!" "#$ #!%&'(
!" "#$ #!%&'(
1 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
)&%)*!+* & )!$+*
5 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
9 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
$%+,($+ )!# #!(! -&!.($+
13 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
)!# #!(!
)!# #!(! /($%+$
/($%+$00 )-+!+$+
)-+!+$+
.(1(% *),2(/+ *) 1&$+$+ $),#/(3
1)!# #!(! $)") (
+%)!%#*(! &/)' ,&.#/#$ )/($%+$+%($ %(!('0
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#
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.
)!# #!(!
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σ
σ
σ
σ
σ
σ
σ
σ
Q
Q
E
ρ
4
σ
4
ε
5
15
E
H
H
εεεε
z
Kondisi umum tegangan
dan regangan
E
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
=
=
εεεεεεεε
z
z
.dz
.dz
0
0
∞
∞
∞
∞
∞
∞
∞
∞
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
( (,(%)
/($%+$+%($0 ),1#!"
( (,(%)
/($%+$+%($0 ),1#!"
+1+*(/ !+/(+
#
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6 7
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;
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+1+*(/ (!"*( &+$$&!
ν
.
◦◦
◦◦
17 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
+$% +2#$+
+$% +2#$+ )"(!"(!
)"(!"(! 00 <)2(!
<)2(! +%+*
+%+*
)& + <&#$$+!)$=
z
z
Q
Q
σ
σ
σ
σ
= Q I
ψ
ψ
ψ
ψ
rr
R
R
z
z
σ
σ
σ
σ
σ
σ
σ
σ
z
z
σ
σ
σ
σ
σ
σ
σ
σ
θ
θ
θ
θ
θ
θ
θ
θ
σ
σ
σ
σ
σ
σ
σ
σ
rr
σ
σ
σ
σ
z
= Q I
σ
σ
σ
σ
z
2
II
σ
σ
σ
σ
σ
σ
σ
σ
=
= 3
3
1
1
2
2
π
π
π
π
π
π
π
π
[1+(r/z)
[1+(r/z)
2
2
]]
5/2
5/2
II
σ
σ
σ
σ
σ
σ
σ
σ
=
= faktor
faktor pengaruh
pengaruh
tegangan
tegangan
ψ
ψ
ψ
ψ
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+$% +2#$+ )"(!"(!
)"(!"(! 00 <)2(!
<)2(! +!"*( (!
+!"*( (!
d
d
θ
θ
θ
θ
θ
θ
θ
θ
dr
dr
load, q
load, q
By integration of
By integration of
Boussinesq
Boussinesq
19
d
d
θ
θ
θ
θ
θ
θ
θ
θ
rr
z
z
σ
σ
σ
σ
σ
σ
σ
σ
z
z
a
a
Boussinesq
Boussinesq
solution over
solution over
complete area:
complete area:
σ
σ
σ
σ
σ
σ
σ
σ
z
z
= q [1
= q [1--
1
1 ] = q.I
] = q.I
σ
σ
σ
σ
σ
σ
σ
σ
[1+(a/z)
[1+(a/z)
2
2
]]
3/2
3/2
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
+$% +2#$+
+$% +2#$+ )"(!"(!
)"(!"(! 00 <)2(!
<)2(! ) $)"+
) $)"+
)!""#!(*(! 1 +!$+1 2)2(! %+%+*3
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)!%#*(
.(!
B
B
L
L
)!%#*(
.(!
)/)$(+*(! .)!"(! " (-+*
)?,( * (%(# 1) $(,((! 0
I
σ
σ
σ
σ
= 1 2mn(m
2
+n
2
+1)
1/2
. m
2
+n
2
+2
+ tan
-1
2mn(m
2
+n
2
+1)
1/2
z
z
σ
σ
σ
σ
σ
σ
σ
σ
z
z
σ
σ
σ
σ
σ
σ
σ
0
1
2
0
0.05
0.1
0.15
0.2
0.25
) #2('(!
) #2('(! )"(!"(!
)"(!"(! &%(/
&%(/
II
σ
σ
σ
σ
σ
σ
σ
σ
2
3
4
5
6
7
8
L/B = 1
L/B = 2
L/B = 10
21
z/B
z/B
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
)!"'+%#!"(!
)!"'+%#!"(! )!# #!(!
)!# #!(!
