kuat geser tanah - widodosuyadi.lecture.ub.ac.id · the mohr-coulomb failure locus is tangent to...
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KUAT GESER TANAH
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Kuat Geser Tanah
� Tanah pada umumnya mempunyai kekasaranKuat gesernya, tergantung kepada tegangan yang diberikan.
� Kuat geser dipengaruhi oleh tegangan effektifnyatekanan air akan punya peran
� Tegangan geser tergantung pada drainase � Tegangan geser tergantung pada drainase pengukuran tegangan dilakukan pada kondisi
1. Deformasi pada volume constan (undrained)
2. Deformasi tanpa menimbulkan excess pore pressures (drained)
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Kriteria Keruntuhan Mohr-Coulomb
Hubungan antara tegangan geser dan tegangan
τσn
Hubungan antara tegangan geser dan tegangan normal :
τ = c + σn tan φDimana c = kohesi
φ = sudut geser
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Kriteria Keruntuhan pada tegangan efektif
τ σ φ= + ′c n' tan '
c′ and φ′ Adalah parameter kuat geser dalam kondisi
Jika tanah dalam kondisi runtuh , kriteria keruntuhan pada tegangan efektif akan memenuhi persamaan sbb;
c′ and φ′ Adalah parameter kuat geser dalam kondisi terdrainase
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Kriteria keruntuhan pada tegangan total
τ σ φ= +cu n utan
Jika tanah dibebani pada kondisi volume konstan (undrained) persamaan kriteria keruntuhan dapat dirumuskan ;
cu dan φu adalah parameter undrained strength cu dan φu adalah parameter undrained strength
Dalam praktek , undrained strength diterapkan pada tanah lempung pada jangka waktu singkat tidak terdrainase.
Jadi jika pore pressures tidak dapat diukur , kriteria tegangan efektif tidak bisa dipakai
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Percobaan Geser Langsung
1. Shear Box Test
Motor penggerak
Load cell untuk mengukur gaya geser
Gaya NormalPlat penutup
penggerak gaya geser
Rollers
Soil
Batu porous
Yang diukur pergerakan horisontal relatif dx
pergerakan vertikal, dy
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� Percobaan pada tanah lempung, kecepatan pembebanan harus rendah, untuk menghindari pengaruh pore pressure
Untuk jenis pasir dan kerikil dapat dilakukan pembebanan dengan kecepatan yang lebih tinggi
Shear box test
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Contoh hasil percobaan geser
She
ar L
oad
(F)
Normal load
Horizontal displacement (dx)
She
ar L
oad
(F)
load increasing
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Contoh pembebanan dengan drained
τ = F/APeak
Ultimate
σ = N/AN1 N2
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Keuntungan dengan percobaan Geser Langsung
� Mudah dan cepat untuk tes pada pasir dan gravel
� Percobaan dengan deformasi yang besar dapat dilakukan untuk mengetahui kuat geser residual
� Sampel ukuran besar dapat dilakukan pada box yang besar
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�Tegangan Efektif tidak bisa ditentukan dari undrained test
�Undrained strengths yang didapat tidak
Kerugian pada Tes Kuat Geser Langsung
tepat , karena tidak mungkin menghindari drainasi tanpa menerapkan pembebanan dengan kecepatan tinggi
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Tes Triaksial
Rubber Cell water
Confining cylinder
Deviator load
Cell pressure Pore pressure
and volume change
Rubber membrane
O-ring seals
Porous filter disc
Soil
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Tegangan yang bekerja pada contoh tanah
σr σr = Radial stress (cell pressure)
F = Deviator loadσr
pressure)
σa = Axial stress
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Tegangan yang terjadi pada contoh tanah
σr σr = Radial stress (cell pressure)
F = Deviator loadσr
pressure)
σa = Axial stress
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Strains in triaxial specimens
Dari pengukuran tinggi dh, dan perubahan volume dV didapatkan
Axial strain
Volume strain
Dimana h0 adalah tinggi awal , dan Vo adalah volume awal
ε adh
h= −
0
ε VdV
V= −
0
Dengan anggapan bahwa deformasi terjadi dengan bentuk silinder Sehingga luas penampang melintang A dapat dihitung dari
A = A
1 + dV
V
1 + dh
h
= A 1 -
1 - o o
v
a
0
0
εε
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Beberapa Jenis Variasi percobaan
� UU (unconsolidated undrained) test.
