BANG TINH TUONG CHAN

SOCIALIST REPUBLIC OF VIETNAM
MINISTRY OF TRANSPORT

PROJECT MANAGEMENT UNIT 85

NHAT TAN BRIDGE CONSTRUCTION PROJECT
DỰ ÁN XÂY DỰNG CẦU NHẬT TÂN
PACKAGE 2/ GÓI THẦU SỐ 2

PHU THUONG INTERCHANGE

CALCULATION REPORT
FOR DESIGN MODIFICATION OF RETAINING
WALLS
(REDESIGN ACCORDING TO NEWLY INVESTIGATED SOIL CONDITIONS)

BLOCK C1-1 TO C1-2 ON BRANCH 1E
SPREAD FOOTING

Hanoi November 28th 2013
Hanoi,


SOCIALIST REPUBLIC OF VIETNAM
MINISTRY OF TRANSPORT

PROJECT MANAGEMENT UNIT 85

NHAT TAN BRIDGE CONSTRUCTION PROJECT
DỰ ÁN XÂY DỰNG CẦU NHẬT TÂN
PACKAGE 2/ GÓI THẦU SỐ 2

PHU THUONG INTERCHANGE

CALCULATION REPORT
FOR DESIGN MODIFICATION OF RETAINING
WALLS
(REDESIGN ACCORDING TO NEWLY INVESTIGATED SOIL CONDITIONS)

BLOCK C1-1 TO C1-2 ON BRANCH 1E
SPREAD FOOTING

Prepared by:

Nguyen Van Duong

Checked by:

Tran The Hiep

Reviewed by:

Pham Dang Hung

Approved by:

Tran Manh Toan

Hanoi, November 28th 2013

CALCULATION REPORT FOR RETAINING WALL - BLOCK C1-1, C1-2
1. GENERAL INFORMATIONS:
- Project:

Nhat Tan Bridge Construction Project
Project.

- Construction Package:

PK2

- Work Item:

Retaining Wall of Phu Thuong Interchange.

- Block:

C1-1, C1-2

2. DATA FOR CALCULATION:
2 1 Design Specifications and References:
2.1.
1). 22TCN 272-05: Vietnamese bridge design specifications.
2). AASHTO LRFD 1998: American highway bridge design specifications.
2.2. Geometry Data of Retaining Wall:

T.R

B

B
B.R

A

A

- The vertical and transversal dimension data:
h1 =

0.760 m

b1 =

0.100 m

h2 =

4.540 m

b2 =

0.300 m

h3 =

1.000 m

b3 =

0.400 m

h4 =

3.600 m

b4 =

4.100 m

h5 =

0.700 m

b5 =

0.400 m

h6 =

4.600 m

b6 =

4.500 m

h=

5.300 m

b7 =

0.700 m

TR =

8.120 m

b8 =

4.100 m

BR =

2.820 m

b=

4.800 m

- The longitudinal dimension (the length for this block):

L=

20 m

- The natural ground level at this block:

G.L =

3.92 m

Page 1


2.3. Material:
a. Concrete:
- Compressive strength of concrete at 28 days

f'c =

25 MPa

- Unit weight of concrete

γc =

24.5 kN/m3

- Modulus of Concrete

Ec

26875.0 MPa

- Yield Strength

fy'

390 MPa

- Modulus of Reinforcement

Es

200000 MPa

b. Reinforcement:

c. Filling soil behind the retaining wall:
- Unit weight of filling soil

- Angle of internal friction

γs =

1800 kg/m3

γs =

17.7 kN/m3

ϕ=

30 degree

3. LOADS AND ACTIONS:
The following loads shall be considered for calculating the retaining wall:
- Self weight of retaining wall.
- Static earth pressure and earth pressure due to earthquake.

- Pedestrian load.
- Live load surcharge.
- Earthquake load.

3.1. Dead Load of Retaining Wall (DC):

Section

N (kN)

H (kN)

M (kN.m)

A-A

2712.6

0.0

2306.5

B-B

1066.2

0.0

120.7

3.2. Vertical Earth Pressure behind the Wall (EV):

Section

N (kN)

H (kN)

M (kN.m)

A-A

7056.1

0.0

-1596.6

B-B

395.5

0.0

-76.3

3.3. Horizontal Earth Pressure (EH):

(Article 3.11.5 - 22TCN 272-05)

3.3.1. Horizontal Active Earth Pressure (EHa):
- Earth pressure shall be assumed to be linearly proportional to the depth of earth and taken as:
2
EH = Pa*L = (γs*H *k)/2*L (kN)

θ

β
γ'
σa = ka γ' H , φ'
Pa = γ'

H 2k

H

a/2

δ

δ

P

0.4

Page 2


Where:

H=

Height of filling soil

HA =

Depth off earth pressure acting on section A-A
=

HB =

Depth of earth pressure acting on section B-B
=

L

5.300 (m)

4.600 (m)

Length of this retaining wall block
= 20.000 (m)

γs =

Unit weight of filling soil

k=

Coefficient of lateral earth pressure.

