Download - KEKUATAN GESER TANAH
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KEKUATAN GESER TANAH
Definisi: perlawanan internal tanah tiap satuan luas terhadap keruntuhan atau pergeseran sepanjang bidang runtuh dalam satu elemen tanah
Tujuan Studi kekuatan geser tanah:Untuk analisis masalah kestabilan tanah, seperti :• daya dukung• stabilitas talud (lereng)• tekanan tanah ke samping pada turap/tembok penahan• dll
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KEKUATAN GESER TANAH
Dasar Teori (Hukum Gesekan Newton):
W
T
R
f
T > W geser
T < W diam
T = W labil
f
f
tan
:
tan
AWA
Ttegangandalam
WT
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KEKUATAN GESER TANAHBasic mechanics applied to soils
Equilibrium and compatibility
The principle of equilibrium states that if a body is in state of rest, the net force acting on the body in any direction is zero.
Thus, in the figure above, the sums of forces in the horizontal and vertical directions will be zero:
H = H1 + H2 + H3 + H4
V = V1 + V2 + V3 + V4
The principle of compatibility states that any movements or changes in shape or volume must be compatible with no material being lost or gained.
When loads are applied to bodies of soil it is assumed that the solid content remains constant (though displaced or re-arranged), but that there may be changes in the volume of water and or air.
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KEKUATAN GESER TANAHMechanical Characteristic of soils
Soils are not solid materials, as are steel and concrete, but are made up of separate
particles, surrounded by voids, which may contain water or air or both.
The particles in sands are rotund, while in clays they are flaky.
Changes in shape and volume, and the strength of soil, are controlled by effective
stress, i.e. the difference between the (external) total stress and the (internal)
pore pressure.
Under different circumstances of occurrence soils may be:
- very dense, ranging through dense, intermediate and loose, to very loose
- very dry and hard, ranging through stiff and soft, to very wet and soft.
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KEKUATAN GESER TANAHCompressibility Characteristic of soils
• Soils are compressible if the voids contain air.
• Soils saturated with water are compressible ONLY if drainage can take place.
• Compression results in a change in the volume of voids (changes in the volume of
the grains are negligible)
• Loose sands are more compressible than dense sands.
• Wet or soft clays are more compressible than dry or hard clays.
• Normally consolidated clays are more compressible than overconsolidated clays.
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KEKUATAN GESER TANAHStrength Characteristic of soils
Soil strength is basically frictional, and is controlled by effective stress.
The ‘strength’ of a soil is defined as the maximum sustainable shear stress that
can be developed under certain specified conditions:
Undrained strength: (e.g. in saturated clay) is constant with respect to effective
normal stress, but decreases with increasing water content.
Drained strength: increases with effective normal stress.
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KEKUATAN GESER TANAHStiffness and Elasticity
Stiffness is the relationship between strain and the stress that will
induce it.
Stiffness behavior relates to the changes in strain that accompany
changes in stress (due to loading and unloading).
A stress-strain curve is used to characterize stiffness behavior.
The stiffness modulus is simply the slope of the stress-strain curve.
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KEKUATAN GESER TANAHStiffness Moduli
When the loading on a body changes the strain induced will be one or a
combination of three types:
o Direct or linear strain: changes in length, breadth, diameter, etc.
o Volumetric strain: changes in volume
o Shear strain: changes in shape
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KEKUATAN GESER TANAHStiffness Moduli
In bodies of elastic material the three stiffness moduli (E´, K´ and G´) are related to
each other and to Poisson’s ratio (’).
It assumed that the material is elastic and isotropic (i.e. linear stiffness is equal in all
directions).
The following relationships can be demonstrated (for proofs refer to a text on the
strength of materials)
G’ = E’/ 2(1-’)
K’ = E’/ 3(1-2’)
´ = Poisson’s ratio for soils, is in the range 0.2 - 0.5
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KEKUATAN GESER TANAHStress-Strain Behaviour of Soils
• The stress-strain behaviour of soils is similar to that of other engineering materials, i.e.
elastic and plastic deformation occur as in steel, concrete, etc.
• It is the variability in behaviour that distinguishes soils from other materials.
• For example, the same soil at different water contents or states of compaction will
exhibit a wide range of stiffness and strength characteristics.
• Relatively recent soils (< 1 Ma old) tend to deform plastically at relatively low
stresses, but with deformation related linearly to the logarithm of stress.