Cell pressure applied without allowing drainage. Then keeping cell pressure constant increase deviator load to failure without drainage.
� CIU (isotropically consolidated undrained) test.
Jenis Percobaan Triaxial
� CIU (isotropically consolidated undrained) test.
Drainage allowed during cell pressure application. Then without allowing further drainage increase q keeping σr
constant as for UU test.
� CID (isotropically consolidated drained) test
Similar to CIU except that as deviator stress is increased drainage is permitted.
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� Contoh tanah menerima tegangan dan regangan yang relatif merata
Perilaku stress-strain-strength dapat diamati semua
Keuntungan penggunaan triaxial test
� Perilaku stress-strain-strength dapat diamati semua
� Dapat dilakukan drained dan undrained tests
� Pore water pressures dapat diukur pada undrained tests
� Dapat diterapkan cell pressure and axial stress yang berbeda besarnya
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Mohr Circles
To relate strengths from different tests we need to use some results from the Mohr circle transformation of stress.
ττ σ φ= +c tan
σσ1σ3
c
The Mohr-Coulomb failure locus is tangent to the Mohr circles at failure
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Lingkaran Mohrτ
σσ1σ3
φ 2α
(τα, σα)
From the Mohr Circle geometry
σσ σ σ σ
αα =+
−−( ) ( )
cos1 3 1 3
2 22
τσ σ
αα =−( )
sin1 3
22
α π φ= −
4 2
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� The Mohr circle construction enables the stresses acting in different directions at a point on a plane to be determined, provided that the stress acting normal to the plane is a principal stress.
� The construction is useful in Soil Mechanics because many practical situations may be approximated as plane strain.
� The sign convention is different to that used in Structural analysis because it is conventional to take compressive
Mohr Circles
analysis because it is conventional to take compressive stresses positive
� Sign convention: Compressive normal stresses positive
Anti-clockwise shear stresses positive (from inside element)
Angles measured clockwise are positive
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Mohr-Coulomb criterion (Principal stresses)τ
σφσ1σ3
c
φ p
R
c cot φ p
Failure occurs if a Mohr circle touches the failure criterion. Then
R = sin φ ( p + c cot φ )
1
3
2 + c
+ c =
1 +
1 - =
4 +
2 = N
σ φσ φ
φφ
π φφ
cot
cot
sin
sintan
1 3 = N + 2 c Nσ σφ φ
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Effective stress Mohr-Coulomb criterion
τ σ φ= + ′c n' tan '
As mentioned previously the effective strength parameters are the fundamental parameters. The Mohr-Coulomb criterion must be expressed in terms of effective stresses
c′ and φ′
′ ′ ′σ σφ φ1 3 = N + 2 c N
φ+ ′1 sinN φ
φφ
=+ ′− ′
1
1
sin
sinwhere
′ = −σ σn n u′ = −σ σ1 1 u
′ = −σ σ3 3 u
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τ
σσ1σ3′σ1′σ 3
u
Effective and total stress Mohr circles
u
u
For any point in the soil a total and an effective stress Mohr circle can be drawn. These are the same size with
′ − ′ = −σ σ σ σ1 3 1 3
The two circles are displaced horizontally by the pore pressure, u.
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1. Drained shear loading
• In laboratory tests the loading rate is chosen so that no excess water pressures will be generated, and the specimens are free to drain. Effective stresses can be determined from the applied total stresses and the known pore water pressure.
Interpretation of Laboratory results
• Only the effective strength parameters c’ and φ’have any relevance to drained tests.
• It is possible to construct a series of total stress Mohr circles but the inferred total stress (undrained) strength parameters are meaningless.