For this case, k is equal to the coefficient of active pressure.

ka =

Sin 2 (θ + ϕ ′ )
TSin 2θ Sin (θ − δ

)

⎡
Sin.(ϕ′ + δ )Sin.(ϕ′ − β ) ⎤
T = ⎢1+
⎥
Sin.(θ − δ )Sin.(θ + β ) ⎦⎥
⎣⎢

In which

2

δ=

Friction angle between fill and wall

=

15.0 (degree)

β=

Angle of fill to the horizontal

=

0.0 (degree)

θ=

Angle of backfill of wall to the vertical

=

85.0 (degree)

ϕ' =

Effective angle of internal friction

=

30.0 (degree)

We have:

T=

ka =

2.607

0.338

Active Horizontal Earth Pressure (EHa)

Section

P (KN)

e (m)

N (KN)

H (KN)

M (KNm)

A-A

1674.8

2.120

572.0

1574.1

4401.0

B-B

1261.6

1.840

430.9

1185.8

2099.9

3.3.2. Horizontal Passive Earth Pressure (EHp):
This is calculated for horizontal passive earth pressure at the front of the retaining wall.
For cohesive soil, passive pressure may be estimated by:
-9
0.5
pp = kp*γs*g*Z*10 + 2*c*(Kp)

Where:
γs =

3
Density of soil (kg/m )

γs =

1800 kg/m3

g=

Gravitational constant (m/s2)

g=

9.81 m/s2

Z=

Depth below surface of soil (mm)

ZA-A =

600 mm

ZB-B =

0 mm

c=

Unit cohension (MPa)

c=

0.080 Mpa

kp =

Coefficient of passive pressure in Figure 1, 2 in 22TCN272-05

kp =

pp =

Passive earth pressure (MPa).

ppA-A =

0.171 MPa

ppB-B =

0.161 MPa

1.0

Passive Horizontal Earth Pressure (EHp)

Section

P (KN)

e (m)

N (KN)

H (KN)

M (KNm)

A-A

1028.9

0.200

-266.3

-993.8

-837.9

B-B

0.0

0.0

0.0

0.0

0.0

Page 3


3.4. Live Load (LS):

(Article 3.11.6.2 - 22TCN 272-05)

a. Pedestrian Load (PL):
This is considered for pedestrian load on the retaing wall.
- Pedestrian load shall be taken from Article. 3.6.1.3 - 22TCN272-05:

qpl =

- Vertical force due to Pedestrian load to Section B-B:

Npl.B-B =

42.0 kN

- Vertical force due to Pedestrian load to Section A-A:

Npl.A-A =

288.0 kN

0.338

/
3 kN/m2

b. Live load surcharge (LS):
The live load surchage (LS) shall be calculated by the following formula:
LS = Δp*H*L = k*γs*heq*H*L
where:
k=

Coefficient of lateral earth pressure.

k=

γs =

Unit weight of filling soil

γs =

17.7 kN/m3

H=

Height of the wall

heq =

Equivalent height of soil for the live load.

heq =

0.86 m

Live Load Surcharge (LS)

Section
LS (KN)

e (m)

N (KN)

H (KN)

M (KNm)

A-A

545.2

2.650

186.2

512.4

1711.7

B-B

473.2

2.300

161.6

444.7

998.7

3.5. Earth Pressure due to Earthquake
(E
q
( AE)):

((Appendix
pp
A11.1 - Section 11 - AASHTO LRFD 1998))

3.5.1. Active Earth Pressure due to Earthquake (EAE):
Active earth pressure due to earthquake shall be calculated by the below formula:

Where:

1
E AE = g.γ.H2 .(1 − k v ).K AE.10−9
2

p
y be taken as:
- Values for the coefficient of active pressure
KEA may

⎡
cos2 (ϕ − θ − β)
sin(ϕ + δ)sin(ϕ − θ − i) ⎤
+
KAE =
x
1

⎢
⎥
cosθ.cos2 β.cos(δ + θ + β) ⎣
cos(δ + θ + β) cos(i − β) ⎦

−2

= 0.378

In which:
g=

Acceleration of gravity (m/s2)

9.81

m/s2

γ=

Density of soil (kg/m3)

1800

kg/m3

H=

Height of soil face (mm)

ϕ=

Angle of Internal friction of soil (DEG)

