Name of Structure : Inverted T-shape Type Retaining Wall (H=15.

8m)
q (t/m2) b11 b12 b13
Location : Tambuo River
Dimension (unit length)
H = 15.75 m B = 12.00 m L = 1.00 m
a
MENU
b11 = 1.41 m b12 = 0.50 m b13 = 0.09 m
b21 = 8.00 m b22 = 2.00 m b23 = 2.00 m
H=h1

h1 = 15.75 m h31 = 2.00 m h32 = 1.50 m

h4 = 0.00 m hw1 = 6.03 m hw2 = 3.70 m
Basically passive earth pressure are not considered.
hw1
h32 Therefore h4 = 0 q = 1.00 t/m2 Kh = 0.16
hw2
h4 Backfill soil gc = 2.40 t/m3 gw = 1.00 t/m3
h31
g soil = 1.80 t/m3
g sat = 2.00 t/m3 a = 0.000 o
(for stability analysis)
b21 b22 b23
B f = 30.0 o a = 6.566 o
(for structural analysis)
c = 0.00 t/m2 b = 0.000 o

Section of Retaining wall Foundation soil

g s' = 1.00 t/m3 Safety factor (normal) (seismic)
fB = 30.0 o Overturning |e| < B/6=2.63 B/3=4.00
cB = 0.00 t/m2 Sliding fs > 2.00 1.25
Friction coefficient Reaction of foundation soil
m = 0.50 qmax > qa=qu/3 qae=qu/2
Uplift coefficient Allowable stress
Um = 1.00 Compressive s ca = 60 90 kg/cm2
Cover of bar Tensile s sa = 1400 2100 kg/cm2
Wall Shear ta = 5.5 8.25 kg/cm2
d back = 7 cm Young's modulus ratio
d front = 10 cm 24 16
Footing
d upper = 10 cm
d lower = 10 cm
 Stability2/28

Inverted T-shape Type Retaining Wall (H=15.8m)

1. Design Data
q (t/m2)
b11 b12 b13
1.1 Dimensions

B = 12.00 m H = 15.75 m
L = 1.00 m (unit length)

b11 = 1.41 m b21 = 8.00 m H=h1

b12 = 0.50 m b22 = 2.00 m
b13 = 0.09 m b23 = 2.00 m

h1 = 15.75 m h4 = 0.00 m hw1

h31 = 2.00 m hw1 = 6.03 m h32 hw2

h4
h32 = 1.50 m hw2 = 3.70 m h31

b2 b2 b2
1.2 Parameters
1 2 3
B
q = 1.00 t/m2 (for normal condition)
= 0.00 t/m2 (for seismic condition) Section of Retaining Wall
gc = 2.40 t/m3
gw = 1.00 t/m3
Backfill soil Foundation soil Safety factor
gsoil = 1.80 t/m3 gs ' = 1.00 t/m3 (=gsat-gw) Overturning
gsat = 2.00 t/m 3 cB = 0.00 t/m 2
normal |e|<B/6=2.00m
c = 0.00 t/m2 fB = 30.00 o
seismic |e|<B/3=4.00m
f = 30.00 o
m = 0.50 (Friction coefficient) Sliding
Um = 1.00 (Uplift coefficient) normal fs > 2.00
b = 0.000 o
seismic fs > 1.25
a = 0.000 o
(for stability analysis) Reaction of foundation soil
= 6.566 o
(for structural analysis) normal qmax<qa
d = 0.000 o
(for stability analysis in normal condition, d = b) qa=qu/3
= 20.00 o
(for structural analysis in normal condition, d = 2/3 f) seismic qmax<qae
= 22.54 o
(for stability analysis in seismic condition, see Section 2.3) qae=qu/2
= 15.00 o
(for structural analysis in seismic condition, d = 1/2 f)
F = 9.090 o
( = Arc tan(Kh) ) Kh = 0.16

2. Stability Calculation

2.1 Case 1 (Normal condition, with vertical live load)

1.41
q = 1.00 t/m2 0.50
0.09

qa1
9

Pa1

Pa2 10 7
15.75 12.25

qa2 11
8
1.50
Pa3 6
6.03 12 4 5
Pw1 Pa4
0.00 3.70
1 2 3 Pp1 2.00 Pw2
Pu1 O
qw1 qa4 qa3 qp1 qw2
qu2 Pu2
qu1
8.00 2.00 2.00

Acting Load in Case 1

 Stability3/28

(1) Vertical Load

No. Description W X WxX

1 2.00 x 8.00 x 2.40 38.400 8.000 307.20
2 3.50 x 2.00 x 2.40 16.800 3.000 50.40
3 2.00 x 2.00 x 2.40 9.600 1.000 9.60
4 0.50 x 1.50 x 8.00 x 2.40 14.400 6.667 96.00
5 0.50 x 1.50 x 2.00 x 2.40 3.600 0.667 2.40
6 0.50 x 12.25 x 1.41 x 2.40 20.727 3.530 73.17
7 12.25 x 0.50 x 2.40 14.700 2.340 34.40
8 0.50 x 12.25 x 0.09 x 2.40 1.323 2.060 2.73
9 0.50 x 12.25 x 1.41 x 1.80 15.545 3.530 54.87
10 8.00 x 9.73 x 1.80 140.040 8.000 1,120.32
11 8.00 x 2.53 x 2.00 40.400 8.000 323.20
12 0.50 x 8.00 x 1.50 x 2.00 12.000 9.333 112.00
q 1.00 x 9.41 9.410 7.295 68.65
T o t a l(1 to q) 336.945 2,254.94
Pu1 6.03 x 12.00 x 0.50 x -1.00 -36.150 8.000 -289.20
Pu2 3.70 x 12.00 x 0.50 x -1.00 -22.200 4.000 -88.80
Total ( 1 to Pu2) 278.595 1,876.94

