Daya Dukung (Bearing Capacity)

(1)

Daya Dukung

(Bearing Capacity)

1 batuan (rock) Tanah kuat

(2)

Pondasi Dangkal

~ untuk melimpahkan beban ke lapisan di bawahnya

~ utamanya untuk tanah kuat atau beban ringan

SIVA

2

batuan (rock)

Tanah kuat

(3)

Footing Performance

Vertical Load Vertical Load V e rt ic a l m o v e m e n t V e rt ic a l m o v e m e n t

Elastic

Plastic

maximum tolerable maximum tolerable settlement settlement maximum service maximum service load load ultimate ultimate capacity capacity safe load safe load SIVA V e rt ic a l m o v e m e n t V e rt ic a l m o v e m e n t

Plastic

Plunging

Failure

Serviceability Limit State Serviceability Limit State

settlement settlement

Ultimate Limit State Ultimate Limit State

Maximum allowable load = Maximum allowable load = min

(4)

Limit States

SIVA 4

Serviceability

(5)

Bearing Pressure Definitions

F

Plan Area, APlan Area, A

Bearing Pressure

Bearing Pressure q

q

_b_b

=

= F / A

F / A

Safe

q

_s_s

=

φφφφφφφφ

.q

_u_u

/

ψ

Allowable

q

_a_a

< q

_s_s (settlement)(settlement)

SIVA

F

Plan Area, APlan Area, A

Ultimate Bearing Capacity

(6)

Foundation Failure

Force

Rotational Failure

SIVA

Soil Heave

(7)

Pola Keruntuhan

General Failure

SIVA

7

Local Shear Failure

(8)

General Failure

SIVA

8

Local Shear Failure

(9)

FOUNDATION FAILURE

1.Generalized Shear Failure

FOUNDATION FAILURE

1.Generalized Shear Failure

Soil Failure Soil Failure q q SIVA Soil Failure Soil Failure Lines Lines rigid rigid radial radial shear shear passive passive log spiral log spiral Settlement Settlement

(10)

2. Local Shear Failure

minor surface minor surface q q SIVA Medium dense Medium dense or firm soils or firm soils minor surface minor surface heave only heave only Settlement Settlement

(11)

3. Punching Shear Failure

q q SIVA Loose or Loose or Soft Soils Soft Soils No surface No surface heave

(12)

Perhitungan Daya Dukung

Untuk menghitung daya dukung dapat dilakukan dengan analisisis berdasarkan :

Data Uji Laboratorium:

Teori Terzaghi Teori Meyerhof

SIVA

12 Teori Meyerhof

Teori Brinch Hansen Teori Vesic

Data Uji Lapangan :

Plate Bearing Test

Cone Penetration Test/CPT (Sondir Standard Penetration Test/SPT

(13)

Aplikasi Teori Daya Dukung

KEMIRINGAN _TERZAGHI _MEYERHOF _HANSEN _VESIC

BEBAN ₀ θ θ θ SIVA 13 MUKA TANAH 0

0

β β DASAR PONDASI 0

0

δ δ

(14)

Daya Dukung Terzaghi

Anggapan-anggapan:

1. Tanah homogen isotropik

2. Mode keruntuhan pondasi adalah adalah general shear failure

3. Pondasi adalah strip dengan permukaan bawah kasar

4. Bidang keruntuhan geser diatas permukaan tanah diabaikan

SIVA

14

permukaan tanah diabaikan 5. Permukaan tanah adalah

horizontal

6. Tidak terdapat gaya horizontal, momen dan eksentrisitas

7. Pondasi terletak pada kedalaman D<B

8. Daerah elastis mempunyai sudut batas yang lurus dengan bid.

(15)

Keseimbangan Gaya

SIVA

15 Keseimbangan gaya-gaya yang bekeja pada

baji tanah (soil wedge) adalah:

Q_u.(2b).1 = - W + 2.CsinΦ _{+ 2.P}

(16)