θ=

arctg (kh/(1-kv)) (DEG)

δ=

Angle of friction between soil and wall (DEG)

A=

Acceleration coefficient

0.12

kh =

Horizontal acceleration coefficient

0.06

kv =

Vertical acceleration coefficient

0.03

mm
30.0

deg

3.5

deg

15.00

deg

i=

Backfill slope angle

0.0

deg

β=

Slope of wall to the vertical (DEG)

5.0

deg

Page 4

Section

Active earth pressure due to earthquake (EAE)
EAE (KN)

e (m)

A-A

1820.1

1.767

621.6

1710.7

4203.3

B-B

1371.1

1.533

468.3

1288.7

1905.7

N (KN)

H (KN)

M (KNm)

3.5.2. Passive Earth Pressure due to Earthquake (EAE):
p
q
Active earth pressure
due to earthquake
shall be calculated byy the below formula:

1
E PE = g.γ.H 2 .(1 − k v ).K PE .10−9
2
Where:
- Values for the coefficient of active pressure KEA may be taken as:

⎡
cos2 (ϕ − θ + β)
sin(ϕ + δ) sin(ϕ − θ + i) ⎤
KAE =
x⎢1−
⎥
2
cos(δ + θ − β) cos(i − β) ⎦

cosθ.cos β.cos(δ + θ − β) ⎣

−2

= 0.341

In which:
g=

Acceleration of gravity (m/s2)

9.81

m/s2

γ=

Density of soil (kg/m3)

1800

kg/m3

H=

Height of soil face (mm)

ϕ=

Angle of Internal friction of soil (DEG)

30.0

deg

θ=

arctg (kh/(1-kv)) (DEG)

3.54

deg

δ=

Angle of friction between soil and wall (DEG)

A=

Acceleration coefficient

0.12

kh =

Horizontal acceleration coefficient

0.06

kv =

Vertical acceleration coefficient

0.03

mm

15.00

deg

i=

Backfill slope angle

0.0

deg

β=

Slope of wall to the vertical (DEG)

0.0

deg

Section

Passive earth pressure due to earthquake (EPE)

EAE (KN)

e (m)

A-A

21.0

0.200

-5.4

-20.3

B-B

0.0

0.000

0.0

0.0

N (KN)

H (KN)

M (KNm)
-17.1

0.0

Page 5


3.6. Earthquake Force:

(Article 3.10 - 22TCN 272-05)

The earthquake force shall be calculated as formula below:

EQ
Q=

C sm * W
R

where:
W=

Weight of retaining wall (kN).

R=

Response Modification factor (Table 3.10.7.1-1_22TCN272-05)

R=

Csm =

The elastic seismic response coefficient.

Cms =

1.5
0.1179

In general, the Csm shall be taken as:

C sm =

1 .2 * A * S
≤ 2 .5 * A
Tm2 / 3

Exception, for soil profiles III and IV, and for modes other than the fundamental mode that have
periods less than 0.3s, Csm shall be taken as:

Csm = A*(0.8 + 4.0*Tm)

(this formula is applied for this retaining wall)

if the period of vibration for any mode exceeds 4.0 s, the value of Csm for that mode shall be
taken as:

C sm =

3* A *S
Tm4 / 3

in which:
A=

Acceleration coefficient (Taken from technical general notes)

A=

0.1200

S=

Site coefficient (Soil profile type III)

S=

1.5

Tm =

Period of vibration, shall be taken as:

Tm =

Tm = 2 * Π *

0.0457 second

f
g

in which:
g=

Gravitational accelaration.

g=

f=

Horizontal displacement
at the top
p
p of the retaining
g wall

9.81 m/s2

For retaining wall on spread foundation, Tm shall be calculated:
T = 2π

f
= 2π
g

( 0 .23Q ) H 3
3 gEI

Q=

Retaining wall weight.

Q=

H=

Height from top of retaining wall to top of footing.

H=

1066.2 kN
4.60 m

In order to calculate the earthquake force, the retaining wall shall be divided into parts as figure below:

Page 6


Earthquake effects acting on the Retaining wall
No.

Section B-B

Part of the Retaining wall
Q (kN)

HEQ (kN)

e (m)

MEQ (kN.m)

1

Part 1

149.0

17.6

4.220

74.1

2

Part 2

35.3

4.2

3.720

15.5

3

Part 3

529.2

62.4

1.800

112.3

4

Part 4

352.8

41.6

1.200

49.9

1066.2

125.7

251.8

83.8

167.9

Total

Total (Consider the Response modification factor)

No.