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� Effective strength parameters are generally used to check the long term stability (that is when all excess pore pressures have dissipated) of soil constructions.
� For sands and gravels pore pressures dissipate rapidly and the effective strength parameters can also be used to check the short term stability.
Interpretation of Laboratory results
the short term stability.
� In principle the effective strength parameters can be used to check the stability at any time for any soil type. However, to do this the pore pressures in the ground must be known and in general they are only known in the long term.
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2. Undrained loading
� In undrained laboratory tests no drainage from the sample must occur, nor should there be moisture redistribution within the sample.
� In the shear box this requires fast shear rates. In triaxial tests slower loading rates are possible because conditions are uniform
Interpretation of Laboratory results
slower loading rates are possible because conditions are uniform and drainage from the sample is easily prevented.
� In a triaxial test with pore pressure measurement the effective stresses can be determined and the effective strength parameters c’, φ’ evaluated. These can be used as discussed previously to evaluate long term stability.
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� The undrained tests can also be used to determine the total (or undrained) strength parameters cu, φu. If these parameters are to be relevant to the ground the moisture content must be the same. This can be achieved either by performing UU tests or by using CIU tests and consolidating to the in-situ stresses.
� The total (undrained) strength parameters are used to assess the short term stability of soil constructions. It is important that no
Interpretation of Laboratory results
short term stability of soil constructions. It is important that no drainage should occur if this approach is to be valid. For example, a total stress analysis would not be appropriate for sands and gravels.
� For clayey soils a total stress analysis is the only simple way to assess stability
� Note that undrained strengths can be determined for any soil, but they may not be relevant in practice
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Relation between effective and total stress criteria
Three identical saturated soil samples are sheared to failure in UU triaxial tests. Each sample is subjected to a different cell pressure. No water can drain at any stage. At failure the Mohr circles are found to be as shown
τ
σσσ1σ3
We find that all the total stress Mohr circles are the same size, and therefore φu = 0 and τ = su = cu = constant
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Relation between effective and total stress criteria
τ
σ
Because each sample is at failure, the fundamental effective stress failure condition must also be satisfied. As all the circles have the same size there must be only one effective stress Mohr circle τ σ φ= + ′c n' tan '
σσ1σ3′σ1′σ 3
′ − ′ = − =σ σ σ σ1 3 1 3 2 cu
′ ′ ′σ σφ φ1 3 = N + 2 c N
We have the following relations
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� The different total stress Mohr circles with a single effective stress Mohr circle indicate that the pore pressure is different for each sample.
� As discussed previously increasing the cell pressure without allowing drainage has the effect of increasing the pore pressure by the same amount (∆u = ∆σ ) with no
Relation between effective and total stress criteria
pore pressure by the same amount (∆u = ∆σr) with no change in effective stress.
� The change in pore pressure during shearing is a function of the initial effective stress and the moisture content. As these are identical for the three samples an identical strength is obtained.
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� It is often found that a series of undrained tests from a particular site give a value of φu that is not zero (cu not constant). If this happens either
– the samples are not saturated, or
– the samples have different moisture contents
Significance of undrained strength parameters
� If the samples are not saturated analyses based on undrained behaviour will not be correct
� The undrained strength cu is not a fundamental soil property. If the moisture content changes so will the undrained strength.
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Example
In an unconsolidated undrained triaxial test the undrained strength is measured as 17.5 kPa. Determine the cell pressure used in the test if the effective strength parameters are c’ = 0, φ’ = 26o and the pore pressure at failure is 43 kPa.
Analytical solutionAnalytical solution
Undrained strength = 17.5 =
Failure criterion
Hence σ1’ = 57.4 kPa, σ3’ = 22.4 kPa
and cell pressure (total stress) = σ3’ + u = 65.4 kPa
′ ′ ′σ σφ φ1 3 = N + 2 c N
( ) ( )σ σ σ σ1 3 1 3
2 2
−=
′ − ′
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Graphical solution
τ
σ
26
17.5
σ′σ1′σ 3
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Graphical solution
τ
σ
26
17.5
σσ1σ3′σ1′σ 3
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