1 2

1

2

γ

=

+

f c q

q

cN

DN

B

N

Strip footing SIVA 16 1 2 1 2 γ γ γ = + + f c q q cN DN B N

(17)

Faktor Daya Dukung Tanah Menurut Terzaghi

dan Berbagai Nilai Nγγγγ yang Berbeda

SIVA

(18)

Terzaghi Bearing Equation

applies to strip footing

N

c

, N

q

and N

γ

are functions of

φ

, and are

usually given in graphical form

q

_{u nett}_{u nett}

= c.N

_c_c

+ p'

_o_o

((N

N

_q_q

-- 1) + 0.5

1) + 0.5B

B

γγγγγγγγ

'N

_{γγγγγγγγ}

SIVA

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

(19)

Terzaghi Bearing Equation

q

_{u nett}_{u nett}

= c.N

_c_c

+ p'

_o_o

((N

N

_q_q

-- 1) + 0.5

1) + 0.5B

B

γγγγγγγγ

'N

_{γγγγγγγγ} SIVA B

p'

_o_o

=

γγγγγγγγ

''

_o_o

D

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 or effective as applicable)

effective as applicable)

Overburden

Failure Zone (depth ≈≈≈≈ 2B)

Adopt weighted average values ! Adopt weighted average values !

(20)

Bearing Capacity Factors

SIVA

(21)

Faktor daya dukung Terzaghi

φ

φ φ π

a

N

e

a

q tg

)

45 (

cos

2

2 2 ) 2 4 3 (

+

=

− SIVA 21

φ

γ

N

tg

N

jika

N

ctg

N

q c q c

).

1 (

2

0 :

7 ,

5 ).

1 (

)

2

45 (

cos

2

+

=

−

=

+

(22)

Faktor daya dukung Terzaghi

φ

π

ctg

N

tg

e

N

q

c

tg

q

).

1 (

)

2

45 (

2 .

−

=

+

=

SIVA 22

φ

γ

N

tg

N

jika

N

ctg

N

q

c

q

c

).

1 (

2

0 :

7 ,

5 ).

1 (

+

=

−

=

(23)

Faktor Daya Dukung

SIVA

23

(24)

Rumus Umum Daya Dukung

Secara umum daya dukung dapat ditulis

sbb:

q

_u

=

ζ

_c

.c N

_c

+

ζ

_q

.

γ

D.N

_q

+

ζ

_γ

.0,5

γ

B.N

_γ SIVA 24

q

_u

=

ζ

_c

.c N

_c

+

ζ

_q

.

γ

D.N

_q

+

ζ

_γ

.0,5

γ

B.N

_γ dimana:

ζ

_c

,

ζ

_q

,

ζ

_γ

= faktor koreksi yang tergantung

pada bentuk,kedalaman,kemiringan: beban,

(25)

Faktor Daya Dukung

1000 1000 100 100 B e a ri n g C a p a c it y F a c to r B e a ri n g C a p a c it y F a c to r NcNc Nq Nq N N_q_q = 33= 33 NN

γγγγγγγγ

N N_{γγγγγγγγ} = 250= 250 SIVA 10 10 1 1 0.1 0.1 0 0 1010 2020 3030 4040 5050 B e a ri n g C a p a c it y F a c to r B e a ri n g C a p a c it y F a c to r

Friction Angle (deg) Friction Angle (deg)

14 14oo N N_c_c = 10= 10 35 35oo 4646oo

(26)

Persamaan Daya Dukung Meyerhof

+ 0.5

γγγγγγγγ

B

d

_q_q

ii

_q_q

+ 0.5

γγγγγγγγ

BN

_{γγγγγγγγ}

s

_{γγγγγγγγ}

d

_{γγγγγγγγ}

ii

_{γγγγγγγγ} SIVA

c

φφφφφφφφ

soil density,

γγγγγγγγ

,

, ((kN/m

kN/m

33

₎₎

B

D

_ff

q =

γγγγγγγγ

.D

_ff

•• Bearing Capacity Factors for soil

Bearing Capacity Factors for soil

cohesion, surcharge and weight

•• functions of friction angle,

functions of friction angle,

φφφφφφφφ

•• determine by equation or from graph

determine by equation or from graph

•• Correction factors for footing shape

Correction factors for footing shape ((s

s)),,

footing depth

footing depth ((d

d)

) and load inclination

and load inclination ((i

i ).

