UJI TRIAXIAL
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CONSOLIDATED- DRAINED TEST (CD TEST)
Step 1: Pada akhir konsolidasi
VC
hC
Total, = Pori, u Effective, ’ +
0
Step 2: Selama penambahan beban
’VC = VC
’hC = hC
VC +
hC 0
’V = VC + = ’1
’h = hC = ’3
Drainage
Drainage
Step 3: At failure
VC + f
hC 0
’Vf = VC + f = ’1f
’hf = hC = ’3f Drainage
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Deviator stress (q or d) = 1 – 3
Consolidated- drained test (CD Test)
1 = VC +
3 = hC
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CD tests How to determine strength parameters c and
Devia
tor
stre
ss,
d
Axial strain
Sh
ea
r st
ress
,
or ’
Mohr – Coulomb
failure envelope
(d)fa
Confining stress = 3a (d)fb
Confining stress = 3b
(d)fc
Confining stress = 3c
3c 1c 3a 1a
(d)fa
3b 1b
(d)fb
1 = 3 + (d)f
3
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CD tests
Strength parameters c and obtained from CD tests
Since u = 0 in CD
tests, = ’
Therefore, c = c’
and = ’
cd and d are used
to denote them
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Some practical applications of CD analysis for
clays
1. Embankment constructed very slowly, in layers over a soft clay deposit
2. Earth dam with steady state seepage
3. Excavation or natural slope in clay
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CONSOLIDATED- UNDRAINED TEST (CU TEST)
Step 1: Pada akhir konsolidasi
VC
hC
Total, = Pori, u Effective, ’ +
0
Step 2: Selama penambahan beban aksial
’VC = VC
’hC = hC
VC +
hC ±u
Drainage
Step 3: At failure
VC + f
hC
No
drainage
No
drainage ±uf
’V = VC + ± u = ’1
’h = hC ± u = ’3
’Vf = VC + f ± uf = ’1f
’hf = hC ± uf = ’3f
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CU tests How to determine strength parameters c and
Devia
tor
stre
ss,
d
Axial strain
Sh
ea
r st
ress
,
or ’
(d)fb
Confining stress = 3b
3b 1b 3a 1a
(d)fa
cu Mohr – Coulomb
failure envelope in
terms of total stresses
ccu
1 = 3 + (d)f
3
Total stresses at failure
(d)fa
Confining stress = 3a
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(d)fa
CU tests How to determine strength parameters c and
Sh
ea
r st
ress
,
or ’ 3b 1b 3a 1a
(d)fa
cu
Mohr – Coulomb
failure envelope in
terms of total stresses
ccu ’3b ’1b
’3a ’1a
Mohr – Coulomb failure
envelope in terms of
effective stresses
’
C’ ufa
ufb
’1 = 3 + (d)f - uf
’3 = 3 - uf
Effective stresses at failure
uf
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CU tests
Strength parameters c and obtained from CD tests
Shear strength
parameters in terms of
total stresses are ccu
and cu
Shear strength
parameters in terms of
effective stresses are c’
and ’
c’ = cd and ’ = d
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Some practical applications of CU analysis for
clays
1. Embankment yang dibangun sangat cepat diatas lempung lunak
2. Penurunan muka air pada belakang bagian dam
3. Rapid construction of an embankment on a natural slope
Note: Total stress parameters from CU test (ccu and cu) can be used for
stability problems where,
Soil have become fully consolidated and are at equilibrium with the
existing stress state; Then for some reason additional stresses are
applied quickly with no drainage occurring
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UNCONSOLIDATED- UNDRAINED TEST (UU TEST)
Data analysis
C = 3
C = 3
No
drainage
Initial specimen condition
3 + d
3
No
drainage
Specimen condition
during shearing