• Geologically old soils, soils that have been overlain by other soils, rocks or ice, are
harder and tend to behave elastically (or nearly so) at the levels of stress associated
with civil engineering projects.
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KEKUATAN GESER TANAHBehaviour of Soft Soils
• Soft soils (including recent natural soils and reconstituted soils) with no history of previous
greater loading behave inelastically; the stress-strain diagram being curved even at low
stresses.
• The slope of the curve (E´ = d´a/da) decreases as the stress increases, eventually
reaching an ultimate stress which remains constant as straining continues.
• Irreversible plastic strain occurs, so that upon unloading permanent deformation (p)
remains.
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KEKUATAN GESER TANAHBehaviour of Soft Soils
• Stiffness values vary with different stress regimes, e.g. uniaxial, triaxial, one-dimensional.
• ‘Typical’ values should not be used in design, except in preliminary stages, feasibility
studies, etc.
• Compression tests are required to ascertain reliable and representative values (refer to the
Soil Mechanics Reference: Compression and swelling)
Typical E range(MPa)Normally consolidated clays 0.2 - 4Organic alluvial clays and peats 0.1 - 0.6
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KEKUATAN GESER TANAHBehaviour of Hard Soils
• Stiff and hard soils have often become overconsolidated, i.e. they have a stress history
in which loading has increased stresses and then unloading has decreased them.
• Deformation is a consequence of changes in effective stress.
• A low stresses the behaviour is elastic (or nearly so), with the stiffness remain almost
constant.
• After the yield point has been reached, plastic deformation occurs
• Work softening occurs in heavily overconsolidated soils, so that the ultimate stress
will be lower than the peak stress.
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KEKUATAN GESER TANAHBehaviour of Hard Soils
• Stiffness values vary with different stress regimes, e.g. uniaxial, triaxial, one-dimensional.
• ‘Typical’ values should not be used in design, except in preliminary stages, feasibility studies, etc.
• Compression tests are required to ascertain reliable and representative values (refer to the Soil mechanics Reference: Compression and swelling)
Typical E range(MPa)Unweathered overconsolidated clays 20 - 50Boulder clay 10 - 20Keuper Marl (unweathered) >150Keuper Marl (moderately weathered) 30 - 150Weathered overconsolidated clays 3 - 10
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KEKUATAN GESER TANAHState of Stress and Strain
• The three orthogonal axial directions are defined in soil mechanics similarly to other
engineering disciplines, except that some special considerations apply.
• The direction of the z-axis is usually vertical; with positive = downward-with-depth in
site problems.
• Stresses relating to soil masses are almost always compressive.
• Distinction must be made between total stresses and effective stresses, e.g. = total normal stress´ = effective normal stress (note the prime)
z
y
x
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KEKUATAN GESER TANAHState of Stress and Strain
z
• a = total axial compressive stress
• ´a = effective axial stress = a - u
• u = internal pore pressure
• a = axial strain (due to ´a)
Uniaxial stress and strain
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KEKUATAN GESER TANAHState of Stress and Strain
Triaxial stresses and strains
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KEKUATAN GESER TANAHState of Stress and Strain
Biaxially symmetrical stresses and strains
• In a triaxial arrangement, normal stresses (x, y, z) and normal
strains (x, y, z) are aligned on three orthogonal axes.
• In the triaxial test, axial directions are referred to as axial or radial.
• Also the two radial values will be equaly, i.e. are biaxially
symmetrical.
• z = a = total axial stress
• x = y = r = total radial stress
• ´z = ´a = effective axial stress = a - u
• ´x = ´y = ´r = effective radial stress = r - u
• u = pore pressure
• a = axial strain
• r = radial strain
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KEKUATAN GESER TANAHState of Stress and Strain
Biaxially symmetrical stresses and strains
The normal stresses are principal stresses (1, 2, 3)
• The deviator and mean normal stresses are defined as:
q´ = deviator stress = ´a - ´r = a - r (= 1 - 3)
p = mean total normal stress = 1/3 (1 + 2 + 3) = 1/2 (a + 2r)
p´ = mean effective normal stress = 1/3 (´1 + ´2 + ´3) = 1/2 (´a + 2 ´r) =
p - u
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KEKUATAN GESER TANAHState of Stress and Strain
Plane strain
• Plane strain conditions occur, for example, under the centre of long strip footings and retaining walls.
