daya dukung tanah

Bearing Capacity
(Daya Dukung Tanah)
Dr. Ir.H. Erizal, MAgr
Definisi
Daya dukung yang diizinkan (allowable bearing cap.)
• tekanan maksimum yang dapat diaplikasikan ke tanah
dimana 2 kondisi diatas dipenuhi.
Daya dukung batas (ultimate bearing cap.)
• tekanan minimum yang menyebabkan keruntuhan geser
(shear failure) pada tanah pendukung secara cepat ke
bawah.
Footing Performance
Vertical Load
Vertical movement
Elastic
maximum tolerable
settlement
safe load maximum service ultimate
load
capacity
Plastic
Serviceability
Ultimate Limit State
Maximum allowable load =
min [safe load, max service load ]
Plunging
Failure
Limit States
Serviceability
Ultimate
Serviceability Limit State
Maximum load at which structure
still performs satisfactorily :
• Settlement
•Horizontal movement
• Rotation
•Sliding
Force (kN)
Applied Load
Bearing Pressure Definitions
Allowable Bearing Pressure qa=< qFs (settlement)
/A
F
Plan Area, A
Ultimate Bearing Capacity qult = Ffail / A
Foundation Failure
Rotational Failure
Soil Heave
Force
Resistance
Generalized Shear Failure
q
Soil Failure
Lines
Settlement
passive
rigid
radial
shear
log spiral
Local Shear Failure
q
minor surface
heave only
Settlement
Medium dense
or firm soils
Punching Shear Failure
q
No surface
heave
Settlement
Loose or
Soft Soils
Methods for calculating bearing
capacity
•
•
•
•
Full scale load tests
Load tests on model footings
Limit equilibrium analysis
Detailed stress analysis such as the FEM
method
Limit equilibrium analysis
solutions for weightless soils:
• Solutions with φ = 0 :
– Prandtl smooth punch : qult = 5.14c
– Prandtl rough punch : qult = 5.7c
• Solutions with φ ≠ 0 :
– Rough punch
passive
active
log spiral
Bearing Capacity for real soils
Exact,
Exact, theoretical
theoretical analytical
analytical solutions
solutions have
have only
only been
been
computed
computed for
for special
special cases
cases -- e.g.
e.g. soils
soils with
with no
no weight,
weight,
no
no frictional
frictional strength,
strength, φφ or
or no
no cohesion,
cohesion, c.
c.
Approximate
Approximate solutions
solutions have
have been
been derived
derived by
by
combining
combining solutions
solutions for
for these
these special
special cases.
cases. The
The
first
first solution
solution was
was by
by Terzaghi
Terzaghi (1943)
(1943) -- father
father of
of soil
soil
mechanics.
mechanics. Others
Others later
later modified
modified this
this solution.
solution.
The
The failure
failure mechanism
mechanism corresponds
corresponds to
to general
general failure.
failure.
Corrections
Corrections are
are applied
applied to
to check
check for
for the
the possibility
possibility of
of
local
local or
or punching
punching shear
shear failure.
failure.
Jenis pondasi berdasarkan kedalamannya
1. Pondasi dangkal (shallow foundation)
bila kedalaman pondasi, Df , lebih kecil dibanding lebar
pondasi, B
2. Pondasi dalam (deep foundation)
bila kedalaman pondasi, Df , lebih besar/dalam dibanding
lebar pondasi, B
Terzaghi’s Bearing Capacity Eqn.
For strip footings:
qult = c΄.Nc + σ΄ZD .Nq + 0.5γ΄BNγ
φ΄
c΄
Terzaghi’s Bearing Capacity Eqn.
For strip footings:
qult = c΄.Nc + q.Nq + 0.5γ΄BNγ
φ
q = γγ΄.D
.Df
Df
c
B
soil density, γ΄ (kN/m3)
Terzaghi’s Bearing Capacity Eqn.
For strip footings:
qult = c΄.Nc + q.Nq + 0.5γ΄BNγ
• Bearing Capacity Factors for soil
cohesion, surcharge and weight
• functions of friction angle, φ
• determine by equation or from graph
Nc
Nγ
Nq
Ø –– in
in Degrees
Degrees
Ø
40
30
20
10
0
70
60
50
40
Nc and Nq
30
100
80
5.7 1.0
20
10
20
Nγ
40
60
General Bearing Capacity Eqn.