Initial volume of the sample = A0 × H0
Volume of the sample during shearing = A × H
Karena tes dilakukan dalam kondisi undrained,
A × H = A0 × H0
A ×(H0 – H) = A0 × H0
A ×(1 – H/H0) = A0 z
AA
1
0
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UNCONSOLIDATED- UNDRAINED TEST (UU TEST)
Step 1: Setelah sampling dilakukan
0
0
= +
Step 2: Setelah pengaplikasian tekanan hidrostatik
uc = B 3
C = 3
C = 3 uc
’3 = 3 - uc
’3 = 3 - uc
No
drainage
Kenaikan air pori karena
penambahan tegangan sel
Kenaikan tegangan sel
Tekanan air pori oleh
skempton, B
Note: Jika tanah fully saturated, B = 1 (karena itu, uc = 3)
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UNCONSOLIDATED- UNDRAINED TEST (UU TEST)
Step 3: Selama pemberian beban aksial
3 + d
3
No
drainage
’1 = 3 + d - uc ud
’3 = 3 - uc ud
ud = ABd
uc ± ud
= +
Kenaikan tekanan air pori
karena tegangan deviator Kenaikan tegangan
deviator
Skempton’s pore water
pressure parameter, A
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UNCONSOLIDATED- UNDRAINED TEST (UU TEST)
Combining steps 2 and 3,
uc = B 3 ud = ABd
u = uc + ud
Total penambahan tekanan air pori pada tiap level, u
u = B [3 + Ad]
Skempton’s pore
water pressure
equation u = B [3 + A(1 – 3]
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UNCONSOLIDATED- UNDRAINED TEST (UU TEST)
Step 1: Setelah sampling
0
0
Total, = Pori, u Effective, ’ +
-ur
Step 2: Setelah aplikasi tekanan sel hidrostatik
’V0 = ur
’h0 = ur
C
C
-ur uc = -ur c
(Sr = 100% ; B = 1)
Step 3: setelah aplikasi tegangan aksial
C +
C
No
drainage
No
drainage -ur c ± u
’VC = C + ur - C = ur
’h = ur
Step 3: At failure
’V = C + + ur - c u
’h = C + ur - c u
’hf = C + ur - c uf =
’3f
’Vf = C + f + ur - c uf = ’1f
-ur c ± uf C
C + f No
drainage
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UNCONSOLIDATED- UNDRAINED TEST (UU TEST)
Total, = Neutral, u Effective, ’ + Step 3: At failure
’hf = C + ur - c uf =
’3f
’Vf = C + f + ur - c uf = ’1f
-ur c ± uf C
C + f No
drainage
Mohr circle in terms of effective stresses do not depend on the cell pressure.
Therefore, we get only one Mohr circle in terms of effective stress for
different cell pressures
’ ’3 ’1 f
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3b 1b 3a 1a f ’3 ’1
UNCONSOLIDATED- UNDRAINED TEST (UU TEST)
Total, = Neutral, u Effective, ’ + Step 3: At failure
’hf = C + ur - c uf =
’3f
’Vf = C + f + ur - c uf = ’1f
-ur c ± uf C
C + f No
drainage
or ’
Mohr circles in terms of total stresses
ua ub
Failure envelope, u = 0
cu
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Some practical applications of UU analysis for
clays
1. Embankment constructed rapidly over a soft clay deposit
2. Large earth dam constructed rapidly with no
change in water content of soft clay
3. Footing placed rapidly on clay deposit
Note: UU test simulates the short term condition in the
field. Thus, cu can be used to analyze the short term
behavior of soils
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UJI GESER LANGSUNG
Step 2: Lower box is subjected to a horizontal displacement at a constant rate
Step 1: Apply a vertical load to the specimen and wait for consolidation
P Test procedure
Pressure plate
Steel ball
Proving ring
to measure
shear force
S
Porous
plates
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1. Siapkan contoh tanah untuk 3 atau 4 kali percobaan. Untuk tiap percobaan, contoh tanah harus mempunyai kepadatan yang sama.
Cara percobaan :
