Summary Sheet

1
Summary Sheet
Session Number
5

Date

09.04.2007

Subject Expert
Dr. M.C. Nataraja Professor Department of Civil
Engineering, Sri Jayachamarajendra College of
Engineering, Mysore 570 006.
Phone[phone] E-mail
nataraja96_at_yahoo.com
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Design and Detailing of Counterfort Retaining wall

• Dr. M.C. NATARAJA

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Counterfort Retaining wall

• When H exceeds about 6m,
• Stem and heel thickness is more
• More bending and more steel
• Cantilever-T type-Uneconomical
• Counterforts-Trapezoidal section
• 1.5m -3m c/c

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Parts of CRW

• Same as that of Cantilever Retaining wall Plus
  Counterfort

Cross section
Plan
5
Design of Stem

• The stem acts as a continuous slab
• Soil pressure acts as the load on the slab.
• Earth pressure varies linearly over the height
• The slab deflects away from the earth face
  between the counterforts
• The bending moment in the stem is maximum at the
  base and reduces towards top.
• But the thickness of the wall is kept constant
  and only the area of steel is reduced.

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Maximum Bending moments for stem

• Maximum ve B.M pl2/16
• (occurring mid-way between counterforts)
• and
• Maximum -ve B.M pl2/12
• (occurring at inner face of counterforts)
• Where l is the clear distance between the
  counterforts
• and p is the intensity of soil pressure

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Design of Toe Slab

• The base widthb 0.6 H to 0.7 H
• The projection1/3 to 1/4 of base width.
• The toe slab is subjected to an upward soil
  reaction and is designed as a cantilever slab
  fixed at the front face of the stem.
• Reinforcement is provided on earth face along the
  length of the toe slab.
• In case the toe slab projection is large i.e. gt
  b/3, front counterforts are provided above the
  toe slab and the slab is designed as a continuous
  horizontal slab spanning between the front
  counterforts.

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Design of Heel Slab

• The heel slab is designed as a continuous slab
  spanning over the counterforts and is subjected
  to downward forces due to weight of soil plus
  self weight of slab and an upward force due to
  soil reaction.
• Maximum ve B.M pl2/16
• (mid-way between counterforts)
• And
• Maximum -ve B.M pl2/12
• (occurring at counterforts)

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Design of Counterforts

• The counterforts are subjected to outward
  reaction from the stem.
• This produces tension along the outer sloping
  face of the counterforts.
• The inner face supporting the stem is in
  compression. Thus counterforts are designed as a
  T-beam of varying depth.
• The main steel provided along the sloping face
  shall be anchored properly at both ends.
• The depth of the counterfort is measured
  perpendicular to the sloping side.

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Behaviour of Counterfort RW

• Important points
• Loads on Wall
• Deflected shape
• Nature of BMs
• Position of steel
• Counterfort details

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PROBLEM-Counterfort Retaining Wall

• A R.C.C. retaining wall with counterforts is
  required to support earth to a height of 7 m
  above the ground level. The top surface of the
  backfill is horizontal. The trial pit taken at
  the site indicates that soil of bearing capacity
  220 kN/m2 is available at a depth of 1.25 m below
  the ground level. The weight of earth is 18 kN/m3
  and angle of repose is 30. The coefficient of
  friction between concrete and soil is 0.58. Use
  concrete M20 and steel grade Fe 415. Design the
  retaining wall.

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• Draw the following
• Cross section of wall near the counterfort
• Cross section of wall between the counterforts
• L/s of stem at the base cutting the counterforts
• Given
• fck 20 N/mm2, fy 415N/mm2, H 7 m above
  G.L, Depth of footing below G.L. 1.25 m, ?
  18 kN/m3,
• µ 0.58, fb SBC 220 kN/m2

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a. Proportioning of Wall Components

• Coefficient of active pressure ka 1/3
• Coefficient of passive pressure kp 3
• The height of the wall above the base
• H 7 1.25 8.25 m.
• Base width 0.6 H to 0.7 H
• (4.95 m to 5.78 m), Say b 5.5 m
• Toe projection b/4 5.5/4 say 1 .2 m
• Assume thickness of vertical wall 250 mm
• Thickness of base slab 450 mm

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• Spacing of counterforts
• l 3.5 (H/?)0.25 3.5 (8.25/18)0.25 2.88 m
• c/c spacing 2.88 0.40 3.28 m say 3 m
• ? Provide counterforts at 3 m c/c.
• Assume width of counterfort 400 mm
• ? clear spacing provided l 3 - 0.4 2.6 m

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Details of wall
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b. Check Stability of Wall
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Stability of walls

• Horizontal earth pressure on full height of wall
• Ph ka?H2 /2 18 x 8.252/(3 x 2) 204.19 kN
• Overturning moment M0
• Ph x H/3 204.19 x 8.25/3 561.52 kN.m.
• Factor of safety against overturning
• ? M / M0 2210.71/561.52 3.94 gt 1.55
• ? safe.