).

(27)

Faktor daya dukung Meyerhof

).

1 (

)

2

45 (

2 .

φ

π

ctg

N

tg

e

N

q

c

tg

q

−

=

+

=

SIVA 27

)

.

4 ,

1 (

).

1 (

0 :

14 ,

5 ).

1 (

φ

γ

N

tg

N

jika

N

ctg

N

q

c

q

c

−

=

−

=

(28)

Faktor daya dukung Hansen

φ

π

ctg

N

tg

e

N

q

c

tg

q

).

1 (

)

2

45 (

2 .

−

=

+

=

SIVA 28

φ

γ

N

tg

N

jika

N

ctg

N

q

c

q

c

).

1 (

5 ,

1

0 :

14 ,

5 ).

1 (

−

=

−

=

(29)

Faktor daya dukung Vesic

φ

π

ctg

N

tg

e

N

q

c

tg

q

).

1 (

)

2

45 (

2 .

−

=

+

=

SIVA 29

φ

γ

N

tg

N

jika

N

ctg

N

q

c

q

c

).

1 (

2

0 :

14 ,

5 ).

1 (

−

=

−

=

(30)

₂₂ BB ' = BB --22 ee 22

(34)

Daya Dukung Berdasar Data Uji Lapangan

(In Situ Test)

Plate Bearing Test

(Uji Pembebanan Pelat)

Standard Penetration Test (SPT)

SIVA

34

Standard Penetration Test (SPT)

Cone Penetration Test/CPT

(35)

Plate Load Tests

SIVA

(36)

Plate Bearing Test

(Uji Pembebanan Pelat)

Tanah dengan kekuatan konstan

B < 4 B

_p

Tanah Dengan Kekuatan Meningkat

p u u

q

=

_, SIVA 36

Tanah Dengan Kekuatan Meningkat

Secara Linear Thd Kedalaman

B < 4 B

_p

Ekstrapolasi Hasil Uji Penurunan

Terzaghi & Peck.

p p u u

B

q

=

_, i q q ρ 5 , 1 1 =

(37)

Standard Penetration Test (SPT)

PONDASI TELAPAK (FOOTING)

MEYERHOF (1956,1974)

Dimana :

q_a,1 = daya dukung ijin utk penurunan 1 inchi

d n a K F N q ft B 1 1 , 4 → = ≤ 2 3 2 1 , 4 _      + = → > B F B F N q ft B _a n SIVA 37

q_a,1 = daya dukung ijin utk penurunan 1 inchi

K_d = 1+0,33 D/B≤_1,33

N_n = SPT yang dikoreksi

F = faktor tergantung energi pukulan SPT

PONDASI PELAT (MAT/RAFT)

d n a K F N q 3 1 , = 1 , a a

q

=

ρ

(38)

Cone Penetration Test/CPT

(Sondir)

SCHMERTMANN (1978)

DAYA DUKUNG BATAS PADA TANAH NON

KOHESIF MENERUS : q_u = 28 – 0,0052(300-q_c)1,5 SIVA 38 u c BUJUR SANGKAR : q_u = 48 – 0,0090(300-q_c)1,5

DAYA DUKUNG BATAS PADA TANAH KOHESIF

MENERUS : q_u = 2 + 0,28 q_c

BUJUR SANGKAR : q_u = 5 + 0,34 q_c

(39)

Belajar

SIVA

39

(40)

Exams

My mama always said, “Exam is like a box

of chocolates; you never know what you

SIVA

40

of chocolates; you never know what you

are gonna get”

(41)