)!%#*(! )"(!"(! :) %+*(/ 0
#,/('*(! )"(!"(! %+(1 /(1+$(! 0
z
z
Q
Q
ψ
εεεε
=
1 [
σ
σ
σ
σ
-
ν
ν
ν
ν
(
σ
σ
σ
σ
+
σ
σ
σ
σ
)]
∞
∞
∞
∞
∞
∞
∞
∞
rr
R
R
z
z
σ
σ
σ
σ
σ
σ
σ
σ
z
z
σ
σ
σ
σ
σ
σ
σ
σ
θ
θ
θ
θ
θ
θ
θ
θ
σ
σ
σ
σ
σ
σ
σ
σ
rr
ψ
εεεε
z
=
1 [
σ
σ
σ
σ
z
-
ν
ν
ν
ν
(
σ
σ
σ
σ
r
+
σ
σ
σ
σ
θ
θ
θ
θ
)]
E
εεεε
z
= Q .
(1
+
ν
ν
ν
ν
).
cos
3
ψ.
ψ.
ψ.
ψ.
(3
cos
2
ψ
ψ
ψ
ψ
-2
ν
ν
ν
ν
)
2pz
2
E
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
=
=
εεεεεεεε
z
z
..dz
dz
0
0
∞
∞
∞
∞
∞
∞
∞
∞
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
= Q
=
Q
(1
(1
--
ν
ν
ν
ν
ν
ν
ν
ν
2
2
))
π
π
π
π
π
π
π
)!# #!(!
)!# #!(! &!.($+
&!.($+ +!"*( (!
+!"*( (!
d
d
θ
θ
θ
θ
θ
θ
θ
θ
dr
dr
Beban
Beban,
, q
q
Di
Di pusat
pusat ::
ρ
ρ
ρ
ρ
= 2
q
(1-
ν
ν
ν
ν
2
).
a
23
d
d
θ
θ
θ
θ
θ
θ
θ
θ
rr
z
z
σ
σ
σ
σ
σ
σ
σ
σ
z
z
a
a
Di
Di tepi
tepi ::
ρ
ρ
ρ
ρ
= 4
q
(1-
ν
ν
ν
ν
2
).
a
π
π
π
π
π
π
π
π
E
E
ρ
ρ
ρ
ρ
= 2
q
(1-
ν
ν
ν
ν
2
).
a
E
E
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
)!# #!(!
)!# #!(! .+
.+
9#!"
9#!" &!.($+
&!.($+ ) $)"+
) $)"+
B
B
L
L
Metode
Metode Schleicher’s
Schleicher’s
1
1 --
ν
ν
ν
ν
ν
ν
ν
ν
2
2
z
z
σ
σ
σ
σ
σ
σ
σ
σ
z
z
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
=
=
q.B
q.B
1
1 --
ν
ν
ν
ν
ν
ν
ν
ν
E
E
II
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
II
=
=
1
1
m ln + ln
m ln + ln
1
1
+ m
+ m
2
2
+ 1
+ 1
m
m
+ m
+ m
2
2
+ 1
+ 1
nz
z
σz= q.I σ x Area covered with uniform normal load, q mz y z
Note: m and n are interchangeable
m = oc
m = 3.0
m = 2.5
m = 2.0
m = 1.8
m = 1.6
m = 1.4 m = 1.2
m = 1.0
m = 0.9
m = 0.8
m = 0.7
m = 0.6
m = 0.5
m = 0.4
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
I
σ
σ
σ
σ
m = 0.3
m = 0.2
m = 0.1
m = 0.0
0
0.01
2 3 4 5
0.1
2
3
4
5
1.0
2 3 4 5
10
0.10
0.08
0.06
0.04
0.02
VERTICAL STRESS BELOW A CORNER OF A UNIFORMLY LOADED FLEXIBLE
RECTANGULAR AREA.
25 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
)!# #!(!
)!# #!(! .+
.+ )!"('
)!"(' &!.($+
&!.($+ ) $)"+
) $)"+
B
B
L
L
L/2
L/2
B
B
B/2
B/2
ρ
ρ
ρ
ρ
centre
= 4
q.B
2
1
1 --
ν
ν
ν
ν
ν
ν
ν
ν
2
2
E
E
II
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
Superposisi untuk titik
yang berbesa
)!# #!(!
)!# #!(! .+2(?('
.+2(?(' (!('
(!('
#(
#(
/(1+$(!
/(1+$(! 00 )%&.)
)%&.) %)+!2 )!!)
