Daya Dukung (Bearing Capacity)

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batuan (rock)

Tanah

kuat

Pondasi Dangkal

~ untuk melimpahkan beban ke lapisan di bawahnya

~ utamanya untuk tanah kuat atau beban ringan

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batuan (rock)

Tanah

kuat

Footing PerformanceFooting Performance

Vertical LoadVertical LoadV

ertic

al m

ovem

ent

Ver

tical

mov

emen

t

ElasticElastic

PlasticPlasticmaximum tolerablemaximum tolerable

settlementsettlement

maximum servicemaximum serviceloadload

ultimateultimatecapacitycapacity

safe loadsafe load

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Ver

tical

mov

emen

tV

ertic

al m

ovem

ent

PlasticPlastic

PlungingPlungingFailureFailure

Serviceability Limit StateServiceability Limit State

settlementsettlement

Ultimate Limit StateUltimate Limit State

Maximum allowable load =Maximum allowable load =min min [[safe load, max service load safe load, max service load ]]

Limit States

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ServiceabilityServiceabilityServiceabilityServiceability UltimateUltimateUltimateUltimate

Bearing Pressure DefinitionsBearing Pressure Definitions

FFFF Plan Area, APlan Area, A

Bearing PressureBearing Pressure qqbb == F / AF / ASafeSafe qqss = = φφφφφφφφ.q.quu / / ψψψψψψψψAllowableAllowable qqaa < q< qss (settlement)(settlement)

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FFFF Plan Area, APlan Area, A

Ultimate Bearing CapacityUltimate Bearing Capacity qquu == FFfailfail / A/ A

Foundation FailureFoundation Failure

ForceForceRotational FailureRotational Failure

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Soil HeaveSoil Heave ResistanceResistance

Pola Keruntuhan

General Failure

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Local Shear Failure

Punching Shear Failure

General Failure

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Local Shear Failure

Punching Shear Failure

FOUNDATION FAILURE1.Generalized Shear FailureFOUNDATION FAILURE1.Generalized Shear Failure

Soil FailureSoil Failure

qq

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Soil FailureSoil FailureLinesLines

rigidrigidradialradialshearshear

passivepassive

log spirallog spiral

SettlementSettlement

2. Local Shear Failure2. Local Shear Failure

minor surfaceminor surface

qq

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Medium denseMedium denseor firm soilsor firm soils

minor surfaceminor surfaceheave onlyheave only

SettlementSettlement

3. Punching Shear Failure3. Punching Shear Failure

qq

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Loose orLoose orSoft SoilsSoft Soils

No surfaceNo surfaceheaveheave SettlementSettlement

Perhitungan Daya Dukung

Untuk menghitung daya dukung dapat dilakukan dengan analisisis berdasarkan :

� Data Uji Laboratorium:Teori TerzaghiTeori Meyerhof

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Teori MeyerhofTeori Brinch HansenTeori Vesic

� Data Uji Lapangan :Plate Bearing TestCone Penetration Test/CPT (SondirStandard Penetration Test/SPT

Aplikasi Teori Daya Dukung

KEMIRINGAN TERZAGHI MEYERHOF HANSEN VESIC

BEBAN 0 θ θ θ

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MUKA TANAH

0 0 β β

DASAR PONDASI

0 0 δ δ

Daya Dukung Terzaghi

Anggapan-anggapan:

1. Tanah homogen isotropik2. Mode keruntuhan pondasi adalah

adalah general shear failure3. Pondasi adalah strip dengan

permukaan bawah kasar4. Bidang keruntuhan geser diatas

permukaan tanah diabaikan

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permukaan tanah diabaikan5. Permukaan tanah adalah

horizontal6. Tidak terdapat gaya horizontal,

momen dan eksentrisitas7. Pondasi terletak pada kedalaman

D<B8. Daerah elastis mempunyai sudut

batas yang lurus dengan bid. horizontal

Keseimbangan Gaya

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Keseimbangan gaya-gaya yang bekeja pada baji tanah (soil wedge) adalah:

Qu.(2b).1 = - W + 2.CsinΦ + 2.Pp

1 2

1

2 γγ γ= + +f c qq cN DN B N

Strip footing

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1 2

1

2 γγ γ= + +f c qq cN DN B N

Faktor Daya Dukung Tanah Menurut Terzaghidan Berbagai Nilai Nγγγγ yang Berbeda

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Terzaghi Bearing EquationTerzaghi Bearing Equation

� applies to strip footing� Nc, Nq and Nγ are functions of φ, and are

usually given in graphical form

qqu nettu nett = c.N= c.Nc c + p'+ p'o o ((NNqq -- 1) + 0.51) + 0.5BBγγγγγγγγ'N'Nγγγγγγγγ

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usually given in graphical form � c, φ and γ' refer to soil properties in the failure

zone below the footing� p'o is the effective overburden pressure at the

founding level� shear strength contribution above footing level

is ignored : conservative for deeper footings

Terzaghi Bearing EquationTerzaghi Bearing Equation

qqu nettu nett = c.N= c.Nc c + p'+ p'o o ((NNqq -- 1) + 0.51) + 0.5BBγγγγγγγγ'N'Nγγγγγγγγ

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Bp'p'o o = = γγγγγγγγ''oo DD

Generalized soil strength : c, Generalized soil strength : c, φφφφφφφφ(drainage as applicable)(drainage as applicable)

Soil unit weight : Soil unit weight : γγγγγγγγ'' (total or(total oreffective as applicable)effective as applicable)

Overburden

Failure Zone (depth ≈≈≈≈ 2B)

Adopt weighted average values !Adopt weighted average values !

Bearing Capacity Factors

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Faktor daya dukung Terzaghi

φ

φφπ

aN

ea

q

tg

)45(cos2 2

2

)24

3(

+=

=−

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φφ

φ

φ

γ tgNN

jikaN

ctgNN

q

c

qc

).1(2

0:7,5

).1(

)2

45(cos2 2

+===

−=

+

Faktor daya dukung Terzaghi

φ

φφπ

ctgNN

tgeN

qc

tgq

).1(

)2

45(2.

−=

+=

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φφ

φ

γ tgNN

jikaN

ctgNN

q

c

qc

).1(2

0:7,5

).1(

+===

−=

Faktor Daya Dukung

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Bearing capacity factors

Rumus Umum Daya Dukung

Secara umum daya dukung dapat ditulis sbb:

qu = ζc.c Nc + ζq.γ D.Nq + ζγ.0,5 γ B.Nγ

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qu = ζc.c Nc + ζq.γ D.Nq + ζγ.0,5 γ B.Nγ

dimana:

ζc, ζq, ζγ = faktor koreksi yang tergantung pada bentuk,kedalaman,kemiringan: beban, muka tanah, dasar pondasi

Faktor Daya DukungFaktor Daya Dukung

10001000

100100

Bea

ring

Cap

acity

Fac

tor

Bea

ring

Cap

acity

Fac

tor

NcNcNqNq

NNqq = 33= 33 NNγγγγγγγγ

NNγγγγγγγγ = 250= 250

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1010

11

0.10.100 1010 2020 3030 4040 5050

Bea

ring

Cap

acity

Fac

tor

Bea

ring

Cap

acity

Fac

tor

Friction Angle (deg)Friction Angle (deg)

1414oo

NNcc = 10= 10

3535oo 4646oo

Persamaan Daya Dukung MeyerhofPersamaan Daya Dukung Meyerhof

qquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = = cc.N.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBBNNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + + qq.N.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.= c.NNccssccddcc ii cc + q.+ q.NNqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBBNNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγqquu = c.N= c.Nccssccddcc ii cc + q.N+ q.Nqqssqqddqq iiqq + 0.5+ 0.5γγγγγγγγBNBNγγγγγγγγssγγγγγγγγddγγγγγγγγii γγγγγγγγ

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cc

φφφφφφφφ

soil density, soil density, γγγγγγγγ, , ((kN/mkN/m33))BB

DDff q = q = γγγγγγγγ.D.Dff

•• Bearing Capacity Factors for soilBearing Capacity Factors for soil

cohesion, surcharge and weightcohesion, surcharge and weight

•• functions of friction angle, functions of friction angle, φφφφφφφφ•• determine by equation or from graphdetermine by equation or from graph

•• Correction factors for footing shape Correction factors for footing shape ((ss )),,

footing depth footing depth ((dd) ) and load inclination and load inclination ((i i ).).