• Strains only occur in a vertical plane, perpendicular to this plane the strain is zero.
z or v = vertical total stress
´z or ´v = vertical effective stress
z or v = vertical strain
x or h = horizontal total stress
´x or ´h = horizontal effective stress
´y = horizontal stress in the direction of zero strain
= K0 ´v
(where K0 = coefficient of earth pressure at rest)
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KEKUATAN GESER TANAHState of Stress and Strain
Plane strain
Mohr circle and the invariants s´ and t´
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KEKUATAN GESER TANAHShear Stress and Strain
• “Engineers’ shear strain” is defined as the angle of distortion of a rectilinear element.
= shear stress (acting tangentially)
= shear strain (angular distortion due to the shear stress)
• On either side of a slip plane the shear stress () has reached a limiting value (f),
which may be termed shear strength, e.g. as in the shear box (or direct shear) test
• The stress-displacement (/dx) curve will have characteristics similar to those of a
shear-stress/shear-strain curve, but cannot be used to measure shear stiffness.
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KEKUATAN GESER TANAHState of Stress and Strain
Stiffness Parameters:
• Changes in volume in soil masses are due to changes in effective stress.
• Changes in shape can be related to both total and effective stresses.
E = Stiffness (Young’s) modulus for direct (axial) straining, i.e. when r = 0
= a/ a i.e.. in terms of total stresses
Eu = Stiffness modulus measured in undrained conditions, i.e. when v = 0
E´ = Stiffness modulus for direct (axial) straining, i.e. when ’r = 0
= ’a/ a i.e. in terms of total stresses
E´o = Young’s modulus for one-dimensional compression, i.e. when r = 0
K´ = Bulk modulus (isotropic stress) = ´/ v
G´ = Shear modulus = /
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KEKUATAN GESER TANAHState of Stress and Strain
Stiffness Parameters:Tangent and Secant values of E’
• Since the stress-strain behaviour of soil produces a curve, E´ is not constant, but decreases with increasing stress. Practical measures of the slope (e.g. to obtain an E´ value for design) can be either a secant value or a tangent value.
• For problems where the stress is simply raised from zero by Ds´, the secant value is appropriate.
• For problems involving small strains around a given level of stress (point A), the tangent value is more suitable.
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STRENGTH AND FAILURE
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KEKUATAN GESER TANAHStrength and Failure
• The strength of a material is often expressed in terms of the applied
stress, e.g.
- in a tie rod: tensile strength
- a concrete cube: compressive strength
- in bolts: shear strength
• In all cases, however, strength is related to a characteristic maximum
shear stress.
• The magnitude of maximum shear stress is given by the radius of the
Mohr circle.
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KEKUATAN GESER TANAH
Kriteria Keruntuhan Menurut MOHR-COLOUMBKeruntuhan terjadi pada suatu material akibat kombinasi kritis antara tegangan normal dan geser, dan bukan hanya akibat tegangan normal maksimum atau tegangan geser maksimum saja.
f = f()
f : sudut geser-internal
c : kohesi
f = c + tanf
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KEKUATAN GESER TANAH
Mohr circle for tensile strength
• In soil mechanics, since stresses are invariably compressive, the sign convention for
the Mohr circle axes is: compressive stresses are positive and plotted on the
x-axis to the right.
• Note that the tensile ‘strength’ will be given by tf = diameter of the Mohr circle.
• The shear strength (f) is given by the radius of the Mohr circle
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KEKUATAN GESER TANAH
Mohr circle for compressive strength
• Note that the angle of the potential plane of failure is 45°
• Maximum shear strength = 1/2 ´c
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KEKUATAN GESER TANAH
Mohr circle for shear strength
• The example in the figure is that of a saturated clay slope, but the same concept
of shear strength applies in all soil constructions.
• The stresses at failure (slipping in this case) are:
• f = shear stress = radius of the Mohr circle
• ´n = normal effective stress = the x-coordinate of the circle centre
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KEKUATAN GESER TANAH
Mohr circle for water
• The stresses at a point within a liquid are equal; they plot at a single point.
• Thus, liquids have no shear strength.
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KEKUATAN GESER TANAH Strength Criteria
• Strength criteria relate to the maximum sustainable shear stress, i.e. the shear
stress at failure.
• For soils, there are really two criteria by which strength (and therefore failure)
may be defined, but one of these is modified to provide a third.
o Tresca - applies to failure in metals and undrained soils
o Mohr-Coulomb (when c´ = 0) - applies the critical state failures in soils
o Mohr-Coulomb (when c´ > 0) - applies to peak state failures in soils.
