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# RETAINING WALLS - ADVANCED FOUNDATION ENGINEERING-1 IT & Software Notes | EduRev

## IT & Software : RETAINING WALLS - ADVANCED FOUNDATION ENGINEERING-1 IT & Software Notes | EduRev

``` Page 1

Module 7
(Lecture 27)
RETAINING WALLS

Topics
1.1 RETAINING WALLS WITH METALLIC STRIP
REINFORCEMENT
? Calculation of Active Horizontal and vertical Pressure
? Tie Force
? Factor of Safety Against Tie Failure
? Total Length of Tie
1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP
REINFORCEMENT
? Internal Stability
? External Stability
? Internal Stability Check
? Tie thickness
? Tie length
? External Stability Check
? Check for overturning
? Check for sliding
? Check for bearing capacity

Page 2

Module 7
(Lecture 27)
RETAINING WALLS

Topics
1.1 RETAINING WALLS WITH METALLIC STRIP
REINFORCEMENT
? Calculation of Active Horizontal and vertical Pressure
? Tie Force
? Factor of Safety Against Tie Failure
? Total Length of Tie
1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP
REINFORCEMENT
? Internal Stability
? External Stability
? Internal Stability Check
? Tie thickness
? Tie length
? External Stability Check
? Check for overturning
? Check for sliding
? Check for bearing capacity

RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT
Reinforced earth walls are flexible walls. Their main components are
1. Backfill, which is granular soil
2. Reinforcing strips, which are thin, wide strips placed at regular intervals
3. A cover on the front face, which is referred to as the skin
Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes
or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the
strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively
flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick
( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high.
In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each
other so that soil cannot flow out between the joints. When metal skins are used, they are bolted
together, and reinforcing strips are placed between the skins.

Figure 7.25 Reinforced earth retaining wall
Calculation of Active Horizontal and vertical Pressure
Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1
and a
friction angle of ???? 1
. Below the base of the retaining wall, the in situ soil has been excavated and
reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit
weight of ???? 2
and a friction angle of ???? 2
, and cohesion of ???? 2
. A surcharge having an intensity of q
per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? =
0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? .

Page 3

Module 7
(Lecture 27)
RETAINING WALLS

Topics
1.1 RETAINING WALLS WITH METALLIC STRIP
REINFORCEMENT
? Calculation of Active Horizontal and vertical Pressure
? Tie Force
? Factor of Safety Against Tie Failure
? Total Length of Tie
1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP
REINFORCEMENT
? Internal Stability
? External Stability
? Internal Stability Check
? Tie thickness
? Tie length
? External Stability Check
? Check for overturning
? Check for sliding
? Check for bearing capacity

RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT
Reinforced earth walls are flexible walls. Their main components are
1. Backfill, which is granular soil
2. Reinforcing strips, which are thin, wide strips placed at regular intervals
3. A cover on the front face, which is referred to as the skin
Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes
or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the
strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively
flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick
( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high.
In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each
other so that soil cannot flow out between the joints. When metal skins are used, they are bolted
together, and reinforcing strips are placed between the skins.

Figure 7.25 Reinforced earth retaining wall
Calculation of Active Horizontal and vertical Pressure
Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1
and a
friction angle of ???? 1
. Below the base of the retaining wall, the in situ soil has been excavated and
reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit
weight of ???? 2
and a friction angle of ???? 2
, and cohesion of ???? 2
. A surcharge having an intensity of q
per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? =
0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? .

Figure 7.26 Analysis of a reinforced earth retaining wall
According to the Rankine active pressure theory
???? ???? = ???? ???? ???? ???? - 2 ???? ? ???? ????
Where
???? ???? = Rankine active pressure at any depth ????
For dry granular soils with no surcharge at the top, ???? = 0, ???? ???? = ???? 1
???? , and ???? ???? = tan
2
(45 - ???? 1
/2).
Thus
???? ???? (1)
= ???? 1
???? ???? ????          [7.30]
When a surcharge is added at the top, as shown in figure 29,
???? ???? = ???? ???? (1)

?
= ???? 1
???? Due to soil only

+ ???? ???? (2)
?