(2) Horizontal Load

Coefficient of Active earth pressure

Cos2(f -a)
Ka =
Sin(f+d) x Sinf 2
Cos2a x Cos(a+d) x 1+
Cos(a+d) x Cosa
(for stability analysis)
a = 0.000 o
d = 0.000 o

Cos (f -a)
2
= 0.750 Sin(f+d) = 0.500
Cos2a = 1.000 Sinf = 0.500
Cos(a+d) = 1.000 Cosa = 1.000

Ka = 0.333 for stability analysis

(for structural analysis)

a = 6.566 o
d = 20.000 o

Cos (f -a)
2
= 0.842 Sin(f+d) = 0.766
Cos2a = 0.987 Sinf = 0.500
Cos(a+d) = 0.894 Cosa = 0.993

Ka' = 0.348 for structural analysis

Coefficient of Passive earth pressure

Cos2(f+a)
Kp =
Sin(f+d) x Sinf 2
Cos2a x Cos(a -d) x 1-
Cos(a -d) x Cosa
a = 0.000 o
d = 0.000 o

Cos (f+a)
2
= 0.750 Sin(f+d) = 0.500
Cos2a = 1.000 Sinf = 0.500
Cos(a -d) = 1.000 Cosa = 1.000

Kp = 3.000

qa1 = Ka x q = 0.333 ton/m

qa2 = Ka x (h1- hw1) x gsoil = 5.835 ton/m
qa3 = qa1 + qa2 = 6.168 ton/m
qa4 = Ka x hw1 x (gsat - gw) = 2.008 ton/m
qw 1 = hw1 x gw = 6.025 ton/m
qw 2 = hw2 x gw = 3.700 ton/m
qp1 = Kp x h4 x (gsat - gw) = 0.000 ton/m
Stability4/28
 Stability5/28

No. Description H Y HxY

Pa1 0.333 x 9.73 3.242 10.888 35.30
Pa2 5.835 x 9.73 x 0.50 28.373 9.267 262.92
Pa3 6.168 x 6.03 37.164 3.013 111.96
Pa4 2.008 x 6.03 x 0.50 6.050 2.008 12.15
Pw1 6.025 x 6.03 x 0.50 18.150 2.008 36.45
Pw2 -3.700 x 3.70 x 0.50 -6.845 1.233 -8.44
Pp1 0.000 x 0.00 x 0.50 0.000 0.000 0.00
Total 86.134 450.33

(3) Stability Calculation

a) Stability against overturning

a) -1 Without Uplift
B = 12.00 m
SWxX-SHxY 2,254.94 - 450.33
X = = = 5.356 m
SW 336.945

B 12.00
e = - X = - 5.356 = 0.644 m < B/6 = 2.000 m OK !
2 2
a) -2 With Uplift
B = 12.00 m
SWxX-SHxY 1,876.94 - 450.33
X = = = 5.121 m
SW 278.595

B 12.00
e = - X = - 5.121 = 0.879 m < B/6 = 2.000 m OK !
2 2

b) Stability against sliding

b)-1 Without Uplift
Sliding force : SH = 86.134 ton
Resistance : HR = m x S W = 0.50 x 336.945 = 168.473 ton
(friction coefficient : m = 0.5 )

HR 168.473
Fs = = = 1.956 < 2.00 Check !
SH 86.134
b)-2 With Uplift
Sliding force : SH = 86.134 ton
Resistance : HR = m x S W = 0.50 x 278.595 = 139.298 ton
(friction coefficient : m = 0.5 )
HR 139.298
Fs = = = 1.617 < 2.00 Check !
SH 86.134

c) Reaction of foundation soil

SW 6xe
q1,2 = x (1 + )
B B

336.945 6x 0.644
q1 = x (1 + ) = 37.120 t/m2 < qa = 40.000 t/m2 OK !
12.00 12.00

336.945 6x 0.644
q2 = x (1 - ) = 19.037 t/m2 < qa = 40.000 t/m2 OK !
12.00 12.00
 Stability6/28

19.037 t/m2 - t/m2

37.120 t/m2
- t/m
2

in case, e > 0 in case, e < 0

(applicable) (not applicable)