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KEKUATAN GESER TANAH
The Tresca Criterion
• At any level of normal stress the Mohr circle diameter (a - r) remains constant.
• The failure envelope is therefore parallel to the ´n axis and the strength independent of
normal stress.
• Failure occurs when the Mohr circle increases in diameter to touch the failure envelope:
• Undrained shear strength, f = cu (or su) = a - r = constant
Strength criteria
Related to undrained condition
In terms of total stresses
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KEKUATAN GESER TANAH
The Mohr-Coulomb (c’ = 0) Criterion
• The Mohr-Coulomb (c´ = 0) criterion relates to the drained critical state strength of soils.
• Shear strength increases linearly with normal stress; the strength being zero at zero normal
stress.
• As the normal stress increases the Mohr circle diameters increase; circles representing
failure stress ultimately touch a straight-line failure envelope.
o Critical state shear strength, f = ´n tan f´
o f´ (or f´c) = the critical angle of friction
Strength criteria
Related to drained critical state strength of soils
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KEKUATAN GESER TANAH
The Mohr-Coulomb (c’ > 0) Criterion
• Strength increases linearly with normal stress, i.e. circle Mohr diameters increase; circles
representing failure stress touch a failure envelope.
• At low stresses the failure envelope is curved, but for practical purpose a straight line is
fitted with a practical normal stress range which gives the ‘cohesion intercept’ on the shear
stress axis.
• Peak state shear strength, f = c´ + ´n tan f´p
o c’ = the cohesion intercept
o f´p = the peak angle of friction
Strength criteria
Related to drained peak state strength of condition
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KEKUATAN GESER TANAH
The Mohr-Coulomb (c’ > 0) Criterion
• Strength increases linearly with normal stress, i.e. circle Mohr diameters increase; circles
representing failure stress touch a failure envelope.
• At low stresses the failure envelope is curved, but for practical purpose a straight line is
fitted with a practical normal stress range which gives the ‘cohesion intercept’ on the shear
stress axis.
• Peak state shear strength, f = c´ + ´n tan f´p
o c’ = the cohesion intercept
o f´p = the peak angle of friction
Strength criteria
Related to drained peak state strength of condition
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BASIC GEOTECHNICAL STRUCTURAL TYPES
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BASIC GEOTECHNICAL STRUCTURAL TYPES
Foundations
Retaining walls
Slopes
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BASIC GEOTECHNICAL STRUCTURAL TYPES
Foundation:
· The main variables are load (F), size (B) and founding depth (D).
· The main design criteria are settlement and stability.
· Sub-types: shallow, deep, piles; pads, strips, rafts; cellular, caissons
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BASIC GEOTECHNICAL STRUCTURAL TYPES
Retaining Wall:
• These are basically vertical structures subject to horizontal loading.
• May be gravity walls, deriving stability from their own weight or embedded walls, which are considered
to be weightless.
• The main variables are depth of support provided (H), depth of embedment (D), base size (B), type of
soil.
• Design criteria include overturning, sliding, cracking, bending, ground-bearing stability and settlement.
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BASIC GEOTECHNICAL STRUCTURAL TYPES
Slope Stability:
• Basically two types:
o Cut slopes: excavations, cuttings - construction decreases loading.
o Built slopes: embankments, dams - construction increases loading.
• Effects of seepage are important - soil strength varies with pore pressures.
• Both short term and long term stability can be critical.
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KEKUATAN GESER TANAH
Kemiringan Bidang Keruntuhan Akibat Geser
Tegangan normal dan tegangan geser pada bidang runtuh:
2sin2
31 n
2cos22
3131
n
1
3
n
f
n
1
3
3 < 1
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KEKUATAN GESER TANAH
Pada saat runtuh: f = n f
tan2cos
22c2sin
2313131
atau
ff
tancos2sin
ctan2
21
331
…………………………………….. (a)
Kriteria keruntuhan Mohr-Coloumb:
f = c + tanf
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KEKUATAN GESER TANAH
Persamaan di atas memberikan hubungan baru:
2450 f
Untuk harga-harga 3 dan c tertentu, kondisi runtuh akan ditentukan oleh harga minimum dari tegangan utama besar 1. Bila harga 1 minimum, maka harga (1/2.sin2-cos2 .tanf) pada Persamaan (a) haruslah maksimum. Sehingga:
0tancos2sindd 2
21 f
0tan.cos.sin2sincos 22 f
ff
tancos2sin
ctan2
21
331
1
3
n
f
n
1
3
3 < 1
2450 f
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KEKUATAN GESER TANAH
Gambar disamping menunjukkan gam-baran separuh lingkaran Mohr yang mewakili kondisi tegangan pada saat keruntuhan pada suatu massa tanah. Garis keruntuhan yang dinyatakan oleh persamaan f = c + tan f me-nyinggung lingkaran Mohr pada titik X.
