 Open Access
 Total Downloads : 858
 Authors : Sarita Singla, Sakshi Gupta
 Paper ID : IJERTV4IS060935
 Volume & Issue : Volume 04, Issue 06 (June 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS060935
 Published (First Online): 27062015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Optimization of Reinforced Concrete Retaining Walls of Varying Heights using Relieving Platforms
Prof. Sarita Singla Civil Engineering Department PEC University of Technology
Chandigarh, India
Er. Sakshi Gupta

Structural Engineering PEC University of Technology
Chandigarh, India
Abstract During development of land, one often comes across with the challenge of creating a difference in terrain elevation over an arbitrary horizontal distance. This can often be done by creating slopes or by constructing retaining walls. Retaining walls are structures that are constructed to retail soil or any such materials which are unable to stand vertically by themselves.
In this paper the study of the behaviour and optimal design of three types of reinforced concrete walls of varying heights namely cantilever retaining wall, counterfort retaining wall and retaining wall with relieving platforms is done. Cost against each optimal design of wall for particular height is calculated by using the volume of concrete and the amount of steel. Amidst the cost estimates of all the three optimal designs for particular height, a comparative study is carried out and the alternative with the least cost estimate is chosen as the best design solution.
Keywords Reinforced concrete retaining walls, cantilever retaining wall, counterfort retaining wall, retaining wall with relieving platforms, optimal design

INTRODUCTION

A retaining wall is a structure designed to sustain the earth behind it. It retains a steep faced slope of an earth mass against rupture of slopes in cuts and fills and against sliding down. The retained material exerts a push on structure and this tends to overturn and slide it.
Besides the selfweight, the main predominant force for analysis and design of the retaining wall is lateral earth pressure. The lateral earth pressure behind the wall depends on the angle of internal friction and the cohesive strength of the retained material, as well as the direction and magnitude of movement of the stems. Its distribution is typically triangular, least at the top of the wall and increasing towards the bottom. The earth pressure could push the wall forward or overturn it if not properly addressed. Retaining walls are encountered and constructed in various fields of engineering such as roads, harbours, dams, subways, railroads, tunnels, mines, and military fortifications.
This paper deals with following three types of reinforced concrete retaining walls namely

Cantilever retaining wall: The wall consists of vertical stem and base slab made up of two distinct regions:
heel slab and toe slab. These walls cantilever loads (like a beam) to a large, structural footing, converting horizontal pressures from behind the wall to vertical pressures on the ground below. Since the backfill acts on the base, providing most of the dead weight, the requirement of construction materials for this wall type is much less than a traditional gravity wall.

Counterfort retaining wall: To improve the resistance against lateral loads, sometimes cantilever retaining walls are provided with walls perpendicular to the stem. Introducing transverse supports reduces bending moments, when the heights are large thus decreasing the size of concrete components and steel requirements. In this study both back and front counterforts are provided. The counterforts subdivide the vertical slab into rectangular panels and support them on two sides and themselves behave essentially as vertical cantilever beams of Tsection and varying depth.

Retaining wall with relieving platforms: The concept of providing pressure relief platforms towards the backfill side of retaining wall reduces the earth pressure on the wall which make the pressure diagram discontinuous at the level of the platform which results in reducing the thickness of the wall and ultimately to get an economic design. Also, the relieving platform carries the weight of the soil above it and any surcharge loading, transferring them as a 'relieving' moment to the vertical stem.
Fig.1 Types of Reinforced Concrete Retaining Walls
II OBJECTIVES
The primary objectives of the study are as under

To study the behaviour of retaining wall through bending moment and shear force in various components.

To design the retaining wall for the optimal cost.

Cost comparison of all the three types of retaining walls and choosing the best alternative for particular height.

Providing approximate design equations for different design variables.

DESIGN OF RETAINING WALL Technically while designing, all the necessary parameters
and requirements (if any) are considered and all the possible solutions are generated. Then a thorough analysis and calculations are carried out considering all the parameters especially cost involved and the risk and the uncertainties involved. Then the solution with the optimal cost is chosen as the best solution. Thus, it is overall a rigorous decision making process.
The design of retaining wall includes the following steps:

Fixation of the base width and other wall dimensions

Performing stability checks and computation of maximum and minimum bearing pressures.