Reaction of Foundation Soil in Case 1

 Stability7/28

2.2 Case 2 (Normal condition, without vertical live load)

1.41
q = 1.00 t/m2 0.50
0.09

qa1
9

Pa1
Pa2 10 7
15.75 12.25

qa2 11
8
1.50
Pa3 6
6.03 12 4 5
Pw1 Pa4
0.00 3.70
1 2 3 Pp1 2.00 Pw2

qa4 qa3 Pu1 O qp1 qw2

qw1 Pu2
qu1 qu2
8.00 2.00 2.00
Acting Load in Case 2

(1) Vertical Load

No. Description W X WxX

1 2.00 x 8.00 x 2.40 38.400 8.000 307.20
2 3.50 x 2.00 x 2.40 16.800 3.000 50.40
3 2.00 x 2.00 x 2.40 9.600 1.000 9.60
4 0.50 x 1.50 x 8.00 x 2.40 14.400 6.667 96.00
5 0.50 x 1.50 x 2.00 x 2.40 3.600 0.667 2.40
6 0.50 x 12.25 x 1.41 x 2.40 20.727 3.530 73.17
7 12.25 x 0.50 x 2.40 14.700 2.340 34.40
8 0.50 x 12.25 x 0.09 x 2.40 1.323 2.060 2.73
9 0.50 x 12.25 x 1.41 x 1.80 15.545 3.530 54.87
10 8.00 x 9.73 x 1.80 140.040 8.000 1120.32
11 8.00 x 2.53 x 2.00 40.400 8.000 323.20
12 0.50 x 8.00 x 1.50 x 2.00 12.000 9.333 112.00
T o t a l (1 to 12) 327.535 2186.29
Pu1 6.03 x 12.00 x 0.50 x -1.00 -36.150 8.000 -289.20
Pu2 3.70 x 12.00 x 0.50 x -1.00 -22.200 4.000 -88.80
Total ( 1 to Pu2) 269.185 1808.29

(2) Horizontal Load

Coefficient of Active earth pressure

Ka = 0.333 (for stability analysis)

Ka ' = 0.348 (for structural analysis)

Coefficient of Passive earth pressure

Kp = 3.000

qa1 = Ka x q = 0.333 ton/m

qa2 = Ka x (h1- hw1) x gsoil = 5.835 ton/m
qa3 = qa1 + qa2 = 6.168 ton/m
qa4 = Ka x hw1 x (gsat - gw) = 2.008 ton/m
qw 1 = hw1 x gw = 6.025 ton/m
qw2 = hw2 x gw = 3.700 ton/m
qp1 = Kp x h4 x (gsat - gw) = 0.000 ton/m
 Stability8/28

No. Description H Y HxY

Pa1 0.333 x 9.73 3.242 10.888 35.30
Pa2 5.835 x 9.73 x 0.50 28.373 9.267 262.92
Pa3 6.168 x 6.03 37.164 3.013 111.96
Pa4 2.008 x 6.03 x 0.50 6.050 2.008 12.15
Pw1 6.025 x 6.03 x 0.50 18.150 2.008 36.45
Pw2 -3.700 x 3.70 x 0.50 -6.845 1.233 -8.44
Pp1 0.000 x 0.00 x 0.50 0.000 0.000 0.00
Total 86.134 450.33

(3) Stability Calculation

a) Stability against overturning

a)-1 Without Uplift
B = 12.00 m
SWxX-SHxY 2,186.29 - 450.33
X = = = 5.300 m
SW 327.535
B 12.00
e = - X = - 5.300 = 0.700 m < B/6 = 2.000 m OK !
2 2
a)-2 With Uplift
B = 12.00 m
SWxX-SHxY 1,808.29 - 450.33
X = = = 5.045 m
SW 269.185
B 12.00
e = - X = - 5.045 = 0.955 m < B/6 = 2.000 m OK !
2 2

b) Stability against sliding

b)-1 without Uplift Pressure
Sliding force : SH = 86.134 ton
Resistance : HR = m x S W = 0.50 x 327.535 = 163.768 ton
(friction coefficient : m = 0.5 )

HR 163.768
Fs = = = 1.90 < 2.00 Check !
SH 86.134
b)-2 with Uplift Pressure
Sliding force : SH = 86.134 ton
Resistance : HR = m x S W = 0.50 x 269.185 = 134.593 ton
(friction coefficient : m = 0.5 )

HR 134.593
Fs = = = 1.56 < 2.00 Check !
SH 86.134

c) Reaction of foundation soil

SW 6xe
q1,2 = x (1 + )
B B
327.535 6x 0.700
q1 = x (1 + ) = 36.848 t/m2 < qa = 40.000 t/m2 OK !
12.00 12.00
327.535 6x 0.700
q2 = x (1 - ) = 17.741 t/m2 < qa = 40.000 t/m2 OK !
12.00 12.00
 Stability9/28

17.741 t/m2 - t/m2

36.848 t/m2
- t/m
2

in case, e > 0 in case, e < 0

(applicable) (not applicable)

Reaction of Foundation Soil in Case 2

 Stability10/28

2.3 Case 3 (Seismic condition)

1.41
0.50
0.09

10 7
15.75 Pa1 12.25

qa1 11
8
1.50
6
6.03 Pa2
12 4 5
Pw1
Pa3 0.00 3.70
1 2 3 Pp1 2.00 Pw2

qw1 qa3 Pu1

qa2 O qp1 qw2
qu1 qu2 Pu2
8.00 2.00 2.00
Acting Load in Case 3

(1) Vertical Load = Same as Case 2

(2) Horizontal Load

f = 30.00 o a = 0.000 o (for stability analysis) F = 9.090 o

b = 0.00 o
a = 6.566 o (for structural analysis) (F = Arc tan(Kh) )
q = 0.00 t/m (for seismic condition)
2
Kh = 0.16

Coefficient of Active earth pressure

Cos2(f-F-a)
Kae =
2
Sin(f+d) x Sin(f-b-F)
CosF x Cos2a x Cos(a+d+F) x 1
Cos(a+d+F) x Cos(a-b)
+
(for stability analysis)
a = 0.000 o
d = 22.54 o

tan d = Sin f Sin ( F + D - b )

1 - Sin f Cos ( F + D - b )
sin D= Sin ( F + b )
Sin f

Sin (F+ b ) == 0.158 Sin f = 0.500

Sin D = 0.316 then D = 18.42
Sin(F+D-b) = 0.462 Cos(F+D-b)= 0.887
tan d = 0.415

Cos2(f-F-a)= 0.873 Sin(f+d) = 0.794

CosF = 0.987 Sin(f-b-F) = 0.357
Cos a2
= 1.000 Cos(a-b) = 1.000
Cos(a+d+F) = 0.851