Jadi, keruntuhan geser yang terjadi pada bidang tertentu dapat kita nyata-kan dengan lingkaran berjari-jari OX, dan bidang tersebut harus membentuk kemiringan sudut = 450 + f/2 ter-hadap bidang utama besar.Lingkaran Mohr dan Garis Keruntuhan
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KEKUATAN GESER TANAH
Bila harga = 450 + f/2 dimasukkan ke dalam Persamaan (a) dan kemudian disederhanakan, akan menghasilkan:
222
31 45tan.c245tan. ff
Akan tetapi, Persamaan (b) juga dapat dengan mudah diturunkan dengan menggunakan lingkaran Mohr dan ilmu ukur sederhana.
…………………………………….. (b)
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KEKUATAN GESER TANAH
Beberapa Cara Penentuan (Pengujian) Kekuatan Geser Tanah:
1. Uji Geser Langsung (direct shear test)
2. Uji Triaxial (triaxial test)
3. Uji Kuat Tekan Bebas (unconfined compressive strength test)
4. Uji Vane Shear
5. Dll.
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KEKUATAN GESER TANAH Uji Geser Langsung
Ni
Ti
batu pori
tanah
batu pori
ring
perata beban
meja
Ni : beban vertikal (normal)Ti : gaya horisontal yang diperlukan
untuk menggeser ring (tanah)A : luas penampang tanahsi : lintasan yang diperlukan sampai
tanah tergeser
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KEKUATAN GESER TANAH Uji Geser Langsung
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KEKUATAN GESER TANAH
Percobaan dengan Menggunakan Pasir
AN1
1 Uji 1:
Uji 2:
Uji 3:
AT1
1 ; ; s1
AN2
2 ;
;
; s2
; s3AN3
3
AT2
2
AT3
3
Hasil Uji:
s
f1
f2
f3
3
2
1
1 2 3
f1
f = . tanf
f2
f3
f
f : sudut geser dalam
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KEKUATAN GESER TANAH
Percobaan dengan Menggunakan Lempung
f : sudut geser dalam
1 2 3
f1
f = c + . tanf
f2
f3
f
c
c : kohesi [kN/m2]
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KEKUATAN GESER TANAH
Luas Sample : A = (5.08 * 5.08) cm2
No. Uji
Arah Normal Arah GeserGaya Tegangan Gaya Tegangan
kg kg/cm2 kg kg/cm2
1 9 0.348751 5.44 0.2109242 14 0.542501 8.30 0.321663 32 1.240002 19.10 0.7399934 45 1.743753 27.26 1.05638
UJI GESER LANGSUNG
CONTOH TANAH PASIR
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KEKUATAN GESER TANAH
Tahanan Geser
y = 0.6022x
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2
Teg. Normal [kg/cm2]
Teg.
Ges
er [k
g/cm
2 ]
f = atan(0.6022) = 310
c = 0
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KEKUATAN GESER TANAH
UJI GESER LANGSUNGCONTOH TANAH LEMPUNG
Diameter Sample : D = 5.0 cmNo. Uji Arah Normal Arah Geser
Gaya Tegangan Gaya Tegangan kg kg/cm2 kg kg/cm2
1 27 1.374545 14.06 0.7157822 40 2.036363 18.06 0.9194183 47 2.392727 20.41 1.0390544 54 2.749091 22.43 1.141891
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KEKUATAN GESER TANAH
f = atan(0.312) = 17.320
c = 0.2868 kg/cm
Tahanan Geser
y = 0.312x + 0.2868
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2 2.5 3
Teg. Normal [kg/cm2]
Teg.
Ges
er [k
g/cm
2 ]
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KEKUATAN GESER TANAH Pengamatan Hasil Uji Geser Langsung:
Diagram tegangan geser vs. perubahan tinggi benda uji karena pergerakan menggeser untuk tanah pasir padat dan lepas (uji geser langsung)
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KEKUATAN GESER TANAH
Hal umum yang dapat ditarik dari gambar di atas berkaitan dengan variasi tegangan geser penghambat dan perpindahan geser, yaitu:
1. Pada pasir lepas (renggang), tegangan geser penahan akan membesar sesuai dengan membesarnya perpindahan geser sampai tegangan tadi mencapai tegangan geser runtuh Setelah itu, besar tegangan geser akan kira-kira konstan sejalan dengan bertambahnya perpindahan geser.
