DOI : 10.17577/IJERTV4IS020033
- Open Access
- Total Downloads : 4008
- Authors : S. S Patil, A. A. R. Bagban
- Paper ID : IJERTV4IS020033
- Volume & Issue : Volume 04, Issue 02 (February 2015)
- Published (First Online): 04-02-2015
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Analysis and Design of Stepped Cantilever Retaining Wall
Dr. S.S Patil1
1Professor and Head, Civil Engineering Department, Walchand Insitute of Technology, Solapur, Maharashtra, India
Abstract A retaining wall is one of the most important types of retaining structures. It is extensively used in variety of situations such as highway engineering, railway engineering, bridge engineering and irrigation engineering. Reinforced concrete retaining walls have a vertical or inclined stem cast with base slab. These are considered suitable up to a height of 6m. It resists lateral earth pressure by cantilever action of stem, toe slab and heel slab. The tendency of wall to slide forward due to lateral earth pressure should be investigated and a factor of safety of 1.5 shall be provided against sliding. Cantilever retaining walls are found best up to a height of 6m.For greater heights earth pressure due to retained fill will be higher due to lever arm effect, higher moments are produced at base, which leads to higher section for stability design as well as structural design. This proves to be an uneconomical design. As an alternative to this, one may go for counter fort retaining wall, which demands greater base area as well as steel. As a solution to this difficulty, a new approach that is to minimize effect of forces coming from retained fill , short reinforced concrete members in the form of cantilever steps are cast along the stem on the retaining face. Addition of these steps would counterbalance the locally appearing forces and will result into lesser moment and shear forces along the stem. Also it will reduce the bending action that is pressure below the base.
The objectives of the study are
To reduce the stresses on the retaining face of the cantilever retaining w all, it is proposed to introduce reinforced concrete steps along the stem.
-
Decide the most economical location of step along length and also along height of w all from number of trials.
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Decide cross section of the R. C. step as per the stresses due to frictional forces in step.
A.A.R.Bagban2
2 Post Graduate Student, Walchand Institute of Technology, Solapur. Maharashtra, India
land reclamation and coastal engineering etc. Reinforced concrete retaining walls have a vertical or inclined stem cast monolithic with a base slab. These are considered suitable up to a height of 6m. It resists the lateral earth pressure by cantilever action of the stem, toe slab and heel slab.
Necessary reinforcements are provided to take care of the flexural stresses. The tendency of the wall to slide forward due to lateral earth pressure should be investigated and if a factor of safety is insufficient, a shear key should be designed to prevent lateral movement of the structure.
-
Cantilever Retaining Walls
These walls are made of reinforced cement concrete. It consists of a thin stem and a base slab cast monolithically. This type of wall is found to be economical up to a height 6 to 8m.
Surcharge
Backfill
Stem
-
-
Stability analysis of Cantilever retaining w all with steps for unit w idth w ill be done. Check for minimum and maximum stresses w ill be observed.
-
Cost comparison shall be carried out for these three
Toe
Fig.1
Heel
different alternatives to give most economical retaining w all type.
Index Terms Mechanism of Concrete plates; Concrete quantity; Steel reinforcement and Cost comparison of Counter fort and Stepped Cantilever retaining wall.
-
INTRODUCTION
A retaining wall is one of the most important types of soil retaining structures. The primary purpose of retaining wall is to retain earth or other material at or near vertical position. It is extensively used in variety of situations such as highway engineering, railway engineering, bridge engineering, dock and harbor engineering, irrigation engineering,
-
Counter fort Retaining Walls
These walls have thin vertical slabs, known as counter forts, spaced across vertical stem at regular intervals. The counter forts tie the vertical stem with the base slab. Thus the vertical stem and the base sla b span between the counter forts. The purpose of providing the counter forts is to reduce the shear force and bending moments in the vertical stem and the base slab. The counter fort retaining walls are economical for a height more than 6 to 8m.
Face Slab
Toe Slab
Fig.2
Heel Slab
Counter forts
pressure which resists complete ly the sliding tendency of wall. A factor of safety of 1.5 is used against sliding.
Bending failure
The stem AB will bend as cantilever so that tensile face will be towards the soil face in case if there is no backfill, where as tensile face will be to wards the water face in case there is backfill. The critical section will be at E and B, where crack may occur at if it is not properly reinforced. The soil side slab will have net pressure acting downwards , and will bent as a cantilever having tensile fac e at top for retaining wall, at the same time the heel slab will be subjected to net upward pressure causing tensile face at bottom. The thickness of stem, toe slab, and heel slab must be sufficient to withstand compressive stresses due to bending also; the stem thickness must
-
-
ANALYSIS OF RETAINING WALLS
-
Cantilever retaining wall 1) Stability
Figure 2.1 shows a cantilever retaining wall subjected to following forces:
Fig.3: Mechanism of Cantilever Retaining Wall
-
Weight W1 of the stem.
-
Weight W2 of the base slab.
-
Weight W3 of the column of soil supported on heel slab.
-
Weight W4 of the soil supported on toe slab.
-
Horizontal force Pa equal to active earth pressure acting at H/3 above base slab.
-
Modes of Failure of a Retaining Wall Overturning about A
The most hazardous mode of failure of retaining wall is due to overturning because of unbalanced moments. Here, a minimum factor of safety is used.
Sliding
The horizontal force tends to slid e the stem and wall away from fill. The tendency to resist this is achieved by the friction at the base. Here, if the wall is found to unsafe against sliding, shear key below the base is provided. Such a key develops passive
be check for uncracked section.
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Design Principal of Cantilever Retaining Wall
The various dimensions of wall are so proportioned that the various failure criteria discussed above are taken care of. The design of wall consist of the fixation of base width, design of stem, design of toe slab, design of heel slab.