Design of various parts like stem, toe slab, heel slab, relieving platforms, back counterfort and front counterfort.
TABLE I RETAINING WALL DESIGN INPUT PARAMETERS
Coefficient of active earth pressure, Ca
0.333
Coefficient of passive earth pressure, Cp
3
Depth of foundation, hf
1.2 m
Equivalent height of surcharge, p
1.2 m
Safe bearing capacity
150 kN/m2
Angle of friction of backfill,
30
Coefficient of friction at base of the wall,
0.5
Grade of concrete, fck
M25
Grade of steel, fy
Fe500
Unit weight of soil, s
18 kN/m3
Unit weight of concrete, c
25 kN/m3
In design of retaining wall, Rankines theory is used for calculation of coefficient of lateral earth pressure. In design of cantilever and counterfort retaining wall, a shear key is provided at the base except for three 3 m height of retaining wall. In case of retaining wall with relieving platform, two relieving platforms are taken up to height of 7 m and above 7 m three relieving platforms are taken in the design to achieve economical design. The relieving platforms are provided at H/3 height.
Where H = Height of retaining wall + depth of foundation
+ height of surcharge
Curtailment of bars is done at h/3 and 2h/3 height of retaining wall.
Where h = Height of retaining wall + depth of foundation For the analysis purpose three reinforced concrete
retaining walls namely cantilever retaining wall, counterfort retaining wall and retaining wall with relieving platforms with height ranging from 3 m to 15 m with interval of 2 m are considered except cantilever retaining wall with 15m as safe bearing capacity used in the design is 150 kN/m2 which is less. Length of relieving platform is kept equal to length heel slab for analysis purpose.


DESIN DIMENSION VARIABLES Figure1 shows the design dimension variables of three
types of reinforced concrete retaining walls with varying
heights.

Cantilever Retaining Wall
Thickness of base slab (x1); thickness of stem at the bottom (x2); length of toe slab (x3)

Counterfort Retaining Wall
Thickness of base slab (x1); thickness of stem at the bottom (x2); length of toe slab (x3); thickness of counterfort (x4); Spacing between counterforts (x5)

Retaining Wall with Relieving Platforms
Thickness of base slab (x1); thickness of stem at the bottom (x2); length of toe slab (x3); thickness of relieving platform (x4)


STABILITY CHECKS
The following stability checks are used in the design of retaining wall:

Eccentricity of the resultant reaction force should lie between 0 and base width/6.

Factor of safety against sliding is taken greater than 1.5.

Factor of safety against overturning is also taken greater than 1.5.

The maximum and minimum bearing pressure is taken greater than 0 and less than safe bearing capacity.

Maximum and minimum reinforcement percentage and reinforcement spacing is taken as per IS 456:2000 Code.

Restrictions on maximum shear stress in different parts are based on concrete grade as per IS 456:2000 code.


FORMULA FOR OPTIMAL COST DESIGN
As mentioned in the objective, the design with the optimal cost is chosen as the best solution, the formula involved in calculation of the optimal cost is given below:
Optimal Cost = (Volume of concrete * Cost of concrete per
m3) + (Amount of steel in kg *cost of steel per kg)

RESULTS AND DISCUSSIONS
In the present study, the behaviour of retaining walls is studied and cost comparison is done for three types of retaining wall of varying heights. The results are compared in tabular form and graphically for the analysis of the retaining wall
TABLE III BENDING MOMENT IN VARIOUS COMPONENTS OF COUNTERFORT RETAINING WALL