Section A-A

Part
Q (kN)

HEQ (kN)

e (m)

MEQ (kN.m)

1

Part 1

149.0

17.6

4.920

86.4

2

Part 2

35.3

4.2

4.420

18.4

3

Part 3

529.2

62.4

2.500

156.0

4

Part 4

352.8

41.6

1.900

79.0

5

Part 5

1646.4

194.1

0.350

67.9

2712.6

319.9

407.8

213.2

271.9

Total
Total (Consider the Response modification factor)

4. LOAD COMBINATIONS:
4.1. Summary of Load:

No.

Section A-A

Load

Section B-B

N (kN)

H (kN)

M (kNm)

N (kN)

H (kN)

M (kNm)

1

Dead load of retaining wall (DC)

2712.6

0.0

2306.5

1066.2

0.0

120.7

2

Vertical earth pressure (EV)

7056 1
7056.1

00
0.0

-1596.6
1596 6

395 5
395.5

00
0.0

-76.3
76 3

3

Active horizontal earth pressure (EHa)

572.0

1574.1

4401.0

430.9

1185.8

2099.9

4

Passive horizontal earth pressure (EHp)

-266.3

-993.8

-837.9

0.0

0.0

0.0

5

Pedestrian load (PL)

288.0

0.0

0.0

42.0

0.0

0.0

6

Live load surcharge (LS)

186.2

512.4

1711.7

161.6

444.7

998.7

7

Active earth pressure at seismic (EAE)

621.6

1710.7

4203.3

468.3

1288.7

1905.7

8

Passive earth pressure at seismic (EPE)

-5.4

-20.3

-17.1

0.0

0.0

0.0

9

Earthquake Forces (EQ)

0.0

213.2

271.9

0.0

83.8

167.9

Page 7


4.2. Load Combinations:
These load combinations as below shall be considered for the retaining wall calculation:
- Combination I (Service limit state):
1.0*DC + 1.0*EV + 1.0*EHa + 1.0*EHp + 1.0*PL + 1.0*LS
- Combination II (Strength I limit state):
1.25*DC + 1.35*EV + 1.5*EHa + 0.9*EHp + 1.75*PL + 1.75*LS

- Combination III (Extremem Event limit state):
1.25*DC + 1.35*EV + +0.5*PL + 0.5*LS + 1.5*EAE + 0.9*EPE + 1.0*EQ
where:

DC =

Dead load of the retaining wall.

EV =

Vertical earth pressure.

EHa =

Active horizontal earth pressure.

EHp =

Passive horizontal earth pressure.

PL =

Pedestrian load on top of retaining wall.

LS =

Live load surcharge.

EAE =

Active earth pressure at seismic.

EPE =

Passive earth pressure at seismic.

EQ =

Earthquake force.

4.3. Load Combination at Service Limit State:
No.

Load

Section A-A

Factor

Section B-B

N (kN)

H (kN)

M (kNm)
(kN )

N (kN)

H (kN)

M (kNm)
(kN )

1

Dead load of retaining wall
(DC)

1.00

2712.6

0.0

2306.5

1066.2

0.0

120.7

2

Vertical earth pressure
(EV)

1.00

7056.1

0.0

-1596.6

395.5

0.0

-76.3

3

Active horizontal earth pressure
(EHa)

1.00

572.0

1574.1

4401.0

430.9

1185.8

2099.9

4

Passive horizontal earth
pressure (EHp)

1.00

-266.3

-993.8

-837.9

0.0

0.0

0.0

5

Pedestrian load
(PL)

1.00

288.0

0.0

0.0

42.0

0.0

0.0

6

Live load surcharge (LS)

1.00

186.2

512.4

1711.7

161.6

444.7

998.7

7

Active earth pressure at seismic
(EAE)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

8

Passive earth pressure at
seismic (EAE)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

8

Earthquake Forces
(EQ)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

10548.7

1092.7

5984.7

2096.3

1630.5

3143.1

Summary

Page 8


4.4. Load Combination at Strength I Limit State:
No.

Load

Section A-A

Factor

Section B-B

N (kN)

H (kN)

M (kNm)

N (kN)

H (kN)

M (kNm)

1

Dead load of retaining wall
(DC)

1.25

3390.8

0.0

2883.2

1332.8

0.0

150.9

2

Vertical earth pressure
(EV)

1.35

9525.8

0.0

-2155.5

534.0

0.0

-103.0

3

Active horizontal earth pressure
((EHa)

1.50

858.0

2361.2

6601.5

646.3

1778.6

3149.9

4

Passive horizontal earth
pressure (EHp)

0.90

-239.7

-894.4

-754.1

0.0

0.0

0.0

5

Pedestrian load
(PL)

1.75

504.0

0.0

0.0

73.5

0.0

0.0

6

Live load surcharge (LS)

1.75

325.9

896.7

2995.5

282.8

778.3

1747.7

7

Active earth pressure at seismic
(EAE)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

8

Passive earth pressure at
seismic (EAE)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

9

Earthquake Forces
(EQ)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

14364.8

2363.5

9570.6

2869.4

2557.0

4945.5

Summary
4.5. Load Combination at Extreme Limit State:
No.