(1973, 1975)
Based on theoretical and experimental work:
qult = c΄.NcFcsFcdFci + q.NqFqsFqdFqi + 0.5γBNγFγsFγdFγi
φ΄
c΄
General Bearing Capacity Eqn.
qult = c΄.NcFcsFcdFci + q.NqFqsFqdFqi + 0.5γBNγFγsFγdFγi
φ
q
γ.D
σ΄=
ZD = fγ΄.D
Df
c
B
soil density, γ΄ (kN/m3)
General Bearing Capacity Eqn.
qult = c΄NcFcsFcdFci + qNqFqsFqdFqi + 0.5γBNγFγsFγdFγi
• Bearing Capacity Factors for soil
cohesion, surcharge and weight
• functions of friction angle, φ
• determine by equation or from graph
or Table 3.3
General Bearing Capacity Eqn.
qult = c΄NcFcsFcdFci + qNqFqsFqdFqi + 0.5γBNγFγsFγdFγi
• Correction factors for footing shape (s),
footing depth (d) load inclination (i );
could have additional base
inclination (b), and ground inclination (g)
• determine from appropriate equations
General Bearing Capacity Factors
(Table 3.3)
50
Nγ Hansen
45
Friction angle (degree)
40
35
30
25
20
Nc
Nγ Meyerhof
15
10
Nq
5
0
1
10
100
Nc, Nq and Nγ
1000
Wall on
Strip Footing
Shape Factors
Bird’s Eye View
Column on
Square Footing
For non-strip footings :
Fcs , Fcq , Fγs ≥ 1
Failure lines
Failure lines
Wall on
Strip Footing
Depth Factors
For “buried” footings :
Fcd , Fqd , Fγd ≥ 1
q = γγ.D
.Dff
increasedstrength
failure generally
line length
increases with depth
VV==1000
906 kN
kN
Inclination Factors
H = 423 kN
For inclined loads :
Fci , Fqi , Fγi ≤ 1
Inclined load = 1000 kN
Load inclination, θ = 25o
Failure surface shallower and shorter
Terzaghi or General
• General is more accurate
• Applies to a broader range of loading and
geometry conditions
• General is more complicated
Contoh 1
• Sebuah pondasi bujur sangkar dengan sisi 2.25 m diletakkan pada
kedalaman 1.5 m pada pasir< di mana parameter kuat gesernya c’=0
dan ø= 38o. Tentukan daya dukung ultimit (a) bila muka air tanah
berada di bawah elevasi pondasi, (b) jika muka air tanah berada pada
permukaan tanah. Berat isi pasir di atas muka air tanah adalah 18
kN/m3, berat isi jenuhnya 20 kN/m3.
• Pondasi bujur sangkarÆ qf = 0.4γBNγ + γDNq
• ø= 38o Æ Nγ = 67, Nq = 49
• qf = (0.4 x 18 x 2.25 x 67) + (18 x 1.5 x 49)
= 1085 + 1323 = 2408 kN/m2
• Daya dukung di bawah muka air:
• qf = 0.4γ’BNγ + γ’DNq Æ γ’ = γsat – γw = 20 – 9.8 = 10.2 kN/m3
• qf = (0.4 x 10.2 x 2.25 x 67) + (10.2 x 1.5 x 49)
= 615 + 750 = 1365 kN/m2
Contoh 2
• Sebuah pondasi jalur didesain memikul beban 800 kN/m pada
kedalaman 0.7 m pada pasir berkerikil. Parameter kekuatan geser yang
tersedia adalah c’=0 danø’=40o. Tentukan lebar pondasi bila faktor
keamanan = 3 dan diasumsikan mungkin muka air tanah mencapai
pondasi. Berat isi pasir adalah 17 kN/m3, berat isi jenuhnya 20 kN/m3.