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• Check for sliding
• Total horizontal force tending to slide the wall
• Ph 204.19 kN
• Resisting force ?µ.W 0.58 x 679.25
• 393.97 kN
• ?Factor of safety against sliding
• ?µ.W / Ph 393.97/204.19
• 1.93 gt 1.55 ... safe.

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• Check for pressure distribution at base
• Let x be the distance of R from toe (T),
• ? x ? M / ? W 2210.71 -561.52 /679.25 2.43
  m
• Eccentricitye b/2 - x 5.5/2 - 2.43 0.32 lt
  b/6 (0.91m)
• ?Whole base is under compression.
• Maximum pressure at toe
• pA ?W / b ( 16e/b) 679.25/5.5 ( 1
  60.32/5.5)
• 166.61 kN/m2 lt f b (i.e. SBC 220 kN/m2)
• Minimum pressure at heel
• pD 80.39 kN/m2 compression.

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• Intensity of pressure at junction of stem with
  toe i.e. under B
• pB 80.39 (166.61 - 80.39) x 4.3/5.5
  147.8kN/m2
• Intensity of pressure at junction of stem with
  heel i.e. under C
• Pc 80.39 (166.61 - 80.39) x 4.05/5.5 143.9
  kN/m2

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b) Design of Toe slab

• Max. BMB psf x (moment due to soil pressure -
  moment due to wt. of slab TB
• 1.5 147.8 x 1.22/2 (166.61 - 147.8) x 1.2
  (2/3 x 1.2)
• -(25x 1.2 x 0.45 x 1.2/2) 174.57 kN-m.
• Mu/bd2 1.14 lt 2.76, URS

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b) Design of Toe slab- Contd.,

• To find steel
• pt0.34 lt0.96, A st 1326 mm2, 16 _at_150
• However, provide 16 _at_110 from shear
  considerations.
• Area provided 1827 mm2 , pt0.47
• Development length 47 x 16750 mm
• Distribution steel 0.12 x 1000 x 450/100 540
  mm2
• Provide 12 mm at 200 mm c/c.
• Area provided 565 mm2

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Check for Shear

• Critical section for shear At distance d ( 390
  mm) from the face of the toe
• pE 80.39 (166.61 - 80.39) (4.3 0.39)/5.5
• 153.9kN/m2
• Net vertical shear
• (166.61 153.9) x 0.81/2 - (25 x 0.45 x 0.81)
  120.7 kN.
• Net ultimate shear Vu.max 1.5 x 120.7 181.05
  kN.
• ?v 181.05x 1000/1000x390 0.46 MPa
• pt 100 x 1827/ (1000 x 390) 0.47
• ?uc 0.36 (0.48 - 0.36) x 0.22/0.25
• 0.47N/mm2 gt ?vsafe

d
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(c) Design of Heel Slab

• Continuous slab.
• ? Consider 1 m wide strip near the outer edge D
• The forces acting near the edge are
• Downward wt. of soil18x7.8xl 140.4 kN/m
• Downward wt. of heel slab 25 x 0.45 x 1 11.25
  kN/m
• Upward soil pressure 80.39 kN/m2 80.39 x 1
  80.39 kN/m
• ? Net down force at D 140.4 11.25 - 80.39
  71.26 kN/m
• Also net down force at C 140.4 11.25 - 143.9
  7.75 kN/m
• Mu (psf) pl2 /12 1.5 x 71.26 x 2.62/12 60.2
  kN-m (Near junction of CF)

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Forces on heel slab
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• To find steel
• Mu/bd260.2x106/(1000x3902) 0.39 lt 2.76, URS
• To find steel
• pt0.114 lt0.12GA (Min.), lt0.96,
• Provide 0.12 of GA
• Ast 0.12x1000x450/100 540 mm2
• Provide 12 mm _at_ 200 mm c/c,
• Area provided 565 mm2
• pt 100 x 565/ (1000 x 390) 0.14

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Check for shear (Heel slab)

• Maximum shear Vu,max 1.5 x 71.26 x 2.6/2
  139 kN
• For Pt, 0.14 and M20 concrete, ?uc 0.28
  N/mm2
• ?v Vumax/bd 0.36 N/mm2 , Shear steel is needed
  
• Using 8 mm 2-legged stirrups,
• Spacing0.87x415x100/(0.36-0.28)x1000
• 452 mm lt (0.75 x 390 290 mm or 300 mm )
• Provide 8 mm 2-legged stirrups at 290 mm c/c.
• Provide for 1m x 1m area as shown in figure

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• Area of steel for ve moment
• (Heel slab)
• Maximum ve ultimate moment psf x pl2/16
• 3/4 Mu 0.75 x 60.2 45.15 kN-m.
• Mu/bd2Very small and hence provide minimum
  steel.
• Ast,min 540 mm2
• Provide 12 mm bars at 200 mm c/c.
• Area provided 565 mm2 gt 540 mm2