Load

Section A-A

Factor

Section B-B

N (kN)

H (kN)

M (kNm)

N (kN)

H (kN)

M (kNm)

1

Dead load of retaining wall
(DC)

1.25

3390.8

0.0

2883.2

1332.8

0.0

150.9

2

Vertical earth pressure
(EV)

1.35

9525.8

0.0

-2155.5

534.0

0.0

-103.0

3

Active horizontal earth pressure
(EHa)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

4

Passive horizontal earth
pressure (EHp)

0.00

0.0

0.0

0.0

0.0

0.0

0.0

5

Pedestrian load (PL)

0.50

144.0

0.0

0.0

21.0

0.0

0.0

6

Live load surcharge (LS)

0.50

93.1

256.2

855.9

80.8

222.4

499.3

7

Active earth pressure at seismic
(EAE)

1.50

932.4

2566.1

6305.0

702.4

1933.0

2858.6

8

Passive earth pressure at
seismic (EAE)

0.90

-4.9

-18.3

-15.4

0.0

0.0

0.0

9

Earthquake Forces (EQ)

1.00

0.0

213.2

271.9

0.0

83.8

167.9

14081.2

3017.2

8145.0

2671.0

2239.2

3573.7

Summary

Page 9


4.6. Summary of Load combinations:

No.

Section A-A

Limit state

Section B-B

N (kN)

H (kN)

M (kNm)

N (kN)

H (kN)

M (kNm)

1

Service limit state

10548.7

1092.7

5984.7

2096.3

1630.5

3143.1

2

Strength I limit state

14364.8

2363.5

9570.6

2869.4

2557.0

4945.5

3

Extreme Event limit state

14081.2

3017.2

8145.0

2671.0

2239.2

3573.7

Page 10


5. CHECK THE CAPACITY OF FOUNDATION
5.1. Data for Calculation
- Load combination to the bottom of the foundation:
Dimension of footing
N

Mx

My

Qx

Qy

L=

20 m

kN

kN.m

kN.m

kN

kN

B=

4.8 m

Strength I limit state

14364.8

9570.6

-

-

2363.5

Extreme Event limit state

14081.2

8145.0

-

-

3017.2

Limit states

For load encentric to the centroid of footing , a reduce effective area B'xL', within the confines of the the physical footing shall
be use in geotechnical design for settlement or bearing resistance. The design bearing pressure on the effctive area shall be
assume to be uniform. The reduce effective area shall be concentric with the load. The reduced dimensions may be taken as:
B' = B - 2*eB

(Article 10.6.3.1.5 - 22TCN272-05)

L' = L - 2*eL
Where:
eB

Eccentricity parallel to dimension B (mm)

eB = MX / N

eL

Eccentricity parallel to dimension L (mm)

eL = MY / N

ECCENTRICITY AND EFFECTIVE DIMENSIONS OF FOOTING
P

Mx

My

eL=My/P

eB=Mx/P

L'

B'

(kN)

(kN.m)

(kN.m)

(m)

(m)

(m)

(m)

Limit states
Strength I limit state

14364.8

9570.6

-

0.00

0.67

20.00

3.47

Extreme Event limit state

14081.2

8145.0

-

0.00

0.58

20.00

3.64

- Boring log for calculation:

BH02, dated 5/11/2013 by VINACONEX

The bottom level of footing is:

2.82

The soil layer "Clay, medium stiff" is considered as the soil under the footing.
This soil layer has the following average properties:
+ Thickness of this layer:

h=

8.0m

+ SPT value:

N=

23

+ Natural unit weight:

γw =

1970 kg/m3 =

+ Unconfined compression test:

qu =

1.66 kG/cm2 =

0.163 Mpa

+ Cohension:

c=

0.82 kG/cm2

0.080 Mpa

+ Internal friction angle:

ϕ=

3.5 degree

19.3 kN/m3

Page 11


5.2. Bearing Resistance of Soils under Footings:
- The factored resistance, qR, at strength limit state shall be taken as:
qR = ϕ*qult

(Article 10.6.3.1 - 22TCN272-05)

where:
ϕ=

Resistance factor specified in Article 10.5.5

qult =

Nominal bearing resistance (Mpa)

ϕ=

0.6 for strength limt state, and =

1.0 for Extreme event limt state

- The nominal bearing resistance of a layer of clay may be taken as:
qult = Su*Ncm + g*γ*Df*Nqm*10-9
where:
Su =