Kae = 0.418 (for stability analysis)

 Stability11/28

(for structural analysis)

a = 6.566 o
d = 15.00 o

Cos (f-F-a)=
2
0.939 Sin(f+d) = 0.707
CosF = 0.987 Sin(f-b-F) = 0.357
Cos a
2
= 0.987 Cos(a-b) = 0.993
Cos(a+d+F)= 0.860

Kae = 0.470 (for structural analysis)

Coefficient of Passive earth pressure

Cos2(f-F+a)
Kpe =
2
Sin(f-d) x Sin(f+b-F)
CosF x Cos2a x Cos(a+d-F) x 1
Cos(a+d-F) x Cos(a-b)
-
a = 0.000 o
d = 22.54 o

Cos (f-F+a)=
2
0.873 Sin(f-d) = 0.130
CosF = 0.987 Sin(f+b-F) = 0.357
Cos2a = 1.000 Cos(a-b) = 1.000
Cos(a+d-F)= 0.973

Kpe = 1.488

qa1 = Kae x ( h1 - hw1) x gsoil = 7.317 ton/m

qa2 = qa2 = 7.317 ton/m
qa3 = Kae x hw1 x (gsat - gw) = 2.518 ton/m
qw 1 = hw1 x gw = 6.025 ton/m
qw 2 = hw2 x gw = 3.700 ton/m
qp1 = Kp x h4 x (gsat - gw) = 0.000 ton/m

No. Description H Y HxY

1 0.16 x 38.40 6.144 1.000 6.14
2 0.16 x 16.80 2.688 1.750 4.70
3 0.16 x 9.60 1.536 1.000 1.54
4 0.16 x 14.40 2.304 2.500 5.76
5 0.16 x 3.60 0.576 2.500 1.44
6 0.16 x 20.73 3.316 7.583 25.15
7 0.16 x 14.70 2.352 9.625 22.64
8 0.16 x 1.32 0.212 7.583 1.61
9 0.16 x 15.55 2.487 11.667 29.02
10 0.16 x 140.04 22.406 10.888 243.95
11 0.16 x 40.40 6.464 4.763 30.78
12 0.16 x 12.00 1.920 3.000 5.76
Pw1 0.50 x 6.03 x 6.03 18.150 2.008 36.45
Pw2 0.50 x -3.70 x 3.70 -6.845 1.233 -8.44
Pa1 0.50 x 7.32 x 9.73 35.579 9.267 329.70
pa2 7.32 x 6.03 44.085 3.013 132.81
Pa3 0.50 x 2.518 x 6.03 7.587 2.008 15.23
Pp1 0.000 x 3.70 x 0.50 0.000 0.000 0.00
Total 150.963 884.24
 Stability12/28

(3) Stability Calculation

a) Stability against overturning

a)-1 Without Uplift
B = 12.00 m
SWxX-SHxY 2,186.29 - 884.24
X = = = 3.975 m
SW 327.535
B 12.00
e = - X = - 3.975 = 2.025 m < B/3 = 4.000 m OK !
2 2
a)-2 With Uplift
B = 12.00 m
SWxX-SHxY 1,808.29 - 884.24
X = = = 3.433 m
SW 269.185
B 12.00
e = - X = - 3.433 = 2.567 m < B/3 = 4.000 m OK !
2 2

b) Stability against sliding

b)-1 Without Uplift
Sliding force : SH = 150.963 ton
Resistance : HR = m x S W = 0.50 x 327.535 = 163.768 ton
(friction coefficient : m = 0.5 )
HR 163.768
Fs = = = 1.08 < 1.25 Check !
SH 150.963
b)-2 With Uplift
Sliding force : SH = 150.963 ton
Resistance : HR = m x S W = 0.50 x 269.185 = 134.593 ton
(friction coefficient : m = 0.5 )
HR 134.593
Fs = = = 0.89 < 1.25 Check !
SH 150.963
c) Reaction of foundation soil

c-1) in case, |e| < B/6 (not applicable)

SW 6xe
q1,2 = x (1 + )
B B

q1 = x ) = - t/m2 qae = - t/m2

q2 = x ) = - t/m2 qae = - t/m2

c-2) in case, B/6 < |e| < B/3 (applicable)

2xSW 2x 327.535
q1' = = = 54.932 t/m2 < qae = 60.000 t/m2 OK !
3 x (B/2-|e|) 3x 3.975
3 x |e| - B/2 = 0.075 m

- t/m2

- t/m2 54.932 t/m2

 Stability13/28

in case, e > 0 and e < B/6 in case, e > 0 and B/6 < e < B/3
(not applicable) (applicable)

- t/m2

- t/m2 - t/m2
in case, e < 0 and |e| < B/6 in case, e < 0 and B/6 < |e| < B/3
(not applicable) (not applicable)

Reaction of Foundation Soil in Case 3

 Stability14/28

2.4 Bearing Capacity of soil

(1) Design Data

fB = 30.00 o cB = 0.00 t/m2 gs' = 1.00 t/m3 (=gsat-gw)