2. Masukkan contoh tanah kedalam kotak geser.
3. Berikan beban vertical ( normal =N )
4. Berikan beban horisontal ( geser = T ) yg berangsur angsur di tambah, catat setiap gerakkan pergeseran sample tanah (dial reading) dan beban horisontal yang diberikan , terutama pada saat runtuh
5. Lakukan pada sample tanah yang lain (min 3 sample)
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Analysis of test results
sample theofsection cross of Area
(P) force Normal stress Normal
sample theofsection cross of Area
(S) surface sliding at the developed resistanceShear stressShear
Note: Cross-sectional area of the sample changes with the horizontal
displacement
UJI GESER LANGSUNG
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Direct simple shear test
Direct shear test = 80 mm
Soil specimen Porous
stones
Spiral
wire in
rubber
membrane
Direct simple shear test
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Tega
nga
n g
ese
r,
Perpindahan geser
Pasir padat/
lempung OC
f Pasir lepas/
lempung
terkonsolidasi
normal
f
Peru
ba
ha
n t
inggi
sam
ple
Exp
an
sion
C
om
pre
ssio
n Perpindahan geser
Hubungan tegangan-regangan
Pasir padat/
lempung OC
Pasir lepas/
lempung
terkonsolidasi
normal
UJI GESER LANGSUNG PADA PASIR
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f1
Normal stress = 1
Bagaimana menentukan parameter c dan ? T
egan
ga
n g
ese
r,
Perpindahan geser
f2
Normal stress = 2
f3
Normal stress = 3
Tega
nga
n g
ese
r sa
at
fail
ure
, f
Normal stress,
Mohr – Coulomb failure envelope
UJI GESER LANGSUNG PADA PASIR
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Standard Penetration Test, SPT
SPT adalah test yang paling banyak digunakan untuk
tanah di lapangan
63.5 kg
0.76 m
Drill rod
0.15 m
0.15 m
0.15 m
Jumlah pukulan = N1
Jumlah pukulan = N2
Jumlah pukulan = N3
Standard penetration resistance (SPT N) = N2 + N3
The test can be conducted at every 1m
vertical intervals
Berbagai macam korelasi dikembangkan untuk
menentukan parameter kuat geser (c, , ect) dari N
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Kuat geser pada tanah jenuh sebagian
Tanah
Air
Tanah jenuh
Tekanan air
pori, u
Effective
stress, ’ Tanah
Tanah tak jenuh
Tekanan air
pori, uw
Tegangan
efektif, ’
Air
Udara Tekanan air
pori, ua
Tekanan air pori bisa negatif di tanah tak jenuh
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Bishop (1959) mengemukakan formula kuat geser untuk tanah tak jenuh
'tan)()(' waanf uuuc
Where, n – ua = Tegangan normal net ua – uw = Matric suction = a parameter tergantung derajat kejenuhan ( = 1 untuk tanah jenuh dan 0 untuk tanah kering)
Fredlund et al (1978) memodifikasi formula di atas menjadi :
b
waanf uuuc tan)('tan)('
Dimana, tanb = Laju kenaikan kuat geser dengan matric suction
Kuat geser pada tanah jenuh sebagian
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b
waanf uuuc tan)('tan)('
Sama seperti tanah jenuh Kohesi berdasarkan
matric suction
Adapun, kekuatan pada tanah tak jenuh lebih besar daripada kekuatan pada
tanah jenuh; karena adanya matric suction
- ua
’
Kuat geser pada tanah jenuh sebagian
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- ua
Bagaimana Istana Pasir bisa
berdiri????
b
waanf uuuc tan)('tan)('
Sama seperti tanah jenuh Kohesi padamatric
suction
’
Apparent
cohesion
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UNCONFINED COMPRESSION TEST 1 = VC +
3 = 0
Confining pressure is zero in the UC test
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UNCONFINED COMPRESSION TEST
Dimensi contoh baik pada saat awal maupun selama
percobaan
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1 = VC + f
3 = 0
Sh
ea
r st
ress
,
Normal stress,
qu
Note: Theoritically qu = cu , However in the actual case qu
< cu due to premature failure of the sample
UNCONFINED COMPRESSION TEST
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Penggambaran tegangan-
regangan untuk mendapatkan
kekuatan tekan tak terkekang, qu
UNCONFINED COMPRESSION TEST
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UNCONFINED COMPRESSION TEST
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LATIHAN SOAL
Pada uji triaksial consolidated drained (CD)
diperoleh data : σ3 = 27,6 kN/m2 dan Δσf =27,6
kN/m2. Kalau benda uji berupa lempung yang
terkonsolidasi normal, maka :
a. Hitung sudut geser dalam
b. Hitung sudut runtuh θ (sudut bidang kegagalan
dengan bidang utama mayor)
c. Hitung tegangan normal (σf’) dan tegangan
geser τf pada saat failure
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TUGAS KELOMPOK (3 KELOMPOK)
Carilah/buatlah soal dan presentasikan pada pertemuan depan (semakin kompleks, nilai semakin tinggi)
1. UU
2. CU
3. CD
***Good Luck***