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• Check the force at junction of heel slab with
  stem
• The intensity of downward force decreases due to
  increases in upward soil reaction. Consider m
  width of the slab at C
• Net downward force 18 x 7.8 25 x 0.45 - 143.9
  7.75 kN/m. ? Provide only minimum reinforcement.
• Distribution steel
• Ast 0.12 x 1000 x 450/100 540 mm2
• Using 12 mm bars, spacing 1000 x 113/468
  241 mm.
• Provide 12 mm at 200 mm c/c.
• Area provided 565 mm2

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(d) Design of Stem (Vertical Slab).

• Continuous slab spanning between the counterforts
  and subjected to earth pressure.
• The intensity of earth pressure
• ph ka ?h 18 x 7.8/346.8 kN/m2
• Area of steel on earth side near counterforts
• Maximum -ve ultimate moment,
• Mu 1.5 x ph 12/12 1.5 x 46.8 x 2.62/12
  39.54 kN.m.
• Required d v (39.54 x 106/(2.76 x 1000)) 119
  mm
• However provide total depth 250 mm
• Mu/bd2 39.54x106/1000x39021.1 lt 2.76, URS

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• To find steel Pt0.34 lt0.96,
• Ast646 mm2, 12 mm _at_ 170 mm c/c,
• However provide 12 mm _at_ 110 mm c/c,
• Area provided 1027.27 mm2,Pt 0.54 .
• As the earth pressure decreases towards the top,
  the spacing of the bars is increased with
  decrease in height.
• Max.ult. shear Vumax 1.5 x 46.8 x 2.6/2
  91.26 kN
• For Pt, 0.54 and M20 concrete ?uc 0.5 N/mm2
  
• ?v Vumax/bd 91.28 x1000/(100X190)0.48 N/mm2,
• Shear steel is not needed and hence safe.

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(e) Design of Counterfort

• At any section at any depth h below the top,
  the total horizontal earth pressure acting on
  the counterfort
• 1/2 kay h2x c/c distance between counterfort
• 18 x h2 x 3 x 1/6 9 h2
• ?B.M. at any depth h 9h2xh/3 3h3
• B.M. at the base at C 3 x 7.83 1423.7 kN.m.
• Ultimate moment Mu 1.5 x 1423.7 2135.60
  kN.m.
• Counterfort acts as a T-beam.
• Even assuming rectangular section,
• d v(2135.6 x 106(2.76 x 400)) 1390 mm

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The effective depth is taken at right angle to
the reinforcement. tan ? 7.8/4.05 1.93, ?
62.5, ? d 4050 sin ? - eff. cover 3535 mm
gt gt 1390 mm Mu/bd22135.6x106/(400x35352) 0.427,
pt0.12, Ast1696mm2 Check for minimum steel
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• Ast.min 0.85 bd/fy 0.85 x 400 x 3535/415
  2896 mm2
• Provided 4- 22 mm 4 - 22 mm,
• Area provided 3041 mm2
• pt 100 x 3041/(400 x 3535) 0.21
• The height h where half of the reinforcement can
  be curtailed is approximately equal to vH
  v7.82.79 m
• Curtail 4 bars at 2.79-Ldt from top i.e,
  2.79-1.03 1.77m from top.

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Design of Horizontal Ties

• The direct pull by the wall on counterfort for 1
  m height at base
• ka?h x c/c distance 1/3x18 x 7.8 x 3 140.4
  kN
• Area of steel required to resist the direct pull
• 1.5 x 140.4 x 103/(0.87 x 415) 583 mm2 per m
  height.
• Using 8 mm 2-legged stirrups, Ast 100 mm2
• spacing 1000 x 100/583 170 mm c/c.
• ? Provide 8 at 170 mm c/c.
• Since the horizontal pressure decreases with h,
  the spacing of stirrups can be increased from 170
  mm c/c to 450 mm c/c towards the top.

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Design of Vertical Ties

• The maximum pull will be exerted at the end of
  heel slab where the net downward force 71.26
  kN/m.
• Total downward force at D
• 71.26 x c/c distance bet. CFs 71.28 x 3
  213.78 kN.
• Required Ast 1.5 x 213.78 x 103/(0.87 x 415)
  888 mm2
• Using 8 mm 2-legged stirrups , Ast 100 mm2
• spacing 1000 x 100/888 110 mm c/c.
• ?Provide 8 mm 2-legged stirrups at 110 mm c/c.
• Increase the spacing of vertical stirrups from
  110 mm c/c to 450 mm c/c towards the end C

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Cross section between counterforts
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Cross section through counterforts
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Backfill
Backfill
Cross section of heel slab
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Thank you very much Good day Dr. M. C. Nataraja