Variation of Bending moment with height
From table 2 and figure 2, it is evident that in case of cantilever retaining wall bending moment increases with increase in the height of the retaining wall because with increase in height lateral earth pressure increases resulting in increase in bending moment. The percentage increase in the bending moment in stem, toe and heel varies from 64.2% – 172.5%, 62.1% – 504.5% and 39.6% – 170.8%.
TABLE II BENDING MOMENT IN VARIOUS COMPONENTS OF CANTILEVER RETAINING WALL
Height of Retaining wall (m)
Bending moment in stem (kNm)
Bending moment in toe (kNm)
Bending moment in heel (kNm)
3
170.942
36.8
91.23
5
467.464
222.577
247.058
7
960.881
550.491
474.699
9
1758.96
1036.705
951.207
11
2830.19
1680.057
1683.307
15
4358.744
2811.87
2349.926
Fig.2 Bending moment in various components of Cantilever Retaining Wall
From table 3 and figure 3, it is evident that in counterfort retaining wall bending moment increases with increase in the height of the retaining wall in case of back counterfort and front counterfort whereas bending moment decreases in case of toe slab and heel slab. In stem bending moment increases up to a height of 9m then decreases because as the height increases thickness of counterfort increases and spacing between counterforts decreases.
Height of Retaini ng wall
(m)
Bending Moment (kNm)
Stem
Toe slab
Heel slab
Back counter
fort
Front counter
fort
3
20.76
96.166
58.929
221.638
78.07
5
28.094
93.824
65.364
795.799
443.754
7
32.361
84.369
53.061
1906.89
988.555
9
37.446
80.24
46.843
3670.486
1899.488
11
36.843
66.323
46.646
6141.615
3542.535
13
23.989
37.258
45.954
8660.018
6468.78
15
21.526
29.431
41.625
12856
9852.375
Fig.3 Bending moment in various components of Counterfort Retaining Wall
From table 4 and figure 4, it is evident that in case of retaining wall with relieving platforms bending moment in each component increases with increase in the height of the retaining wall except in stem and relieving platform in the case of retaining wall of 9 m height because in 9 m number of relieving platforms are increased from 2 to 3. The percentage increase in the bending moment in stem, toe, heel and relieving platform varies from 61.2% – 324.75%, 56.4% –
319.1%, 4.4% – 203.1% and 18.4% – 114.2%
.
TABLE IV BENDING MOMENT IN VARIOUS COMPONENTS OF RETAINING WALL WITH RELIEVING PLATFORMS
Height of Retaining wall (m)
Bending Moment (kNm)
Stem
Toe slab
Heel slab
Relieving platforms
3
22.845
20.269
9.57
26.436
5
97.035
84.93
17.05
56.274
7
224.88
207.24
51.677
120.54
9
216.6
310.549
146.568
118.023
11
582.9
611.586
155.412
152.139
13
1054.73
1036.15
166.028
188.155
15
1699.5
1619.98
173.2
222.731
Fig.4 Bending moment in various components of Retaining Wall with Relieving Platforms

Variation of Shear force with height
From table 5 and figure 5, it is evident that in case of cantilever retaining wall shear force increases with increase in the height of the retaining wall because with increase in height lateral earth pressure increases resulting in increase in shear force. The percentage increase in the shear force in stem, toe and heel varies from 33.3% – 91.75%, 30.9% – 128.9% and 26.6% – 93.5%.
TABLE V SHEAR FORCE IN VARIOUS COMPONENTS OF CANTILEVER RETAINING WALL
Height of Retaining wall (m)
Shear force (kN)
Shear force in stem (kN
m)
Shear force in toe (kN
m)
Shear force in heel (kN
m)
3
110.684
114.009
127.486
5
212.236
260.892
246.694
7
338.1067
412.142
368.037
9
500.072
571.768
497.686
11
695.949
779.437
685.543
13
927.655
1019.738
867.493
Fig.5 Shear force in various components of Cantilever Retaining Wall
From table 6 and figure 6, it is proved that in counterfort retaining wall shear force increases with increase in the
height of the retaining wall in heel slab, back counterfort and front counterfort. In case of stem shear force increases up to a height of 11m and then decreases because as the height increases thickness of counterfort increases and spacing between counterforts decreases. Similarly, in case of toe slab shear force increases up to a height of 9m and then decreases.
TABLE VI SHEAR FORCE IN VARIOUS COMPONENTS OF COUNTERFORT RETAINING WALL
Heigh t of Retai ning wall
(m)
Shear force in kN
Stem
Toe slab
Heel slab
Back counter
fort
Front counterf ort
3
53.805
249.113
65.523
181.34
81.663
5
73.608
245.826
111.956
410.844
165.62
7
89.271
232.74
112.313
724.72
315.369
9
105.979
227.121
120.11
1106.972
509.483
11
113.945
205.121
142.296
1537.32
731.817
13
98.583
153.116
274.143
1854
765.497
15
93.351
135.835
282.732
2405.31
1008.46
Fig.6 Shear force in various components of Counterfort Retaining Wall
From table 6 and figure 6, it is evident that in case of retaining wall with relieving platforms shear force in each component increases with increase in the height of the retaining wall except in relieving platform in the case of retaining wall of 9 m height because in 9 m number of relieving platforms are increased from 2 to 3. The percentage increase in the bending moment in stem, toe, heel and relieving platform varies from 8.9% – 100.7%, 25.8% –
116.6%, 0.5% – 75.3% and 15.3% – 72.1%.
TABLE VII SHEAR FORCE IN VARIOUS COMPONENTS OF RETAINING WALL WITH RELIEVING PLATFORMS
Height of
Retaining wall (m)
Shear force in kN
Stem
Toe slab
Heel slab
Relieving platform
3
34.715
77.621
32.665
53.405
5
69.675
168.124
42.185
91.875
7
117.05
274.792
78.417
152.101
9
127.482
345.503
180.337
141.345
11
177.675
482.107
180.632
173.873
13
238.473
633.104
183.868
206.763
15
307.005
797.849
185.278
238.215
Fig.7 Shear force in various components of Retaining wall with relieving platforms