B = 12.00 m z = 0.00 m L = 1.00 m (unit length)

f
(2) Ultimate Bearing Capacity of soil, (qu) ###
###
Calculation of ultimate bearing capacity will be obtained by applying the following ###
Terzaghi's formula : ###
###
qu = (a x c x Nc) + (gsoil' x z x Nq) + (b x gsoil x B x Ng) ###
###
Shape factor (Table 2.5 of KP-06) ###
a = 1.00 b = 0.50
Shape of footing : 1 (strip)
Shape of footing a b
1 strip 1.00 0.50
2 square 1.30 0.40
3 rectangular, B x L 1.11 0.40
(B < L) (= 1.09 + 0.21 B/L)
(B > L) (= 1.09 + 0.21 L/B)
4 circular, diameter = B 1.30 0.30

Bearing capacity factor (Figure 2.3 of KP-06, by Capper)

Nc = 36.0 Nq = 23.0 Ng = 20.0
f Nc Nq Ng
0 5.7 0.0 0.0
5 7.0 1.4 0.0
10 9.0 2.7 0.2
15 12.0 4.5 2.3
20 17.0 7.5 4.7
25 24.0 13.0 9.5
30 36.0 23.0 20.0
35 57.0 44.0 41.0
37 70.0 50.0 55.0
39 > 82.0 50.0 73.0

(a x c x Nc) = 0.000
(gsoil x z x Nq) = 0.000
(b x gsoil x B x Ng) = 120.000

qu = 120.000 t/m2

(3) Allowable Bearing Capacity of soil, (qa)

qa = qu / 3 = 40.000 t/m2 (safety factor = 3 , normal condition)

qae = qu / 2 = 60.000 t/m2 (safety factor = 2 , seismic condition)

 Structure15/28

3. Structure Calculation

3.1 Normal Condition

(1) Wall 1.41

q = 1.00 t/m2 0.50
0.09

qa1

Pa1
12.25 Pa2

A A
qa2
2.53 Pw1 Pa4 Pw2 0.20
Pa3 B B
1.50
qw1 qa4 qa3 qw2
2.00 2.00

8.00 2.00 2.00

Load Diagram on Wall in Normal Condition

Ka = 0.348
a = 6.566 o

d = 20.00 o

cos (a+d) = 0.894

Kha = Ka x cos (a+d) = 0.311

a) Section A - A

h = 9.73 m
qa1 = ha q
K x = 0.311 ton/m
qa2 = Kha x h x gsoil = 5.443 ton/m

No. Description Ha Y (from A-A) Ha x Y

Pa1 0.311 x 9.73 3.024 4.863 14.702
Pa2 5.443 x 9.73 x 0.50 26.464 3.242 85.789
Total 29.488 100.491

Sa = 29.488 ton Ma = 100.491 ton m

b) Section B - B

h = 9.73 m hw1 = 2.53 m hw2 = 0.20 m

qa1 = Kha x q = 0.311 ton/m
qa2 = Kha x h x gsoil = 5.443 ton/m
qa3 = qa1 + qa2 = 5.753 ton/m
qa4 = Kha x hw2 x (gsat - gw) = 0.785 ton/m
qw1 = hw1 x gw = 2.525 ton/m
qw2 = hw2 x gw = 0.200 ton/m

No. Description Hb Y (from B-B) Ha x Y

Pa1 0.311 x 9.73 3.024 7.388 22.337
Pa2 5.443 x 9.73 x 0.50 26.464 5.767 152.611
Pa3 5.753 x 2.53 14.528 1.263 18.341
Pa4 0.785 x 2.53 x 0.50 0.991 0.842 0.834
Pw1 2.525 x 2.53 x 0.50 3.188 0.842 2.683
Pw2 -0.200 x 0.20 x 0.50 -0.020 0.067 (0.001)
Total 48.175 196.806

Sb = 48.175 ton Mb = 196.806 ton m

 Structure16/28

(2) Footing
Case 1 (with vertical live load) Case 2 (without vertical live load)
q = 1.00 t/m2 q = 1.00 t/m2

9.73 9.73
4 4

2.53 2.53
D C D C
1.50 1.50
2.00 2.00
3 1 3 1

D C D C
8.00 2.00 2.00 8.00 2.00 2.00

5
4 4

3 3 1
1

in case, e > 0 in case, e > 0

6 6
2 2
19.037 t/m2 17.741 t/m2
31.092 t/m2 30.479 t/m2
34.106 t/m2 33.664 t/m2
37.120 t/m2 36.848 t/m2

in case, e < 0 in case, e < 0

2 2
6 6

- t/m2 - t/m2 - t/m2 -

- t/m2 - t/m2 - t/m2 -

Load Diagram on Footing in Normal Case

a) Section C - C

Case 1 (with vertical live load)

No. Description Hc X (from C-C) Hc x X
1 2.000 x 2.00 x 2.40 9.600 1.000 9.600
1.500 x 2.00 x 2.40 x 0.50 3.600 0.667 2.400
2 -34.106 x 2.00 -68.212 1.000 -68.212
-3.014 x 2.00 x 0.50 -3.014 1.333 -4.018
Total -58.026 -60.231

Case 2 (without vertical live load)

No. Description Hc X (from C-C) Hc x X
1 2.000 x 2.00 x 2.40 9.600 1.000 9.600
1.500 x 2.00 x 2.40 x 0.50 3.600 0.667 2.400
2 -33.664 x 2.00 -67.327 1.000 -67.327
-3.185 x 2.00 x 0.50 -3.185 1.333 -4.246
Total -57.312 -59.573

Case 1 Sc = -58.026 ton Mc = -60.231 ton m

Case 2 Sc = -57.312 ton Mc = -59.573 ton m
 Structure17/28

b) Section D - D

Case 1 (with vertical live load)