2. Pada pasir padat, tegangan geser penghambat akan naik sejalan dengan membesarnya perpindahan geser hingga tegangan geser runtuh (maksimum) f
tercapai. Harga f ini disebut sebagai kekuatan geser puncak (peak shear strength). Bila tegangan runtuh telah dicapai, maka tegangan geser penghambat yang ada akan berkurang secara lambat laun dengan bertambahnya perpindahan geser sampai pada suatu saat mencapai harga konstan yang disebut kekuatan geser akhir maksimum (ultimate shear strength).
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KEKUATAN GESER TANAH Uji Triaxial:
PRINCIPLES OF THE TRIAXIAL COMPRESSION TESTThe triaxial compression test is used to measure the shear strength of a soil under controlleddrainage conditions. In the conventional triaxial test, a cylindrical specimen of soil encased in a rubber membrane is placed in a triaxial compression chamber, subjected to a confining fluidpressure, and then loaded axially to failure. Connections at the ends of the specimen permitcontrolled drainage of pore water from the specimen.
The test is called "triaxial" because the three principal stresses are assumed to be known and are controlled. Prior to shear, the three principal stresses are equal to the chamber fluid pressure. During shear, the major principal stress, 1 is equal to the applied axial stress (P/A) plus the chamber pressure, 3.
The applied axial stress, 1 - 3 is termed the "principal stress difference" or sometimes the "deviator stress".
The intermediate principal stress, 2 and the minor principal stress, 3 are identical in the test,and are equal to the confining or chamber pressure hereafter referred to as 3.
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KEKUATAN GESER TANAH
1. Consolidated-drained test atau drained test (CD test)
2. Consolidated-undrained test (CU test)
3. Unconsolidated-undrained test atau undrained test (UU test)
Tiga tipe standar dari uji triaxial yang biasanya dilakukan:
Uji Triaxial:
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KEKUATAN GESER TANAH Uji Triaxial:
PENGUJIAN KUAT GESER DENGAN
TRIAXIAL
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Uji Triaxial:
cell body
load ring
cell piston
strain dial gauge
load dial gauge
porous discs1. The cell pressure connection
to the chamber2. The back pressure connection
to the top of the sample3. The pore pressure connection
Three essential connections to triaxial cell:
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KEKUATAN GESER TANAH Uji Triaxial:
TABUNG TRIAXIAL SELANG PENYALUR DAN PENGUKUR TEKANAN (BEBAN)
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Kran
u
d
d
3 3
3
3
Kran
u
3 3
3
3
Tahap 1:Confining Pressure
Tahap 2:Shear Pressure
3 : konstan
d : bertahap sampai runtuh (d)f
Prinsip Uji Triaxial
Pemberian Beban:
KEKUATAN GESER TANAH
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KEKUATAN GESER TANAH
Confining Pressure Shear Pressure
Jenis Uji Kran Teg. Air Pori (u) Kran Teg. Air Pori (u)
CD Buka u = uc = 0 Buka u = uc+ud = 0
CU Buka u = uc = 0 Tutup u = uc+ud = ud
UU Tutup u = uc Tutup u = uc+ud
Perbedaan Tipe Standard Pengujian Triaxial
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KEKUATAN GESER TANAH Hasil Uji Triaxial CD
Garis keruntuhan untuk tegangan efektif dari uji CD pada pasir dan lempung NC
Total = Effective
c’ ~ 0
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KEKUATAN GESER TANAH Hasil Uji Triaxial CD
Garis keruntuhan untuk tegangan efektif dari uji CD pada lempung OC
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KEKUATAN GESER TANAH Contoh 9-2:
Hasil uji triaxial cara air teralirkan-terkonsolidasi (CD) pada tanah lempung NC adalah sebagai berikut:
3 = 276 kN/m2
(d)f = 276 kN/m2
Tentukan:a) Sudut geser, fb) Sudut (sudut antara bidang keruntuhan dengan bidang utama besar/major
principal plane)c) Tegangan normal ’ dan tegangan geser f pada bidang keruntuhan
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KEKUATAN GESER TANAH Penyelesaian:
Untuk tanah NC, persamaan garis keruntuhannya adalah:
f = ’ tan f
Pada uji triaxial baik tegangan utama besar maupun kecil pada saat terjadi keruntuhan adalah:
1’ = 1 = 3 + ((d)f = 276 + 276 = 552 kN/m2
dan,
3’ = 3 = 276 kN/m2
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KEKUATAN GESER TANAH
Atau
sin f = 333.0276552276552
''''
31
31
f = 19.45o
ooo 73.54245.1945
245
fb)
a) Lingkaran Mohr dan garis keruntuhan dapat dilihat pada gambar depan, dimana:
sin f =
2''
2''
31
31
OAAB
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KEKUATAN GESER TANAH
Dengan memasukkan harga 1’ = 552 kN/m2, 3’=276 kN/m2, dan = 54,73o di atas akan didapatkan
2kN/m 368.0354.73)cos(22
2765522
276552σ'
dan,
2f kN/m 130.1254.73)sin(2
2276552τ
c) dengan menggunakan persamaan (6-8) dan (6.9):
’ (pada bidang keruntuhan) = 2cos2
''2
'' 3131
dan,
2sin2
'' 31 f
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KEKUATAN GESER TANAH Contoh 9-4:
Dua buah benda uji dari tanah lempung yang sama mula-mula dikonsolidasi dengan tegangan penyekap sebesar 600 kN/m2. Kemudian kedua benda benda uji tersebut diuji triaxial CD dengan tekanan penyekap yang berbeda dan jauh lebih kecil dari tegangan penyekap mula-mula di atas. Hasil kedua uji tadi adalah sebagai berikut:
Benda uji 1 : 3 =100 kN/m2
(d)f =410.6 kN/m2
Benda uji 2 : 3 =50 kN/m2
(d)f =384.37 kN/m2
Tentukan parameter-parameter dari kekuatan geser sampel tanah.
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KEKUATAN GESER TANAH Penyelesaian:
Untuk benda uji 2, tegangan-tegangan utamanya adalah:3’ = 3 = 50 kN/m2
1’ = 1 = 3 + ((d)f = 50 + 384.37= 434.37 kN/m2
Untuk benda uji 1, tegangan-tegangan utama pada saat runtuh adalah:3’ = 3 = 100 kN/m2
1’ = 1 = 3 + ((d)f = 100 + 410.6 = 510.6 kN/m2
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KEKUATAN GESER TANAH
………………………………..(a)
245tan2
245tan1006.510 112 ff oo c
Benda uji 2:
245tan2
245tan5037.434 112 ff oo c ………………………………..(b)
Kedua benda uji ini adalah terkonsolidasi lebih (OC). Jadi, dengan menggunakan hubungan pada Persamaan (9-7):
245tan2
245tan'' 112
31ff oo c
Benda uji 1:
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KEKUATAN GESER TANAH
Dengan memasukkan f =12 ke Persamaan (a), didapatkan :
212
45tan22
1245tan1006.510 2 oo c
510.6 = 152.5 + 2.47c
c = 145 kN/m2
Bila Persamaan (a) dikurangi Persamaan (b) didapat:
245tan5023.76 12 fo
oo 51223.76tan
245 11
f
atau f = 12o
50
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KEKUATAN GESER TANAH Hasil Uji Triaxial CU
Garis keruntuhan untuk tegangan total & efektif dari uji CU pada pasir dan lempung NC
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KEKUATAN GESER TANAH Hasil Uji Triaxial CU
Garis keruntuhan untuk tegangan total dari uji CU pada lempung OC
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KEKUATAN GESER TANAH Contoh 9-5:
Sebuah benda uji dari tanah pasir jenuh air diberi tekanan penyekap (confining pressure) sebesar 60 lb/in2. Kemudian tegangan aksial dinaikkan tanpa memperbolehkan terjadinya drainase (dari dan ke dalam benda uji). Benda uji tersebut mencapai keruntuhan pada saat tegangan aksial mencapai 50 lb/in2. Tegangan air pori pada saat runtuh adalah 41.35 lb/in2. Tentukan: a) Sudut geser kondisi CUb) Sudut geser kondisi CD
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KEKUATAN GESER TANAH Penyelesaian:
bagian a)
Pada saat runtuh, 3 = 60 lb/in2
1’ = 1 = 3 + (d)f = 60 + 50 = 110 lb/in2
(d) f = (d)failure = (d)pada saat runtuh
Dari gambar:
sin f(cu) = ''
''
31
31
OAAB
294.0
17050
6011060110
=atau
f(cu) =17.1o
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KEKUATAN GESER TANAH
Penyelesaian:
bagian b)3’ = 3 - (ud)f = 60 – 41.35 = 18.65 lb/in2
1’ = 1 - (ud)f = 110 – 41.35 = 68.65 lb/in2
sin f(CD) = ''
''
31
31
OAAB
5727.0
3.8750
65.1865.6865.1865.68
=
f(CD) =34.94o
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KEKUATAN GESER TANAH Hasil Uji Triaxial UU
Lingkaran Mohr untuk tegangan total dan garis keruntuhan dari uji UU