%)+!2 )!!)
q
q
X
X
ρ
ρ
ρ
ρ
corner
=
q.B
1
1 --
ν
ν
ν
ν
ν
ν
ν
ν
2
2
E
E
II
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
II
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
=
=
F
F
1
1
+
+
F
F
2
2
1
1--
ν
ν
ν
ν
ν
ν
ν
ν
1
1--2
2
ν
ν
ν
ν
ν
ν
ν
ν
27
H
H
B
B
E
E
Kaku
X
X
Y
Y
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
2
L/B = 1
L/B = 2 F1
Values of F ( ) and F ( )
1 2=
H
/B
(*%&
(*%&
)!"( #'
)!"( #'
)%&.)
)%&.)
%)+!2 )!!)
%)+!2 )!!)
4 6 8 10L/B = 5
L/B = 10
L/B = oo
L/B = 1
L/B = 2
L/B = 5
L/B = 10 L/B = oo
)!# #!(!
)!# #!(! .+2(?('
.+2(?(' (!('
(!(' <) /(1+$
<) /(1+$ 00
q
q
H
H
B
B
E
E
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
=
=
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
((
H
H
1
1
,,
E
E
1
1
) +
) +
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
((
H
H
1
1
+
+
H
H
2
2
,,
E
E
2
2
)
) --
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
((
H
H
1
1
,,
E
E
2
2
)
)
29
H
H
1
1
E
E
1
1
“
“
Rigid
Rigid
”
”
H
H
2
2
E
E
2
2
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
#1) 1&$+$+
#1) 1&$+$+ ,)!""#!(*(!
,)!""#!(*(!
)%&.)
)%&.)
%)+!2 )!!)
%)+!2 )!!)
L
L
B
B
)!"( #'
)!"( #'
).#!"
).#!" @(!"
@(!" <) .)*(%(!
<) .)*(%(!
31 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
&!.($+
&!.($+ /)*$+2)/
/)*$+2)/
(*#
(*#
F
F
F
F
Tegangan
Tegangan
Defleksi
Defleksi
Defleksi
(*%&
(*%&
& )*$+
& )*$+ ).(/(,(!
).(/(,(!
)1%'
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0.9
1
1.1
F
a
c
to
r
B
B
z
z
33
0.5
0.6
0.7
0.8
0
2.5
5
7.5
10
D
e
p
th
F
z/B
B
B
z
z
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
$%+,($+ )!# #!(! -&!.($+
&!$&/+.($+
+,)
#(%# -)!&,)!( 1) #2('(! :&/#,) >(!" .(1(% %) 9(.+
1(.( %(!(' 1($+ .(! /),1#!"
)2+' $) +!" +.)!%+* %) 9(.+ 1(.( /(1+$(! /),1#!"
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&-%)! 1&& /> )$%+,(%). +! /(2
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35 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
9+9+
).&,)%)
).&,)%)
(2& (%& +#,
(2& (%& +#,
) #2('(! %+!""+ 2)!.( #9+
∆
'
<)2(!
!"*( 1& + )
)"(!"(!
σ
Pengukuran/data :
Hubungan
Hubungan yang
yang
dicari
dicari
<)2(!
# :( 1) #2('(! %+!""+ .(! ?(*%#
# :( 1) #2('(! %+!""+ .(! ?(*%#
h
h
o
o
T
in
g
g
i
T
in
g
g
i
Interval
Interval Waktu
Waktu pengukuran
pengukuran t :15s
t :15s, 30s,
, 30s,
1m, 2m, 3m, 5m, 10m, 15m, 30m, 1h, 2h,
1m, 2m, 3m, 5m, 10m, 15m, 30m, 1h, 2h,
3h, 6h, 12h, 24h, 36h, 48h, 60h ….etc.
3h, 6h, 12h, 24h, 36h, 48h, 60h ….etc.
37
log
log tt
Elastis
Elastis
Konsolidasi
Konsolidasi
utama
utama
Konsolidasi
Konsolidasi sekunder
sekunder
Dibuat
Dibuat untuk
untuk tegangan:12.5
tegangan:12.5, 25, 50, 100, 200, 400, 800 and 1600
, 25, 50, 100, 200, 400, 800 and 1600 KPa
KPa
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
ff
e
e
1.00
1.00
e = 0.8
e = 0.8
Volume
Volume relatif
relatif
Berat
Berat jenis
jenis
1
1
2.65
2.65
1 + e
1 + e
1.917
1.917
e = 0.8
e = 0.8
h = 1.9 cm
h = 1.9 cm
diameter
diameter = 6.0 cm
= 6.0 cm
W = 103.0 g
W = 103.0 g
0
1
2
0
0.05
0.1
0.15
0.2
0.25
) #2('(!
) #2('(! )"(!"(!