No. Description Hd X (from D-D) Hd x Y
3 2.000 x 8.00 x 2.40 38.400 4.000 153.600
1.500 x 8.00 x 2.40 x 0.50 14.400 2.667 38.400
4 9.725 x 8.00 x 1.80 140.040 4.000 560.160
2.525 x 8.00 x 2.00 40.400 4.000 161.600
1.500 x 8.00 x 2.00 x 0.50 12.000 5.333 64.000
5 1.000 x 8.00 8.000 4.000 32.000
6 -19.037 x 8.00 -152.296 4.000 -609.184
-12.055 x 8.00 x 0.50 -48.221 2.667 -128.590
Total 52.723 271.986

Case 2 (without vertical live load)

No. Description Hd X (from D-D) Hd x Y
3 2.000 x 8.00 x 2.40 38.400 4.000 153.600
1.500 x 8.00 x 2.40 x 0.50 14.400 2.667 38.400
4 9.725 x 8.00 x 1.80 140.040 4.000 560.160
2.525 x 8.00 x 2.00 40.400 4.000 161.600
1.500 x 8.00 x 2.00 x 0.50 12.000 5.333 64.000
6 -17.741 x 8.00 -141.928 4.000 -567.712
-12.738 x 8.00 x 0.50 -50.952 2.667 -135.872
Total 52.360 274.176

Case 1 Sd = 52.723 ton Md = 271.986 ton m

case 2 Sd = 52.360 ton Md = 274.176 ton m
 Structure18/28

3.2 Seismic Condition

(1) Wall 1.41

0.50
0.09

Pa1 1 2 3
12.25
13.75
A A

qa1
Pa2
2.53 Pw1 Pa3 Pw2 0.20
B B
1.50 qw2
2.00 qw1 qa3 qa2 2.00

8.00 2.00 2.00

Load diagram on Wall for Seismic case

Kae = 0.47
a = 6.566 o

d = 15.00 o

cos (a+d) = 0.930

Khea = Kae x cos (a+d) = 0.437 Kh = 0.16

a) Section A - A

h = 9.73 m
qa1 = Khae x h x gsoil = 7.651 t/m

No. Description Hae Y (from A-A) Hae x Y

1 0.500 x 9.725 x 1.119 x 2.400 x 0.160 2.090 3.242 6.775
2 9.725 x 0.500 x 2.400 x 0.160 1.867 4.863 9.079
3 0.500 x 9.725 x 0.071 x 2.400 x 0.160 0.133 3.242 0.432
Pa1 7.651 x 9.725 x 0.500 37.205 3.242 120.606
Total 41.296 136.893

Sae = 41.296 ton Mae = 136.893 ton m

b) Section B - B

h = 9.73 m hw1 = 2.53 m hw2 = 0.20 m

K
qa1 = hae x h x g soil = 8.227 t/m
qa2 = qa1 = 8.227 t/m
qa3 = Khae x hw1 x ( gsat - gw) = 1.104 t/m
qw1 = hw1 x gw = 2.525 ton/m
qw2 = hw2 x gw = 0.200 ton/m

No. Description Hbe Y (from B-B) Hbe x Y

Pa1 8.227 x 9.73 x 0.50 40.005 5.767 230.698
Pa2 8.227 x 2.53 20.774 1.263 26.227
Pa3 1.104 x 2.53 x 0.50 1.393 0.842 1.173
Pw1 2.525 x 2.53 x 0.50 3.188 0.842 2.683
Pw2 -0.200 x 0.20 x 0.50 -0.020 0.067 -0.001
1 0.500 x 12.25 x 1.41 x 2.40 x 0.16 3.316 4.083 13.542
2 12.250 x 0.50 x 2.40 x 0.16 2.352 6.125 14.406
3 0.500 x 12.25 x 0.09 x 2.40 x 0.16 0.212 4.083 0.864
Total 71.221 289.592

Sbe = 71.221 ton Mbe = 289.592 ton m

 Structure19/28

(2) Footing
in case, e < B/6 in case, B/6 < e < B/3

9.73 9.73
4 4

2.53 2.53
D C D C
1.50 1.50
2.00 2.00
3 1 3 1

D C D C
8.00 2.00 2.00 8.00 2.00 2.00

4 4
3 1 3 1

in case, e > 0 ande < B/6 in case, e > 0 and B/6 < e < B/3

5 6
2 3 |e| - B/2 = 0.075 2
- t/m2 36.506 t/m2
- t/m2
- t/m2 45.719 t/m2
- t/m2 54.932 t/m2

in case, e < 0 and |e| < B/6 in case, e < 0 and B/6 < |e| < B/3
2
2 6
6

- t/m2 - t/m2 - t/m2 -

- t/m2 - t/m2 - t/m2

Load Diagram on Footing in Seismic Case

a) Section C - C

No. Description Hce X (from C-C) Hce x X

1 2.000 x 2.00 x 2.40 9.600 1.000 9.600
1.500 x 2.00 x 2.40 x 0.50 3.600 0.667 2.400
2 -45.719 x 2.00 -91.438 1.000 -91.438
-9.213 x 2.00 x 0.50 -9.213 1.333 -12.284
Total -87.451 -91.722

Sce = -87.451 ton Mce = -91.722 ton m

b) Section D - D

No. Description Hde X (from D-D) Hde x X

3 2.000 x 8.00 x 2.40 38.400 4.000 153.600
1.500 x 8.00 x 2.40 x 0.50 14.400 2.667 38.400
4 12.250 x 8.00 x 1.84 180.440 4.000 721.760
1.500 x 8.00 x 2.00 x 0.50 12.000 5.333 64.000
5 0.000 x 0.00 0.000 0.000 0.000
-36.506 x 7.93 x 0.50 -144.656 2.642 -382.132
Total 100.584 595.628

