Teknik Pondasi: kuat geser tanah Farid Maruf
Pokok Bahasan
Kurva kuat geser vs regangan Tanah
Memiliki nilai tegangan puncak (peak stress) Dilatansi positif (ekspansi)
Tanah
padat atau OCR > 2
lepas atau OCR = 1
Tidak memiliki tegangan puncak, kecuali pada tekanan normal yang sangat kecil Dilatansi negatif (tanah terkompresi)
keywords Hukum
friksi Coulomb:
τ f = c + σ f tan φ
Hukum
Taylor
τ cs = σ cs tan φcs
Kurva keruntuhan mohr coulomb
Kurva keruntuhan mohr coulomb Sudut
sin φ ' =
keruntuhan σ '1 f −σ '3 f σ '1 f
sin φ ' =
2 + σ '3 f 2
Tegangan
τf =
3
1
σ '1 −σ '3 2
−1
σ '1 f σ '3 f
+1
normal σn dan tegangan geser τf
σ n = σ ' +2σ ' + σ ' −2σ ' sin φ ' 1
σ '1 f σ '3 f
3
cos φ '
Keruntuhan geser Tanah biasanya runtuh karena geser
embankment strip footing
failure surface
mobilised shear resistance
Pada saat runtuh, gaya geser disepanjang bidang runtuh mencapai kuat gesernya.
Keruntuhan geser
8
failure surface Butir tanah bergerak satu dengan yang lain di sepanjang bidang runtuh.
No crushing of individual grains.
Keruntuhan geser
9
Pada saat runtuh, gaya geser di bidang geser (τ) mencapai kuat gesernya (τf ).
Soil strength Kuat geser tanah berasal dari: Kohesi antar butiran (stress independent component)
Sementasi antar butiran pasir Gaya elektrostatik antara butiran lempung
Friksi
antar butiran (stress dependent component)
Kuat geser: kohesi Kohesi
(c ), adalah parameter yang menggambarkan gaya yang menyatukan butiran tanah. Kohesi tidak tergantung tekanan
Kuat geser: sudut geser dalam ϕ Sudut
geser dalam (ϕ), parameter yg menggambarkan kuat geser karena friksi Sudut geser dalam tergantung tekanan normalion
Kriteria keruntuhan Mohr-Coulomb Teori ini menyatakan bahwa material runtuh karena kombinasi kritis dari tegangan normal dan tegangan geser, bukan dari nilai maksimum salah satu tegangan tersebut
Kriteria keruntuhan Mohr-Coulomb τ
τ f = c + σ tan φ φ
kohesi
τf
Sudut geser dalam
c σ
σ
τf adalah tegangan geser maksimum yang bisa ditahan oleh tanah tanpa runtuh saat tegangan normal adalah σ.
Kriteria keruntuhan Mohr-Coulomb Kuat geser terdiri atas dua komponen: kohesi dan friksi.
τ
τ f = c + σ f tan φ
τf σf tan φ
φ
Komponen friksi
c
c σf
σ
c dan φ adalah parameter untuk menunjukkan kuat geser Semakin tinggi nilainya, semakin tinggi kuat gesernya
Lingkaran mohr & kurva keruntuhan
τ
X
X Y
Y σ
Soil elements at different locations
X
~ failure
Y
~ stable
Lingkaran mohr & kurva keruntuhan The soil element does not fail if the Mohr circle is contained within the envelope GL ∆σ σc Y
σc σc Initially, Mohr circle is a point
∆σ
σc+∆σ
Lingkaran mohr & kurva keruntuhan As loading progresses, Mohr circle becomes larger…
GL ∆σ σc Y
σc σc
.. and finally failure occurs when Mohr circle touches the envelope
Orientasi bidang runtuh Failure plane oriented at 45 + φ/2 to horizontal
Y GL
45 + φ/2
45 + φ/2
∆σ σc Y
φ
σc
90+φ
σc
σc+∆σ
Mohr circle in terms of σ & σ’ σv
σv’ σh
X
=
u σh’
X
+
effective stresses
σh’
σv’
X
total stresses
σh
σv u
u
Envelopes in terms of σ & σ’ Identical specimens initially subjected to different isotropic stresses (σc) and then loaded axially to failure
∆σf σc
σc
σc
σc
uf Initially…
Failure c, φ in terms of σ
At failure,
σ3 = σc; σ1 = σc+∆σf
c’, φ’
σ 3 ’ = σ 3 – uf ; σ 1 ’ = σ 1 - u f
in terms of σ’
σ1- σ3 Relation at Failure σ1 σ3
X X
soil element at failure
σ3
σ1
σ 1 = σ 3 tan (45 + φ / 2) + 2c tan( 45 + φ / 2) 2
σ 3 = σ 1 tan ( 45 − φ / 2) − 2c tan( 45 − φ / 2) 2
Stress Point
σv σh
X
t
τ stress point
σh
(σvσh)/2
(σv+σh)/ 2
s=
σv
t=
σv +σh 2
stress point
s
σ
σv −σh 2 24
Stress Path During loading…
t
τ
Stress path is the locus of stress points Stress path s
σ
Stress path is a convenient way to keep track of the progress in loading with respect to failure envelope. 25
Failure Envelopes t
τ φ
failur e tan-1 (sin φ)
c cos φ
c
stress path s
σ During loading (shearing)….