)"(!"(! &%(/
&%(/
II
σ
σ
σ
σ
σ
σ
σ
σ
2
3
4
5
6
7
8
L/B = 1
L/B = 2
L/B = 10
39
z/B
z/B
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
) #2('(!
) #2('(! )*(!(!
)*(!(! & +
& + .(!
.(!
)"(!"(!
)"(!"(! -)*%+-
-)*%+-∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
=
=
∆
∆
∆
∆
∆
∆
∆
∆
u +
u +
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
′′′′′′′′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
ff
Pada
Pada t
t = 0 :
= 0 :
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
=
=
∆
∆
∆
∆
∆
∆
∆
∆
u
u
Pada
)"(!"(!
)"(!"(!
&!
&!66 +!+)
+!+)
q
q
net
net
41
z
z
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
)"(!"(!
)"(!"(!
&!
&!66 +!+)
+!+)
1
1.1
1.2
C
C
rr
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
=
=
Σ
Σ
Σ
Σ
Σ
Σ
Σ
Σ
1+
1+
C
C
r
r
e
e
H
H
log + log
log + log
o
o
C
C
c
c
H
H
1+
1+
e
e
c
c
p
p
′′′′′′′′
c
c
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
ii
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
ff
p
p
′′′′′′′′
c
c
0.4
0.5
0.6
0.7
0.8
0.9
10
100
1000
Clay
C
C
c
c
p
p
′′′′′′′′
c
c
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
ii
σ′
σ′
σ′
σ′
σ′
σ′
σ′
σ′
ff
e
e
σ
σ
σ
σ
σ
σ
σ
σ
v
v
&)-+$+)!
&)-+$+)! ),(,1(%(!
),(,1(%(! A&/#,)
A&/#,)
1
1.1
1.2
Clay
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
=
=
Σ
Σ
Σ
Σ
Σ
Σ
Σ
Σ
m
m
v
v
..
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
∆σ
′′′′′′′′
..
∆
∆
∆
∆
∆
∆
∆
∆
H
H
43
0.4
0.5
0.6
0.7
0.8
0.9
0
200
400
600
800
1000
(1+
(1+
e
e
o
o
).
).
m
m
v
v
e
e
σ
σ
σ
σ
σ
σ
σ
σ
v
v
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
(9#
(9# &!$&/+.($+
&!$&/+.($+
Flow
Flow
h = H
h = H
Flow
Flow
h = H
h = H
/ 2
/ 2
T = c
T = c
v
v
tt
ii
/
/
H
H
2
2
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&)-+$+)! &!$&/+.($+
&)-+$+)! *&!$&/+.($+3 8: , >
($+/ #9+ /(2& (%& +#, .+*)!(/
,),2) +*(! '($+/ >(!" /)2+' )!.('
#!.) )$%+,(%)
#!.) )$%+,(%)
<) "(!%#!" 1(.( ,)%&.) #!%#*
,)!)!%#*(! 8: >(!" 2) "(!%#!" 1(.(
1)!)!%#(! -(*%& ?(*%# : ,+$(/ #!%#*
,)!8(1(+ B C *&!$&/+.($+
45 Dr.Eng. Agus S. Muntohar Department of Civil Engineering
&!$&/+.($+ )*#!.)
α
)2("(+ -)!&,)!( (>(1(! 8 ))1
+.(* %) 9(.+ 1) #2('(! %)*(!(! 1& +
#/(+ %) 9(.+ 1(.( (*'+ *&!$&/+.($+ 1 +,)
#/(+ %) 9(.+ 1(.( (*'+ *&!$&/+.($+ 1 +,)
α
≈
c
c
α
α
α
α
α
α
α
α
=
=
∆
∆
∆
∆
∆
∆
∆
∆
e
e
log
log
((
tt
2
2
/ t
/ t
1
1
))
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
= log
= log
((
tt
2
2
/t
/t
1
1
))
c
c
α
α
α
α
α
α
α
α
H
H
(1+
(1+
e
e
p
p
))
)!# #!(!
)!# #!(! &%(/
&%(/
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
tot
tot
=
=
RF
RF
x
x
DF
DF
(
(
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
elas
elas
+
+
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
pr.con
pr.con
+
+
ρ
ρ
ρ
ρ
ρ
ρ
ρ
ρ
sec
sec
))
47
RF = roughness factor (0.8 ~ 1)
DF = depth factor
Dr.Eng. Agus S. Muntohar Department of Civil Engineering
&!%&'
&!%&' )!"'+%#!"(!
)!"'+%#!"(!