Undrained shear strength (MPa)

g=

Gravitational acceleration (m/s2)

g=

9.81 m/s2

γ=

Density of clay (kg/m3)

γ=

1970 kg/m3

Df =

Embedment depth taken to the bottom of the footing

Df =

Ncm, Nqqm =

Modified bearing capacity factors that are functions of footing shape, embedment depth, soil compressibility, and load inclination

Su = qu/2

Su =

0.081 MPa

1.1 m

+ For Df/B ≤ 2.5, B/L ≤ 1.0 and H/V ≤ 0.4:
Ncm = Nc * [ 1 + 0.2*(Df/B) ] * [ 1 + 0.2*(B/L) ] * [ 1 - 1.3*(H/V) ] (2)
+ For Df/B > 2.5 and H/V ≤ 0.4:
Ncm = Nc * [ 1 + 0.2*(Df/B) ] * [ 1 - 1.3*(H/V) ] (3)
Nc =

5.0 for use in Equation 2 on relatively level soil
7.5 for use in Equation 3 on relatively level soil

Nqm =

1.0 for saturated clay and relative level ground surfaces.

- The factored resistance force [P] at strength limit state shall be calculated:
[P] = qR*(B'*L')
- Checking for Bearing resistance:
P ≤ [P]
where:

P=

The factored vertical load at the bottom of footing.

Limit states

B'

L'

Ncm

qR = ϕ.qult

qult
2

[P]

P

2

(kN)

(kN)

Check

(m)

(m)

Strength I limit state

3.47

20.00

4.32

373.4

224

15537

14365

OK

Extreme Event limit state

3.64

20.00

3.96

344.1

344

25069

14081

OK

kN/m

(kN/m )

Page 12


5.3. Checking for Overturning:

(Article 10.6.3.1.5 and 10.6.3.2.5 - 22TCN272-05)

- For foundations on soil, the location of the resultant of the reaction forces shall be within the middle one-half of the base.
- For foundations on rock, the location of the resultant of the reaction forces shall be within the middle three-fourths of the base.

Force

P

M
e = M/P

Checking

ResultantF

P

Mx

My

eB=Mz/P

EB' /2

(kN)

(kN.m)

(kN.m)

(m)

= B'/4

Strength I limit state

14364.8

9570.6

-

0.67

1.20

OK

E = 1/2*L (On soil
E = 3/4*L (On rock)

Extreme Event limit state

14081.2

8145

-

0.58

1.20

OK

Width dimension L (or B)

Limit states

Check

Page 13

5.4. Checking for Sliding

(Article 10.6.3.3 - 22TCN272-05)

- The factored resistance against failure by sliding, in N, may be taken as:
QR = ϕQn = ϕT QT + ϕep Qep
Where:
ϕT =

ϕT

=

Resistance factor for shear resistance between soil and foundation.

QT

=

Nominal shear resistance between soil and foundation.

ϕep

=

Resistance factor for passive resistance.

Qep

=

Nominal passive resistance of soil available throughout the design life of the structure.

0.8 for strength limit state, and

1.0 for Extreme event limt state

QR = ϕQn = ϕT QT

- For safety, the factored resistance shall be taken only the part of shear resistance between soil and foundation:
- For footing on soil:
+ If the soil is cohensionless:
QT = V * tan(δ)
for which:
tanδ = tanϕf for concrete cast against soil.
= 0.8 * tanϕf for precast concrete footing.
ϕf =

Internal friction angle of soil.

N=

Total vertical force.

+ If the soil is clay:
The sliding resistance may be taken as the cohension of the clay.
QT = Su * (B'*L')
- Checking for sliding:
Q ≤ QR
Where:

P=

The factored horizontal load at the bottom of footing.
N

Qy

B'

L'

QT

QR

Q

kN

kN

(m)

(m)

(kN)

(kN)

(kN)

Strength I limit state

14364.8

2363.5

3.47

20.00

5646.7

4517

2363

OK

Extreme Event limit state

14081.2

3017.2

3.64

20.00

5932.7

5933

3017

OK

Limit states

Check

Page 14


6. CHECK THE RETAINING WALL (SECTION B-B:)

T.R

B

B
B.R

A

A

Summary table of loads acting on section B-B
Limit state

Shear force (kN)

Moment (kN.m)

Strength I limit state (Comb. II)

2557.0

4945.5

Extreme Event limit state (Comb. III)

2239.2

3573.7

S i lilimit
it state
t t (C
b I)
Service
(Comb.