26
Direct shear test Test procedure
P
Steel ball Pressure plate
Porous plates S
Proving ring to measure shear force
Step 1: Apply a vertical load to the specimen and wait for consolidation
Direct shear test Test procedure
P
Steel ball Pressure plate
Porous plates S
Proving ring to measure shear force
Step 1: Apply a vertical load to the specimen and wait for consolidation Step 2: Lower box is subjected to a horizontal displacement at a constant rate
Direct shear test Shear box
Dial gauge to measure vertical displacement
Proving ring to measure shear force
Loading frame to apply vertical load
Dial gauge to measure horizontal displacement
Direct shear test Analysis of test results
Normal force (P) σ = Normal stress = Area of cross section of the sample Shear resistance developed at the sliding surface (S) τ = Shear stress = Area of cross section of the sample Note: Cross-sectional area of the sample changes with the horizontal displacement
Direct shear tests on sands
Shear stress, τ
How to determine strength parameters c and φ
Normal stress = σ3 Normal stress = σ2
τf3
τf2
τf1
Normal stress = σ1
Shear stress at failure, τf
Shear displacement
Mohr – Coulomb failure envelope
φ
Normal stress, σ
Triaxial Shear Test Piston (to apply deviatoric stress)
Failure plane
O-ring
Soil sample
Soil sample at failure Perspex cell
impervious membrane Porous stone Wate r
Cell pressure Back pressure pedestal
Pore pressure or volume change
Triaxial Shear Test Specimen preparation (undisturbed sample)
Sampling tubes Sample extruder
Triaxial Shear Test Specimen preparation (undisturbed sample)
Edges of the sample are carefully trimmed
Setting up the sample in the triaxial cell
Triaxial Shear Test Specimen preparation (undisturbed sample)
Sample is covered with a rubber membrane and sealed
Cell is completely filled with water
Triaxial Shear Test Specimen preparation (undisturbed sample) Proving ring to measure the deviator load Dial gauge to measure vertical displacement
CU tests
How to determine strength parameters c and φ σ’1 = σ3 + (∆σd)f - uf
uf
Shear stress, τ
Mohr – Coulomb failure envelope in terms of effective stresses
C’
Effective stresses at failure
φ’
Mohr – Coulomb failure envelope in terms of total stresses
ccu
σ’3
a
σ’3b σ3 a
b
φc
u
ufa
σ3
σ’3 = σ3 - uf
σ’1a (∆σd)f a
ufb
σ’1b σ1a
σ1b
σ or σ’
Standard Penetration Test Rotary-drilled Borehole
Standard Penetration Test (SPT) Procedures: ASTM D 1586 N = measured Number of Blows to drive sampler 300 mm into soil.
40
Anchored Cone Rig Mud Island, Downtown Memphis, TN 6-tonne Geostar truck with 20-tonne hydraulic pushing system No special license Twin earth anchors Has penetrated to depths over 32+ meters at sites in SC, AL, MO, TN, & AL
CPT Profile, Downhole Memphis qt (MPa)
Depth (meters)
0
fs ub qt
20
40
u b (kPa)
fs (kPa) 60
0
500
1000
-200
0
0
0
4
4
4
8
8
8
12
12
12
16
16
16
20
20
20
24
24
24
28
28
28
0
200 400 600 800