Sde = 100.584 ton Mde = 595.628 ton m

 Structure20/28

3.3 Design Bending Moment and Shear Force

(1) Bending moment and shear force in each case

Description Bending Moment Shear Force

Normal Seismic Normal Seismic
Case 1 Case 2 Case 3 Case 1 Case 2 Case 3
Section A-A 100.491 100.491 136.893 29.488 29.488 41.296
Section B-B 196.806 196.806 289.592 48.175 48.175 71.221
Section C-C 60.231 59.573 91.722 58.026 57.312 87.451
Section D-D 271.986 274.176 595.628 52.723 52.360 100.584

(2) Design bending moment and shear force

Description Bending Moment Shear Force

Normal Seismic Normal Seismic
Section A-A 100.491 136.893 29.488 41.296
Section B-B 196.806 289.592 48.175 71.221
Section C-C 60.231 91.722 58.026 87.451
Section D-D 196.806 289.592 52.723 100.584
Notes: - Moment at Section C-C < Moment at Section B-B
- Moment at Section D-D < Moment at Section B-B
 Structure21/28

t/m2

t/m2
 Structure22/28

Hae x Y

Hbe x Y
 Structure23/28

t/m2
 Re-bar 24/28

Reinforcement Bar Arrangement and Stress

Normal Condition
Name of Structure : Inverted T-shape Type Retaining Wall (H=15.8m)
Location : Tambuo River

Wall (upper) Wall (lower) Footing (toe) Footing (heel)

Section A-A Section B-B Section C-C Section D-D
back front back front lower upper upper lower
Bending moment M kgfcm 10,049,125 19,680,551 6,023,078 19,680,551
Shearing force (joint) S kgf 29,488 48,175 58,026 52,723
Axial force N kgf 0 0 0 0

Height of member h cm 169.1 200.0 350.0 350.0

Covering depth d' cm 7.0 7.0 10.0 10.0
Effective height d cm 162.1 193.0 340.0 340.0
Effective width b cm 100.0 100.0 100.0 100.0
Young's modulus ratio n - 24 24 24 24

Required R-bar Asreq cm2 48.57 81.78 13.27 44.09

R-bar arrangement 32@250 12@250 32@125 16@250 16@125 12@250 22@125 16@250

Reinforcement As cm2 32.17 4.52 64.34 8.04 16.08 4.52 30.41 8.04
Perimeter of R-bar U ｃｍ 40.21 check 80.42 check 40.21 ok 55.29 ok

Dist. from neutral axis x cm 42.90 63.29 47.51 63.53

Compressive stress sc kgf/cm2 31.7 36.2 7.8 19.4

Allowable stress sca kgf/cm2 60.0 60.0 60.0 60.0
ok ok ok ok
Tensile stress ss kgf/cm2 2113.8 1779.4 1155.5 2029.9
Allowable stress ssa kgf/cm2 1400.0 1400.0 1400.0 1400.0
check check ok check
Shearing stress at joint t kgf/cm2 1.82 2.50 1.71 1.55
Allowable stress ta kgf/cm2 5.50 5.50 5.50 5.50
ok ok ok ok

Resisting Moment Mr kgfcm 5,837,628 14,135,676 4,767,971 9,957,474

Mr for compression Mrc kgfcm 7,613,731 14,135,676 17,348,426 24,343,475
x for Mrc cm 30.859 46.554 33.837 46.071
ss for Mrc kgf/cm2 2877.7 2170.7 6312.9 4545.0
Mr for tensile Mrs kgfcm 5,837,628 16,342,821 4,767,971 9,957,474
x for Mrs cm 37.799 60.042 37.498 52.868
sc for Mrs kgf/cm2 40.3 61.8 15.1 22.2

Distribution bar (>As/6 and >Asmin) 12@250 12@250 16@250 12@250 12@250 12@250 16@250 12@250
Reinforcement As cm2 4.52 4.52 8.04 4.52 4.52 4.52 8.04 4.52
check ok check ok ok ok ok ok

Minimum requirement of reinforcement bar As min = 4.5 cm2

 Re-bar 25/28

Reinforcement Bar Arrangement and Stress

Seismic Condition
Name of Structure : Inverted T-shape Type Retaining Wall (H=15.8m)
Location : Tambuo River

Wall (upper) Wall (lower) Footing (toe) Footing (heel)

Section A-A Section B-B Section C-C Section D-D
back front back front lower upper upper lower
Bending moment M kgfcm 13,689,295 28,959,208 9,172,206 28,959,208
Shearing force (joint) S kgf 41,296 71,221 87,451 100,584
Axial force N kgf 0 0 0 0

Height of member h cm 169.1 200.0 350.0 350.0

Covering depth d' cm 7.0 7.0 10.0 10.0
Effective height d cm 162.1 193.0 340.0 340.0
Effective width b cm 100.0 100.0 100.0 100.0
Young's modulus ratio n - 16 16 16 16

Required R-bar Asreq cm2 43.44 78.74 13.36 42.78

R-bar arrangement 32@250 12@250 32@125 16@250 16@125 12@250 22@125 16@250

Reinforcement As cm2 32.17 4.52 64.34 8.04 16.08 4.52 30.41 8.04
Perimeter of R-bar U ｃｍ 40.21 check 80.42 check 40.21 ok 55.29 ok