•• determine from appropriate equationsdetermine from appropriate equations

Faktor daya dukung Meyerhof

).1(

)2

45(2.

φ

φφπ

ctgNN

tgeN

qc

tgq

−=

+=

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).4,1().1(

0:14,5

).1(

φφ

φ

γ tgNN

jikaN

ctgNN

q

c

qc

−===

−=

Faktor daya dukung Hansen

φ

φφπ

ctgNN

tgeN

qc

tgq

).1(

)2

45(2.

−=

+=

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φφφ

γ tgNN

jikaN

ctgNN

q

c

qc

).1(5,1

0:14,5

).1(

−===

−=

Faktor daya dukung Vesic

φ

φφπ

ctgNN

tgeN

qc

tgq

).1(

)2

45(2.

−=

+=

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φφφ

γ tgNN

jikaN

ctgNN

q

c

qc

).1(2

0:14,5

).1(

−===

−=

Pengaruh Muka air

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Pondasi dengan Beban MomenPondasi dengan Beban Momen

P

M

eP

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e

e = MPekivalen eksentrisitas beban

Cara Meyerhof menentukan eksentrisitas beban

Cara Meyerhof menentukan eksentrisitas beban

ee

L

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PP

ee

2e LL' = LL -- 22ee

B

Eksentrisitas 2 arahEksentrisitas 2 arah

ee11

LL

22ee22

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PP

ee11

22ee11 LL' = LL -- 22ee11

BB ee2 2

BB' =

BB--

22ee22

Daya Dukung Berdasar Data Uji Lapangan (In Situ Test)

� Plate Bearing Test (Uji Pembebanan Pelat)Standard Penetration Test (SPT)

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� Standard Penetration Test (SPT)� Cone Penetration Test/CPT

(Sondir)

Plate Load Tests

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Plate Bearing Test(Uji Pembebanan Pelat)

� Tanah dengan kekuatan konstanB < 4 Bp

� Tanah Dengan Kekuatan Meningkat puu qq ,=

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� Tanah Dengan Kekuatan Meningkat Secara Linear Thd Kedalaman

B < 4 Bp

� Ekstrapolasi Hasil Uji Penurunan Terzaghi & Peck.

ppuu B

Bqq ,=

i

qq ρ

5,11 =

Standard Penetration Test (SPT)

� PONDASI TELAPAK (FOOTING)MEYERHOF (1956,1974)

Dimana :qa,1 = daya dukung ijin utk penurunan 1 inchi

dn

a KF

NqftB

11,4 =→≤

2

3

21,4

+=→>B

FB

F

NqftB n

a

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qa,1 = daya dukung ijin utk penurunan 1 inchiKd = 1+0,33 D/B≤1,33Nn = SPT yang dikoreksiF = faktor tergantung energi pukulan SPT

� PONDASI PELAT (MAT/RAFT)

dn

a KF

Nq

31, =

1,aa qq ρ=

Cone Penetration Test/CPT(Sondir)

SCHMERTMANN (1978)� DAYA DUKUNG BATAS PADA TANAH NON

KOHESIF

MENERUS : qu = 28 – 0,0052(300-qc)1,5

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u cBUJUR SANGKAR : qu = 48 – 0,0090(300-qc)1,5

� DAYA DUKUNG BATAS PADA TANAH KOHESIF

MENERUS : qu = 2 + 0,28 qcBUJUR SANGKAR : qu = 5 + 0,34 qc

qu dan qc dalam tsf atau kg/cm2

Belajar

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