Due to the surcharge
[7.31]
The magnitude of ???? ???? (2)
can be calculated by using the 2:1 method of stress distribution described
in equation (14 chapter 4) and figure 6 (from chapter 4). It is shown in figure 27a. According to
Laba and Kennedy (1986),

Page 4

Module 7
(Lecture 27)
RETAINING WALLS

Topics
1.1 RETAINING WALLS WITH METALLIC STRIP
REINFORCEMENT
? Calculation of Active Horizontal and vertical Pressure
? Tie Force
? Factor of Safety Against Tie Failure
? Total Length of Tie
1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP
REINFORCEMENT
? Internal Stability
? External Stability
? Internal Stability Check
? Tie thickness
? Tie length
? External Stability Check
? Check for overturning
? Check for sliding
? Check for bearing capacity

RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT
Reinforced earth walls are flexible walls. Their main components are
1. Backfill, which is granular soil
2. Reinforcing strips, which are thin, wide strips placed at regular intervals
3. A cover on the front face, which is referred to as the skin
Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes
or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the
strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively
flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick
( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high.
In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each
other so that soil cannot flow out between the joints. When metal skins are used, they are bolted
together, and reinforcing strips are placed between the skins.

Figure 7.25 Reinforced earth retaining wall
Calculation of Active Horizontal and vertical Pressure
Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1
and a
friction angle of ???? 1
. Below the base of the retaining wall, the in situ soil has been excavated and
reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit
weight of ???? 2
and a friction angle of ???? 2
, and cohesion of ???? 2
. A surcharge having an intensity of q
per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? =
0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? .

Figure 7.26 Analysis of a reinforced earth retaining wall
According to the Rankine active pressure theory
???? ???? = ???? ???? ???? ???? - 2 ???? ? ???? ????
Where
???? ???? = Rankine active pressure at any depth ????
For dry granular soils with no surcharge at the top, ???? = 0, ???? ???? = ???? 1
???? , and ???? ???? = tan
2
(45 - ???? 1
/2).
Thus
???? ???? (1)
= ???? 1
???? ???? ????          [7.30]
When a surcharge is added at the top, as shown in figure 29,
???? ???? = ???? ???? (1)

?
= ???? 1
???? Due to soil only

+ ???? ???? (2)
?
Due to the surcharge
[7.31]
The magnitude of ???? ???? (2)
can be calculated by using the 2:1 method of stress distribution described
in equation (14 chapter 4) and figure 6 (from chapter 4). It is shown in figure 27a. According to
Laba and Kennedy (1986),

Figure 7.27 (a) notation for the relationship of ???? ???? (2)
- equations (32 and 33); (b) notation for the
relationship of ???? ???? (2)
- equations (35 and 36);
???? ???? (2)
=
???????? '
???? '
+ ????      (for ???? = 2 ???? '
)         [7.32]
And
???? ???? (2)
=
???????? '
???? '
+
???? 2
+ ???? '
(for ???? > 2 ???? '
)        [7.33]
Also, when a surcharge is added at the top, the lateral pressure at any depth is
???? ???? = ???? ???? (1)

?
= ???? ???? ???? 1
???? Due to soil only

+ ???? ???? (2)
?
Due to the surcharge
[7.34]
According to Laba and Kennedy (1986), ???? ???? (2)
may be expressed (figure 30b) as
???? ???? (2)
= ???? ?
2 ???? ???? ( ???? - sin ???? cos2 ???? ) ?
?
[7.35]
Where
???? = 1.4 -
0.4 ???? '
0.14 ???? = 1          [7.36]
The net active (lateral) pressure distribution on the retaining wall calculated by using equations.
(34, 35 and 36) is shown in figure 29b.
Tie Force
Refer again to figure 29. The tie force per unit length of the wall developed at any depth z is
Page 5

Module 7
(Lecture 27)
RETAINING WALLS

Topics
1.1 RETAINING WALLS WITH METALLIC STRIP
REINFORCEMENT
? Calculation of Active Horizontal and vertical Pressure
? Tie Force
? Factor of Safety Against Tie Failure
? Total Length of Tie
1.2 STEP-BY-STEP DESIGN PROCEDURE (METALLIC STRIP
REINFORCEMENT
? Internal Stability
? External Stability
? Internal Stability Check
? Tie thickness
? Tie length
? External Stability Check
? Check for overturning
? Check for sliding
? Check for bearing capacity

RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT
Reinforced earth walls are flexible walls. Their main components are
1. Backfill, which is granular soil
2. Reinforcing strips, which are thin, wide strips placed at regular intervals
3. A cover on the front face, which is referred to as the skin
Figure 25 is a diagram of a reinforced earth wall. Note that, at any depth, the reinforcing stripes
or ties are placed with a horizontal spacing of ???? ???? center-to-center; the vertical spacing of the
strips or ties is ???? ???? center-to-center. The skin can be constructed with sections of relatively
flexible thin material. Lee et al. (1973) showed that, with a conservative design, a 0.2-in.thick
( Ëœ 5 mm) galvanized steel skin would be enough to hold a wall about 45-50 ft (14-15 m) high.