Dist. from neutral axis x cm 36.02 53.58 39.33 52.86

Compressive stress sc kgf/cm2 50.6 61.7 14.3 34.0

Allowable stress sca kgf/cm2 90.0 90.0 90.0 90.0
ok ok ok ok
Tensile stress ss kgf/cm2 2835.5 2569.9 1745.0 2953.9
Allowable stress ssa kgf/cm2 2100.0 2100.0 2100.0 2100.0
check check ok check
Shearing stress at joint t kgf/cm2 2.55 3.69 2.57 2.96
Allowable stress ta kgf/cm2 8.25 8.25 8.25 8.25
ok ok ok ok

Resisting Moment Mr kgfcm 8,076,378 18,671,840 6,961,868 14,321,085

Mr for compression Mrc kgfcm 9,900,749 18,671,840 22,089,531 31,140,978
x for Mrc cm 26.181 39.910 28.241 38.633
ss for Mrc kgf/cm2 3662.2 2791.3 7903.2 5716.8
Mr for tensile Mrs kgfcm 8,076,378 21,780,133 6,961,868 14,321,085
x for Mrs cm 30.902 49.137 30.706 43.225
sc for Mrs kgf/cm2 65.6 94.7 26.4 38.1

Distribution bar (>As/6 and >Asmin) 12@250 12@250 16@250 12@250 12@250 12@250 16@250 12@250
Reinforcement As cm2 4.52 4.52 8.04 4.52 4.52 4.52 8.04 4.52
check ok check ok ok ok ok ok

Minimum requirement of reinforcement bar As min = 4.5 cm2

Reinforcement Bar Arrangement

1.41 0.50 0.09

D32@250
D12@250

D12@250
### D12@250

A A
D32@125 D16@250
D12@250
D16@250
D16@250 D12@250
6.03 D22@125 C D12@250
D
B B 1.50

2.00

D16@250 D C
D12@250 D16@125 D12@250

8.00 2.00 2.00

Section of Retaining wall

4. Wooden Pile (Not applicable for this Project)

4.1 Bearing Capacity of a Pile

(1) Design data

Diameter of wooden pile D = 15.0 cm

Length of pile L = 2.00 m
Area of pile section A = 1/4 x p x D2 = 0.018 m2
Perimeter of pile W = pxD = 0.471 m
SPT N-Value = 30
Ni : Average N value in a soil layer = 30
fi : friction of soil = 0.20 x Ni = 6.00 t/m2

(2) Ultimate vertical bearing capacity, (qu)

qu = (40 x N x A) + (W x fi x li)
= ( 40 x 30.0 x 0.018 )+( 0.471 x 6.00 x 2.0 )
= 21.206 + 5.655 = 26.861 ton/pile

(3) Ultimate vertical bearing capacity, (qu)

qa = qu/n = 26.861 / 3 = 8.954 ton/pile

(safety factor : n = 3)

4.2 Allowable horizontal bearing capacity

Horizontal bearing capacity depend on displacement of a pile

(1) Design data

Class of timber (pile) : III Class

E = 80,000 kg/cm2 (Young's modulus)
d = Allowable horizontal displacement = 0.01 m
N = SPT N-value is assumed as = 30

p x D4
I = = 2,485.0 cm4 (I : Moment of Inertia for a pile)
64

(2) Horizontal bearing capacity of one pile (Ha)

a = 0.20 E = 28 x N
Kh = a x E x D-3/4
= 0.20 x( 28 x 30.0 )x( 15.0 )-3/4 = 22.041 kg/cm3

4 Kh x D 4 22.041 x 15.0
b = = = 0.025 cm
4 EI 4 x 80,000 x 2,485.0

Kh x D 22.041 x 15.0
Ha = x d = x 1 = 13,020.22 kg
b 0.025
= 13.020 ton
(3) Allowable horizontal bearing capacity due to the stress of a pile itself

Ha = 2 x b x Ma

s = Allowable stress of timber III class = 75.00 kg/cm2

p x D3
W = = 331.34 cm3 ; (W : section modulus of a pile)
32
Ma = s x W = 75.00 x 331.34 = 24,850.5 kg cm

Ha = 2 x b x Ma
= 2 x 0.025 x 24,850.5 = 1,262.06 kg/pile = 1.262 ton/pile

Allowable horizontal bearing capacity acting on the pile top depend upon the allowable
stress of pile itself.

4.3 Spacing of Pile

(1) For horizontal load

Ha = 1.262 ton/pile ; (Ha : Horizontal load carried by pile)

Hr = H - Hf = H - V x tan(2f/3) = 150.963 - 122.638 = 28.325 ton/m

Ha 1.262
Spacing of pile = = = 0.04 m
Hr 28.325

Spacing of pile = 0.04 m (center to center) by horizontal force

(2) For vertical load

V = 336.945 ton/m : Vertical load carried by pile

qa = 8.954 ton/pile : Allowable vertical bearing capacity of a pile

qa 8.954
Spacing of pile = = = 0.03 m
V 336.945

Spacing of pile can be determined 0.75 m for a pile ( f 150, L = 2.00 m ),

Vp = -20.819 ton/m : Vertical load carried by pile

qa = 8.954 ton/pile : Allowable vertical bearing capacity of a pile

qa 8.954
Spacing of pile = = = -0.43 m
Vp -20.819

Spacing of pile can be determined 1.50 m for a pile ( f 150, L = 2.00 m ),