1630 5
1630.5

3143 1
3143.1

b
a'

h

a

0.85*f'c*a*

a

fy•A

Page 15


Data

Value

Unit

• Factored moment

Mu

4945.5

kN.m

• Factored shear force

Vu

2557.0

kN

h

700

mm

• Height of section
• Width of section

b

20000

mm

Ac

1.40E+07

mm2

Ig

5.7E+11

mm4

Thickness concrete cover.

dc

100

mm

Distance to extreme compression fiber.

ds

600

mm

Diameter.

∅

20

mm

Spacing of bars.

@

150

mm

n

132

As

41448

mm2

Thickness concrete cover

d'c

100

mm

Distance to extream compression fiber

d's

100

mm

• Total area of section
• Moment of inertia
• Reinforcement in tension:

Number.
Total area.
• Reinforcement in compression:

Diameter

∅'

12

mm

Spacing of bars.

@

150

mm

Number

n'

132

A's

14916

• Resistance factor

Φ

0.90

• Effective height of section

de

600

• Stress block factor

β1

0.85

• Depth of equivalent stress block (a = c•β1)

a

38.03

mm

• Distance from neutral axis to extreme compression filber

c

44.75

mm

Mn

9391.4

kN.m

Mr = Φ•Mn

8452.3

kN.m

Total area

mm2

Flexural resistance

• Nominal resistance

• Factored flexural moment

Mr > Mu

• Check the flexural resistance capacity

mm

O.K

Check the minimum content of reinforcement (Article 5.7.3.3.2 - 22TCN272-05)
• Ratio of tension reinforcement to gross area
• Limit value

ρ min = As/(b•d)

0.296%

0.03•f'c/fy

0.192%

ρ min > 0.03•f'c/fy

O.K

fr = 0.63•f'c0.5

3.15

Mpa

Mcr = fr•Ig/yt

5145.00

kN.m

• Limit value 1

1.2•Mcr

6174.00

kN.m

• Limit value 2

1.33*Mu

6577.56

kN.m

• Check the minimum reinforcement
Check on cracking moment (Article 5.7.3.3.2 - 22TCN272-05):
• Modulus of rupture of concrete
• Cracking moment

• Check the cracking moment

Φ•Mn > Min(1.2•Mcr,1.33•Mu)

O.K

Check the maximum content of reinforcement (Artcile 5.7.3.3 - 22TCN272-05)
• Maximum content of reinforcement
• Check the maximum content of reinforcement

c/de

0.07

c/de < 0.42

O.K

Page 16


Shear resistance
• Factored shear force

Vu

2557.0

• Shear resistance factor

Φ

0.90

• Height of section in shear

dv

540

mm

• Effective width of web in shear

bv

20000

mm

• Angle of inclination of diagonal compressive stresses

θ

45

degree

• Angle of inclination of transverse reinforcement to longitudinal axis

α

90

degree

β

• Factor indicated possibiliy of concrete in being inclining cracked to transmit tension

• Value

0.1•f'c•bv•dv

kN

2
27000

kN

• Spacing of stirrups

s

150

mm

• Diameter of stirrup

∅

D 13

mm

• Number of stirrup reinforcement in the range of spacing s

n

0

• Total area of stirrups

Av

-

mm2

• Nominal resistance of concrete

Vc

8964.0

kN

• Resistance of stirrups in shear

Vs

-

kN

0.25•f'c•bv•dv

67500.0

kN

• Nominal resistance of components

Vn

8964.0

kN

• Factored resistance

Vr

8067.6

kN

• Value

Vr > Vu

• Check

O.K

Check on cracking
• Load combination used for checking

Service limit state

• Bending moment

Mu
n = Es/Ec

• Ratio of elastic modulus
• Reinforcement content

ρ = As/(b•de)

• Value

2

• Value
• Stress of reinforcement in tension

3143.1

kN.m

7.44
0.0035

%

0.7

0.20

j = 1 - k/3

0.93

fs = Ms/(AS•j•de)

135.5

Mpa

k = -ρ•n + [(ρ•n) + 2•ρ•n]

• Information of cracking width

Z

17500

N/mm

• Value

dc

50

mm

• Result of concrete area which covers reinforcement overs
number of steel bars

A

15151.5

mm2

fsa = Z/(dc•A)1/3

192.0

Mpa

0.6•fy

234.0

Mpa

• Tensile stress in reinforcement at service limit state
• Value
• Check

fs < fsa

O.K

• Check

fsa < 0.6•fy

O.K

Page 17


7. CHECK THE RETAINING FOOTING (SECTION C-C:)

T.R

C
B

B
B.R

A

A

C
Summary table of loads acting on section B-B
Limit state

Shear force (kN)

Moment (kN.m)

Strength I limit state (Comb. II)

2557.0

4945.5

Extreme Event limit state (Comb. III)

2239.2

3573.7

S i lilimit
it state
t t (C
b I)
Service
(Comb.