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KEKUATAN GESER TANAH Hasil Uji Triaxial UU
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Contoh Kasus Penggunaan Paramater CD:
KEKUATAN GESER TANAH
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KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CD:
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KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CU:
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KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CU:
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KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CU:
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KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater UU:
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KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater UU:
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KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater UU:
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COMPARISON OF THE TRIAXIAL AIND THE DIRECT SHEAR TEST
The advantages of the triaxial test over the direct shear test are: Progressive effects are less in the triaxial. The measurement of specimen volume changes
are more accurate in the triaxial. The complete state of stress is assumed to be
known at all stages during the triaxial test, Whereas only the stresses at failure are known in
the direct shear test. The triaxial machine is more adaptable to special
requirements.
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The advantages of the direct shear test are: Direct shear machine is simpler and
faster to operate. A thinner soil sample is used in the direct
shear test, thus facilitating drainage of the pore-water from a saturated specimen.
COMPARISON OF THE TRIAXIAL AIND THE DIRECT SHEAR TEST
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KEKUATAN GESER TANAH Uji Kuat Tekan Bebas
uu
f cq
22
1
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KEKUATAN GESER TANAH Uji Vane Shear
T
h
d
T T = Me + Ms + Me
T : momen torsi Me : momen tahanan pada muka atas
dan bawah silinder runtuh Ms : momen tahanan pada dinding silinder
runtuh
)(c dh)( M2d
us 8
due
3 c M
Dimana: d : diameter baling-balingh : tinggi baling-baling
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KEKUATAN GESER TANAH
)a = ½ tahanan geser termobilisasi dianggap berbentuk segi tiga)b = 2/3 tahanan geser termobilisasi dianggap seragam)c = 3/5 tahanan geser termobilisasi dianggap berbentuk parabola
cu
d/2d/2 d/2d/2 d/2d/2
T = Me + Ms + Me
4d
2hdc.
32u
4d
2hd
Tc32u
Uji Vane Shear
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KEKUATAN GESER TANAH Uji Vane Shear
VANE SHEAR LABORATORIUM
VANE SHEAR LAPANGAN
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KEKUATAN GESER TANAH
FAKTOR-FAKTOR YANG MEMPENGARUHI BESARNYA KEKUATAN GESER TANAH:
1. Keadaan tanah: ukuran butiran, angka pori, bentuk2. Jenis tanah: kerikil, pasir, lanau, lempung, berpasir, berlempung3. Kadar air: terutama pada lempung4. Jenis dan tingkat beban: pembebanan yang terlalu cepat menghasilkan
tekanan air pori yang berlebih5. Anisotropis: kuat geser arah tegak lurus berbeda dengan arah sejajar
bidang geser
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KEKUATAN GESER TANAH
FAKTOR-FAKTOR YANG MEMPENGARUHI HASIL UJI KUAT GESER DI LABORATORIUM:
1. Metoda pengujian2. Derajat ketergangguan contoh tanah3. Kadar air contoh tanah saat diuji4. Tingkat regangan
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KEKUATAN GESER TANAH
METODA EMPIRIS PENENTUAN KUAT GESER:(korelasi cukup memadai untuk rentang harga-harga LL = 20 45 dan PI = 15 30)
Index Plastisitas, PI [%]
Sudu
t Ges
er D
alam
.f [.
.0 ]
0
30
20
20
10
40
40 60 80 1000
Lempung
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KEKUATAN GESER TANAH
0 20 40 60 80 100
30
20
10
40
0
Sudu
t Ges
er D
alam
.f [.
.0 ]
Persentase Lempung [% < 0.002 mm]
Batas Nilai
METODA EMPIRIS PENENTUAN KUAT GESER:
Pasir