• ø’=40o ÆNγ=95 dan Nq=64
• qf = ½γ’BNγ + γBNq
= (½ x 10.2 x B x 95) + (17 x 0.7 x 64)
= 485B + 762
• qnf =qf – γD ;
qn = q - γD ;
F = qnf / qn
= 485B + 762 – (17 x 0.7)
= (800/B) – (17 x 0.7)
= 485B + 750
= (800/B) – 12
1
800
(485
B
+
750)
=
− 12 Æ B = 1.55 m
•
3
B
Ultimate Bearing Capacity of Shallow Footings with
Concentric Loads
Ultimate Bearing Capacity with Ground Water Effect
Example: Determine the Allowable Bearing
Capacity for A Rough Base Square Footing
Using A Safety Factor Of 3.
d=D=5
γ T = 125 pcf
′
B=6 ′
γ sub = 63 pcf
φ = 20 °
c = 500 psf
Solution: Assuming A General Shear
Condition, Enter the Bearing Capacity
Chart for φ= 20° and Read Nc = 14, Nq = 6,
Nγ = 3. Also note that formula for bearing
capacity must account for the square
footing and the water table within the
failure zone.
B
qult = (1 + 0 .3 )CNc + [ γ ′sub D + ( γ T − γ sub )d ]Nq + 0.4 γ ′sub BN γ
L
= (1.3)(500)14 + [63(5) + (125 − 63)5 ]6 + 0.4(63)(6)(3)
= 9100
+ 3750
+ 450
qult = 13,300psf
q all
q ult
=
3
13 , 300
=
3
≅ 4 , 430
psf
What is the Effect on Bearing
Capacity of Excavation of Soil
Cover Over a Spread Footing?
Student Mini-Exercise on Bearing Capacity
q ult
= cN c + P o N q + 1/2
Properties and Dimensions
(Assume Continuous Rough Footing)
γ = Unit Weight
D = Footing Embedment
B = Footing Width
A.
B.
C.
D.
Initial Situation γT = 120 pcf, D = 0, B = 5’,
deep water table
Effect of embedment D = 5’, γT = 120 pcf, B =
5’, deep water table
Effect of width, B = 10’, γT = 120 pcf, D = 0’,
deep water table
Effect of water table at surface, γsub = 57.6
pcf, D = 0’,
B = 5’
γ BN
γ
Cohesive Soil
Cohesionless Soil
φ = 0°
c = 1000psf
φ = 30°
c=0
qult (psf)
qult (psf)
5530
5400
Student Mini-Exercise on Bearing Capacity
q ult
=
cN
c
+ P o N q + 1/2
Properties and Dimensions
(Assume Continuous Rough Footing)
B.
C.
D.
γ
Cohesive Soil
Cohesionless Soil
φ = 0°
c = 1000psf
φ = 30°
c=0
qult (psf)
qult (psf)
Initial Situation γT = 120 pcf, D = 0, B = 5’,
deep water table
5530
5400
Effect of embedment D = 5’, γT = 120 pcf, B =
5’, deep water table
6130
17400
Effect of width, B = 10’, γT = 120 pcf, D = 0’,
deep water table
5530
10800
5530
2592
γ = Unit Weight
D = Footing Embedment
B = Footing Width
A.
γ BN
Effect of water table at surface, γsub = 57.6
pcf, D = 0’,
B = 5’
STUDENT EXERCISE NO.5
Footing Bearing Capacity
Objective:
Find the Allowable Bearing Capacity Using a Safety Factor = 3, for
the Condition Shown Below.
Rough Base Footing 10′ × 50′
Final Grade
4′
30′
10′
Sand
γ = 115 pcf
φ = 35°
C=0
SOLUTION TO EXERCISE No. 5
Footing
Length
Width
=
50
10
=5>9
Water Level 30 − 4
=
= 2.6
Width
10
∴Use Rectangular Formula
∴
= 2.6 > 1.5 Footing Widths
Footing Base
∴No Water Effect
qult = γ DN q + 0.4γ BNγ
Qall =
= (115)(4)(37) + (0.4)(115)(10)(42)
= 17,020 + 19,320
= 36,340 PSF
36,340
= 12,113 psf
3
below
How is bearing capacity theory
related to the “rule of thumb”
equation for stability;
SAFETY FACTOR
H
Soft clay layer
Compact Sand
6 C
γ H
=
γ = Unit
Weight
cohesion = C
Spread Footing Design
Bearing Capacity
• Explain how footing embedment, width, and
water table affect footing bearing capacity
Activities: Bearing capacity
analysis