1630 5
1630.5

3143 1
3143.1

b
a'

h

a

0.85*f'c*a*

a

fy•A

Page 18


Data

Value

Unit

• Factored moment

Mu

4945.5

kN.m

• Factored shear force

Vu

2557.0

kN

h

700

mm

• Height of section
• Width of section

b

20000

mm

Ac

1.40E+07

mm2

Ig

5.7E+11

mm4

Thickness concrete cover.

dc

100

mm

Distance to extreme compression fiber.

ds

600

mm

Diameter.

∅

20

mm

Spacing of bars.

@

150

mm

n

132

As

41448

mm2

Thickness concrete cover

d'c

100

mm

Distance to extream compression fiber

d's

100

mm

• Total area of section
• Moment of inertia
• Reinforcement in tension:

Number.
Total area.
• Reinforcement in compression:

Diameter

∅'

12

mm

Spacing of bars.

@

150

mm

Number

n'

132

A's

14916

• Resistance factor

Φ

0.90

• Effective height of section

de

600

• Stress block factor

β1

0.85

• Depth of equivalent stress block (a = c•β1)

a

38.03

mm

• Distance from neutral axis to extreme compression filber

c

44.75

mm

Mn

9391.4

kN.m

Mr = Φ•Mn

8452.3

kN.m

Total area

mm2

Flexural resistance

• Nominal resistance
• Factored flexural moment

Mr > Mu

• Check the flexural resistance capacity

mm

O.K

Check the minimum content of reinforcement (Article 5.7.3.3.2 - 22TCN272-05)
• Ratio of tension reinforcement to gross area
• Limit value

ρ min = As/(b•d)

0.296%

0.03•f'c/fy

0.192%

ρ min > 0.03•f'c/fy

O.K

fr = 0.63•f'c0.5

3.15

Mpa

Mcr = fr•Ig/yt

5145.00

kN.m

• Limit value 1

1.2•Mcr

6174.00

kN.m

• Limit value 2

1.33*Mu

6577.56

kN.m

• Check the minimum reinforcement
Check on cracking moment (Article 5.7.3.3.2 - 22TCN272-05):

• Modulus of rupture of concrete
• Cracking moment

• Check the cracking moment

Φ•Mn > Min(1.2•Mcr,1.33•Mu)

O.K

Check the maximum content of reinforcement (Artcile 5.7.3.3 - 22TCN272-05)
• Maximum content of reinforcement
• Check the maximum content of reinforcement

c/de

0.07

c/de < 0.42

O.K

Page 19


Shear resistance
• Factored shear force

Vu

2557.0

• Shear resistance factor

Φ

0.90

• Height of section in shear

dv

540

mm

• Effective width of web in shear

bv

20000

mm

• Angle of inclination of diagonal compressive stresses

θ

45

degree

• Angle of inclination of transverse reinforcement to longitudinal axis

α

90

degree

β

• Factor indicated possibiliy of concrete in being inclining cracked to transmit tension

• Value

0.1•f'c•bv•dv

kN

2
27000

kN

• Spacing of stirrups

s

150

mm

• Diameter of stirrup

∅

D 13

mm

• Number of stirrup reinforcement in the range of spacing s

n

0

• Total area of stirrups

Av

-

mm2

• Nominal resistance of concrete

Vc

8964.0

kN

• Resistance of stirrups in shear

Vs

-

kN

0.25•f'c•bv•dv

67500.0

kN

• Nominal resistance of components

Vn

8964.0

kN

• Factored resistance

Vr

8067.6

kN

• Value

Vr > Vu

• Check

O.K

Check on cracking
• Load combination used for checking

Service limit state

• Bending moment

Mu
n = Es/Ec

• Ratio of elastic modulus
• Reinforcement content

ρ = As/(b•de)

• Value

2

• Value

• Stress of reinforcement in tension

3143.1

kN.m

7.44
0.0035

%

0.7

0.20

j = 1 - k/3

0.93

fs = Ms/(AS•j•de)

135.5

Mpa

k = -ρ•n + [(ρ•n) + 2•ρ•n]

• Information of cracking width

Z

17500

N/mm

• Value

dc

50

mm

• Result of concrete area which covers reinforcement overs
number of steel bars

A

15151.5

mm2

fsa = Z/(dc•A)1/3

192.0

Mpa

0.6•fy

234.0

Mpa

• Tensile stress in reinforcement at service limit state
• Value
• Check

fs < fsa

O.K

• Check

fsa < 0.6•fy

O.K

Page 20


Page 21