Comparison of Optimal Cost
It is very evident from Tables 8, 9 and 10 and figures 8, 9 and 10 that the optimal cost increases with increase in height for all the three types of retaining walls, but the increase in optimal cost may vary from wall to wall. Among all the cases the optimal cost required is least in case of retaining wall with relieving platform because presence of relief platforms towards the backfill side of retaining wall reduces the earth pressure on the wall which make the pressure diagram discontinuous at the level of the platform which results in reducing the thickness of the wall and ultimately to get an economic design.
The percentage reduction in retaining walls with relieving platform from counterfort retaining wall varies from 2% to 48% for all heights. While the reduction in retaining walls with relieving platform from cantilever retaining wall varies from 31% to 52% for all heights respectively.
TABLE VIII COMPARISON OF OPTIMAL COST
Height of Retaining wall (m)
Optimal cost in Rs
Cantilever retaining
wall
Counterfort retaining wall
Retaining wall with relieving platforms
3
13410
11999
9160
5
29666
23817
19026
7
53964
36842
35859
9
96167
58929
53735
11
142574
90560
73794
13
199583
166280
101573
15
250626
135896
300000
250000
200000
150000
100000
50000
0
3 5 7 9 11 13 15
Height of wall (m)
Cantilever
Relieving Platform
Counterfort
Fig. 7. Comparison of Spectral Acceleration in Xdirection
Fig. 8. Comparison of Spectral Acceleration in Zdirection
D. Base shear
Amount of steel (kg)
Fig. 8 Comparison of Optimal cost
Fig.8 Shear force in various components of Retaining wall with relieving platforms

Approximate Design Equations
Based on optimal solution obtained from all types of the wall, several approximate design equations are made for design dimension variables given in tables 9, 10, 11 and 12
and figures 9, 10 and 11.
TABLE IX DIMENSIONS FOR OPTIMAL SOLUTION FOR CANTILEVER RETAINING WALL
Height of Retaining
wall (m)
x1
x2
x3
l
3
0.3
0.32
0.62
2.7
5
0.43
0.545
1.63
4
7
0.625
0.715
2.49
5.51
9
0.725
0.965
3.53
7.7
11
0.93
1.115
4.26
9.4
13
1.03
1.395
5.55
11.13
Where x1, x2, x3 and l are base slab thickness, thickness of stem at the bottom, toe slab length and length of retaining wall.
TABLE X DIMENSIONS FOR OPTIMAL SOLUTION FOR COUNTERFORT RETAINING WALL
Height of Retaining wall (m)
x1
x2
x3
x4
x5
l
3
0.22
0.18
0.56
0.175
2.49
2.7
5
0.255
0.22
1.36
0.18
2.47
4
7
0.27
0.23
2
0.275
2.45
5.77
9
028
0.295
2.75
0.28
2.4
7.65
11
0.335
0.32
3.81
0.38
2.32
9.1
13
0.38
0.36
5.64
0.6
2.06
9.93
15
0.4
0.4
6.92
0.74
2
11.57
Where x1, x2, x3, x4, x5 and l are base slab thickness, thickness of stem at the bottom, toe slab length, counterfort thickness, counterfort spacing and length of retaining wall.
TABLE XI DIMENSIONS FOR OPTIMAL SOLUTION FOR RETAINING WALL WITH RELIEVING PLATFORMS
Height of Retaining wall (m)
x1
x2
x3
x4
l
3
0.165
0.2
0.5
0.185
1.66
5
0.28
0.315
0.96
0.25
2.5
7
0.33
0.465
1.45
0.36
3.5
9
052
0.63
1.77
0.26
4.07
11
0.65
0.635
2.505
0.325
4.89
13
0.685
0.7
3.25
0.365
5.77
15
0.75
078
4.06
0.38
6.71
Where x1, x2, x3 and l are base slab thickness, thickness of stem at the bottom, toe slab length, relieving platform and length of retaining wall.
Fig.9 Dimensions for optimal solution for cantilever retaining wall
14
12
10
8
6
4
2
0
3
5
7
9
11 13 15
Height of wall (m)
Base slab thickness Stem thickness
Toe slab length
Clear Counterfort spacing
Length of retaining wall
Wall dimensions (m)
Fig.10 Dimensions for optimal solution for counterfort retaining wall
Fig.11 Dimensions for optimal solution for retaining wall with relieving platforms
TABLE XII APPROXIMATE DESIGN EQUATIONS FOR DESIGN DIMENSION VARIABLE
Wall/Slab thickness
Approximate design equations
1. Cantilever retaining
wall
Base slab thickness x1, m
0.15 h + 0.1483
Stem base thickness x2, m
0.2096 h + 0.109
Toe slab length x3, m
0.962 h – 0.3587
Length of retaining wall (l),
m
1.405 h + 1.26, for h < 8 m
1.715 h + 5.98, for h >8 m
2. Counterfort
retaining wall
Base slab thickness x1, m
0.017 h + 0.215, for h < 9 m
0.0405 h + 0.2475, for h > 9 m
Stem base thickness x2, m
0.04 h + 0.14, for h< 6m
0.0215 h + 0.275, for h> 6 m
Toe slab thickness x3, m
0.721 h – 0.135, for h < 9 m
1.565 h + 2.3333 , for h > 9 m
Counterfort thickness x4, m
0.005 h + 0.27, for h= 3 m 5 m and 7 m 9 m
0.095 h + 0.085, for h= 5 m 7 m
0.16 h + 0.1, for h > 9 m
Counterfort spacing x5, m
0.0811 h + 2.6443
Length of retaining wall l, m
1.4896 h + 1.2829
3. Retaining wall
with relieving platform
Base slab thickness x1, m
0.103 h + 0.0707
Stem base thickness x2, m
0.1325 h + 0.0617, for h< 8m
0.0515 h + 0.5575, for h> 8 m
Toe slab thickness x3, m
0.475 h + 0.02, for h < 8 m
0.7615 h + 0.9925, for h > 8 m
Relieving platform x4, m
0.0875 h + 0.09, for h < 8 m
0.04 h + 0.2325, for h > 8 m
Length of retaining wall l, m
0.8243 h + 0.86