In most cases, precast concrete slabs can be used as skin. The slabs are grooved to fit into each
other so that soil cannot flow out between the joints. When metal skins are used, they are bolted
together, and reinforcing strips are placed between the skins.

Figure 7.25 Reinforced earth retaining wall
Calculation of Active Horizontal and vertical Pressure
Figure 26a shows a retaining wall with a granular backfill having a unit weight of ???? 1
and a
friction angle of ???? 1
. Below the base of the retaining wall, the in situ soil has been excavated and
reccopacted, with granular soil used as backfill. Below the backfill, the in situ soil has a unit
weight of ???? 2
and a friction angle of ???? 2
, and cohesion of ???? 2
. A surcharge having an intensity of q
per unit area lies atop the retaining wall. The wall has reinforcement ties at depths ???? =
0, ???? ???? , â€¦ . . , ???????? ???? . The height of the wall is ???????? ???? = ???? .

Figure 7.26 Analysis of a reinforced earth retaining wall
According to the Rankine active pressure theory
???? ???? = ???? ???? ???? ???? - 2 ???? ? ???? ????
Where
???? ???? = Rankine active pressure at any depth ????
For dry granular soils with no surcharge at the top, ???? = 0, ???? ???? = ???? 1
???? , and ???? ???? = tan
2
(45 - ???? 1
/2).
Thus
???? ???? (1)
= ???? 1
???? ???? ????          [7.30]
When a surcharge is added at the top, as shown in figure 29,
???? ???? = ???? ???? (1)

?
= ???? 1
???? Due to soil only

+ ???? ???? (2)
?
Due to the surcharge
[7.31]
The magnitude of ???? ???? (2)
can be calculated by using the 2:1 method of stress distribution described
in equation (14 chapter 4) and figure 6 (from chapter 4). It is shown in figure 27a. According to
Laba and Kennedy (1986),

Figure 7.27 (a) notation for the relationship of ???? ???? (2)
- equations (32 and 33); (b) notation for the
relationship of ???? ???? (2)
- equations (35 and 36);
???? ???? (2)
=
???????? '
???? '
+ ????      (for ???? = 2 ???? '
)         [7.32]
And
???? ???? (2)
=
???????? '
???? '
+
???? 2
+ ???? '
(for ???? > 2 ???? '
)        [7.33]
Also, when a surcharge is added at the top, the lateral pressure at any depth is
???? ???? = ???? ???? (1)

?
= ???? ???? ???? 1
???? Due to soil only

+ ???? ???? (2)
?
Due to the surcharge
[7.34]
According to Laba and Kennedy (1986), ???? ???? (2)
may be expressed (figure 30b) as
???? ???? (2)
= ???? ?
2 ???? ???? ( ???? - sin ???? cos2 ???? ) ?
?
[7.35]
Where
???? = 1.4 -
0.4 ???? '
0.14 ???? = 1          [7.36]
The net active (lateral) pressure distribution on the retaining wall calculated by using equations.
(34, 35 and 36) is shown in figure 29b.
Tie Force
Refer again to figure 29. The tie force per unit length of the wall developed at any depth z is

???? = active earth pressure at depth ???? × area of the wall to be supported by the tie
= ( ???? ???? )( ???? ???? ???? ???? )          [7.37]
Factor of Safety Against Tie Failure
The reinforcement ties at each level and thus the walls cold fail by either (a0 tie breaking or (b)
tie pullout.
The factor of safety against tie breaking may be determined as
???????? ( ???? )
=
yield or breaking strength of each tie
maximum tie force in any tie

=
???????? ???? ???? ???? ???? ???? ???? ???? ????           [7.38]
Where
???? = width of each tie
???? = thickness of each tie
???? ???? = yield or breaking strength of the tie material
A factor of safety of about 2.5-3 is generally recommended for ties at all levels.
Reinforcing ties at any depth, z, will fail by pullout if the frictional resistance developed along
their surfaces is less than the force to which the ties are being subjected. The effective length of
the ties along which the frictional resistance is developed may be conservatively taken as the
length that extends beyond the limits of the Rankine active failure zone, which is the zone ???????????? in
figure 29. Line ???????? in figure 29 makes an angle of 45 + ???? 1
/2 with the horizontal. Now, the
maximum friction force ???? ???? that can be realized for a tie at depth z is
???? ???? = 2 ???? ???? ???? ???? ???? tan ???? ????           [7.39]
Where
???? ???? = effective length
???? ???? = effective vertical pressure at a depth ????
???? ???? = soil - tie friction angle
Thus the factor of safety against tie pullout at any depth z is
???????? ( ???? )
=
???? ???? ????            [7.40]
Where ???????? ( ???? )
= factor of safety against tie pullout
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