kekuatan geser tanah

100

Click here to load reader

Upload: widya-yunita

Post on 23-Aug-2014

640 views

Category:

Documents


30 download

TRANSCRIPT

Page 1: KEKUATAN GESER TANAH

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

Page 2: KEKUATAN GESER TANAH

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

Page 3: KEKUATAN GESER TANAH

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.

Page 4: KEKUATAN GESER TANAH

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.

Page 5: KEKUATAN GESER TANAH

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.

Page 6: KEKUATAN GESER TANAH

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.

Page 7: KEKUATAN GESER TANAH

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.

Page 8: KEKUATAN GESER TANAH

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

Page 9: KEKUATAN GESER TANAH

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

Page 10: KEKUATAN GESER TANAH

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.

Page 11: KEKUATAN GESER TANAH

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.

Page 12: KEKUATAN GESER TANAH

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

Page 13: KEKUATAN GESER TANAH

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.

Page 14: KEKUATAN GESER TANAH

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

Page 15: KEKUATAN GESER TANAH

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

Page 16: KEKUATAN GESER TANAH

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

Page 17: KEKUATAN GESER TANAH

KEKUATAN GESER TANAHState of Stress and Strain

Triaxial stresses and strains

Page 18: KEKUATAN GESER TANAH

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

Page 19: KEKUATAN GESER TANAH

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

Page 20: KEKUATAN GESER TANAH

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)

Page 21: KEKUATAN GESER TANAH

KEKUATAN GESER TANAHState of Stress and Strain

Plane strain

Mohr circle and the invariants s´ and t´

Page 22: KEKUATAN GESER TANAH

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.

Page 23: KEKUATAN GESER TANAH

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 = /

Page 24: KEKUATAN GESER TANAH

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.

Page 25: KEKUATAN GESER TANAH

STRENGTH AND FAILURE

Page 26: KEKUATAN GESER TANAH

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.

Page 27: KEKUATAN GESER TANAH

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

Page 28: KEKUATAN GESER TANAH

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

Page 29: KEKUATAN GESER TANAH

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

Page 30: KEKUATAN GESER TANAH

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

Page 31: KEKUATAN GESER TANAH

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.

Page 32: KEKUATAN GESER TANAH

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.

Page 33: KEKUATAN GESER TANAH

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

Page 34: KEKUATAN GESER TANAH

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

Page 35: KEKUATAN GESER TANAH

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

Page 36: KEKUATAN GESER TANAH

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

Page 37: KEKUATAN GESER TANAH

BASIC GEOTECHNICAL STRUCTURAL TYPES

Page 38: KEKUATAN GESER TANAH

BASIC GEOTECHNICAL STRUCTURAL TYPES

Foundations

Retaining walls

Slopes

Page 39: KEKUATAN GESER TANAH

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

Page 40: KEKUATAN GESER TANAH

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.

Page 41: KEKUATAN GESER TANAH

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.

Page 42: KEKUATAN GESER TANAH

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

Page 43: KEKUATAN GESER TANAH

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

Page 44: KEKUATAN GESER TANAH

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

Page 45: KEKUATAN GESER TANAH

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

Page 46: KEKUATAN GESER TANAH

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)

Page 47: KEKUATAN GESER TANAH

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.

Page 48: KEKUATAN GESER TANAH

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

Page 49: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Uji Geser Langsung

Page 50: KEKUATAN GESER TANAH

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

Page 51: KEKUATAN GESER TANAH

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]

Page 52: KEKUATAN GESER TANAH

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

Page 53: KEKUATAN GESER TANAH

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

Page 54: KEKUATAN GESER TANAH

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

Page 55: KEKUATAN GESER TANAH

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 ]

Page 56: KEKUATAN GESER TANAH

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)

Page 57: KEKUATAN GESER TANAH

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).

Page 58: KEKUATAN GESER TANAH

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.

Page 59: KEKUATAN GESER TANAH

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:

Page 60: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Uji Triaxial:

PENGUJIAN KUAT GESER DENGAN

TRIAXIAL

Page 61: KEKUATAN GESER TANAH
Page 62: KEKUATAN GESER TANAH

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:

Page 63: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Uji Triaxial:

TABUNG TRIAXIAL SELANG PENYALUR DAN PENGUKUR TEKANAN (BEBAN)

Page 64: KEKUATAN GESER TANAH

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

Page 65: KEKUATAN GESER TANAH

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

Page 66: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Hasil Uji Triaxial CD

Garis keruntuhan untuk tegangan efektif dari uji CD pada pasir dan lempung NC

Total = Effective

c’ ~ 0

Page 67: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Hasil Uji Triaxial CD

Garis keruntuhan untuk tegangan efektif dari uji CD pada lempung OC

Page 68: KEKUATAN GESER TANAH

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

Page 69: KEKUATAN GESER TANAH

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

Page 70: KEKUATAN GESER TANAH

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

Page 71: KEKUATAN GESER TANAH

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

Page 72: KEKUATAN GESER TANAH

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.

Page 73: KEKUATAN GESER TANAH

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

Page 74: KEKUATAN GESER TANAH

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:

Page 75: KEKUATAN GESER TANAH

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

Page 76: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Hasil Uji Triaxial CU

Garis keruntuhan untuk tegangan total & efektif dari uji CU pada pasir dan lempung NC

Page 77: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Hasil Uji Triaxial CU

Garis keruntuhan untuk tegangan total dari uji CU pada lempung OC

Page 78: KEKUATAN GESER TANAH

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

Page 79: KEKUATAN GESER TANAH

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

Page 80: KEKUATAN GESER TANAH

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

Page 81: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Hasil Uji Triaxial UU

Lingkaran Mohr untuk tegangan total dan garis keruntuhan dari uji UU

Page 82: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Hasil Uji Triaxial UU

Page 83: KEKUATAN GESER TANAH

Contoh Kasus Penggunaan Paramater CD:

KEKUATAN GESER TANAH

Page 84: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CD:

Page 85: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CU:

Page 86: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CU:

Page 87: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater CU:

Page 88: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater UU:

Page 89: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater UU:

Page 90: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Contoh Kasus Penggunaan Paramater UU:

Page 91: KEKUATAN GESER TANAH

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.

Page 92: KEKUATAN GESER TANAH

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

Page 93: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Uji Kuat Tekan Bebas

uu

f cq

22

1

Page 94: KEKUATAN GESER TANAH

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

Page 95: KEKUATAN GESER TANAH

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

Page 96: KEKUATAN GESER TANAH

KEKUATAN GESER TANAH Uji Vane Shear

VANE SHEAR LABORATORIUM

VANE SHEAR LAPANGAN

Page 97: KEKUATAN GESER TANAH

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

Page 98: KEKUATAN GESER TANAH

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

Page 99: KEKUATAN GESER TANAH

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

Page 100: KEKUATAN GESER TANAH

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