CONCLUSIONS
The following conclusions are made from the present study:

The retaining wall with relieving platform is proved to be most cost effective and advantageous over the cantilever and counterfort retaining wall.

Due to discontinuous lateral earth pressure diagram in case of retaining wall with relieving platform, there is better stability in the retaining wall.

Reduction in crosssectional in retaining wall with relieving platforms area reduces the requirement of the construction material like volume of concrete and amount of steel thus reducing overall cost.


REFERENCES

Chaudhuri P Ray, Garg A. K. Design of retaining walls with relieving shelves IRC Journal, Vol35, page:289 325,1973.

Bentler J.G., Labuz, J. F., Performance of a cantilever retaining wall. Journal of geotechnical and geo environmental engineering, Page: 10621070, 2006.

Padhye R. D, Ullagaddi P. B Analysis of retaining wall with pressure relief shelf by Coulombs Method Proceedings of Indian Geotechnical Conference, Paper No. K106, Page: 671 673, 1517 Dec 2011.

Patil S. M, Wagh K. S Reduction in construction material: Effect of the provision of the loft behind the cantilever retaining wall Indian Geotechnical Conference, Page: 227230, 1618Dec2010.

Donkada Shravya, Menon Devdas Optimal design of reinforced concrete retaining walls The Indian Concrete Journal, April 2012.

Sharma Chetan, Baradiya Vijay, Evaluation of the effect of lateral soil pressure on cantilever retaining wall with soil type variation IOSR Journal of Mechanical and Civil Engineering, Volume 11, Issue 2, Ver. III, Page: 3642, Mar Apr 2014.

I.S. 456:2000 Plain and Reinforced Concrete Code of Practice (Fourth Revision)

Dr. Syal I.C., Reinforced concrete structures, S.Chand and company Pvt. Ltd., New Delhi, 2013.

Ramamrutham S. And Narayan R. Retaining Walls, Design of Reinforced Concrete Structures (Conforming To IS 456), Fifteenth Revised and Enlarged Edition.
WHAT IS THE PARAMETER FOR Fck IN RETAINING WALL WHERE H=2.5M ,M20 CONCRETE Fe=415
SBC =20T/M TO THE POWER OF 2
ANGEL OF REPOSE 30°