Fixation of base width
The base width of wall is so chosen that the resultant of forces remain within middle third of base slab, the uplift pressure is zero at heel slab side also it should be safe from consideration of sliding.
Design of stem
The vertical stem is designed as cantilever for triangular loading with Ka h as base of triangle h as height of it. The main reinforcement is provided at 0.3 % of the area o f cross section along the length of wall.
Design of toe slab
I t i s a l s o d e s i g n a s a c a nt i l e v e r b e a m o r s l a b . T he ma i n r e i n fo r c e me n t i s p r o vi d e d a t l o we r f a c e o r b o t t o m s i d e a s up w a r d s o i l p r e s s ur e l o a d i s a c t i n g o n t ha t f a c e . T hi c k ne s s i s c h e c ke d f o r m a x i mu m c a n t i l e v e r mo me n t a nd d e fl e c t i o n c r i t e r io n.
Design of heel slab
It is also design as a cantilever beam or slab. The main reinforcement is provided at the upper face or top side of heel slab as active load is acting there in form of overburden pr essure. The design reinforcement for effective moment due to upward soil pressure should also provide at bottom side of heel slab. The thickness is checked for maximum cantilever moment and deflection criterion for cantilever action.
-
-
-
Analysis of counter-fort retaining wall
The counter forts support both the vertical stem as well as base slab. Design principles for various
component parts are discussed below in brief. The same criterion is adopted for fixing the base width as cantilever retaining wall.
-
Design of stem
Unlike the stem of cantilever retaining wall, the stem of counter fort retaining wall acts as a continuous slab supported on counters forts. Due to varying pressure over the height of stern, the stem slab deflects outwards and henc e main reinforcement is provided along the length of the wall as per design conditions.
Pc – Effect of counter fort
Lc – Spacing of counter forts along length of wall
Fig.4: Mechanism of Counter fort Retaining Wall
The reaction of the stem is taken by the counter forts, to which it is firmly anchored. The maximum bending moment occurs at Base. The uniformly distributed earth pressure load or water pressure load is calculated for unit height.
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Design of Heel slab
The action is similar that of stem. The Heel slab is subjected to the downward load due to weight of soil and self weight, upward load due to upward soil pressure below heel slab. The maximum net pressure is found to act on a strip of unit width near outer edge, since the upward soil react ion is minimum there, the total reaction from the heel slab is transferred to the counter forts, and this load helps to provide a balancing moment against its overturning. The heel slab is firmly attached to the counter forts by means of vertical ties.
-
Design of Toe slab
The action of Heel slab is similar to that of cantilever retaining wall.
-
Design of Counter forts
The counter fort takes reactions, both from the stem as well as Heel slab. As sh own in fig. 4.2, the counter forts are subjected to tensile stresses along the outer face AC of the counter forts. The angle ABC between stem and slab has a tendency to increase from 900, and counter forts resist this tendency. Thus the counter fort may be considered to bend as a cantilever, fixed at BC .
T he counter fort acts as an inverted T beam of varying rib depth. The maxi mum depth of this T beam is at the j unction B . T he depth is measured perpendicular to the sloping face AB, i. e. depth dl=BB 1. At B, This depth thus goes on decreasing towards Al where the bending moment also decreases. The width of counter fort is kept constant throughout its height, main reinforcement is provided parallel to AC . T he faces AB and B C of the counter fort remain in compression. The compressive stresses on face AB a re counterbalanced by the vertical upward reaction transferred by the slab. In addition to the main reinforcement, the counter forts are j ointed firmly to the stem and base slab by horizontal and vertical ties respectively.
-
-
Stepped cantilever retaining wall (New Approach)
For retaining back fill of heights more than 10 – 11 meters. The conventional walls like cantilever and counter fort becomes very massive and al most uneconomical hence a suitable modification to these walls so as to economize the reta ining wall construction. The proposed modified alternative is
Stepped cantilever retaining wall. The general outline of concept will be clear from figure as shown.
P – Stabilizing frictional force Pa – Active pressure component
L – Spacing of concrete steps along length of wall Fig.5Mechanism of stepped cantilever retaining wall
T he main concept in this type is supporting the high ste m at critical points indirectly by means of pulling force developed due to surface friction of concrete steps with backfill. Here the effect of self weight of these steps in stabilizing wall against active pressure is not considered as it may be negligible.
C o n v e n t i o n a l l y i n c a s e o f s h e e t p i l e w a l l s , t h e r e w a s u s e o f a n c h o r r o d s a n d t h e c o n c r e t e p l a t e s o r c o n c r e t e d e a d m a n w a s u s e d t o d e v e l o p f r i c t i o n a l f o r c e . I n c a s e o f s h e e t p i l e w a l l w i t h v e r t i c a l c o n c r e t e p l a t e s t h e m e c h a n i s m o f p u l l i n g f o r c e w a s d u e t o p a s s i v e r e s i s t a n c e o f s o i l m a s s b o u n d e d b y h e i g h t o f c o n c r e t e w a l l
a n d i n t h a t c a s e t h e r o l e o f c o n c r e t e w a l l w a s d i f f e r e n t f r o m f r i c t i o n a l r e s i s t a n c e f u n c t i o n . I n c a s e o f s h e e t p i l e w a l l s t h e t h i c k n e s s o f s t e m w a s v e r y s m a l l b u t i t i s c o n t i n u o u s w a l l w i t h m e m b r a n e a c t i o n t h a n b e a m/ s l a b a c t i o n b u t i n t h i s c a s e , t h e s e c o n c r e t e s t e p s a r e u s e d a s s u p p o r t i n g m e c h a n i s m f o r c o n v e n t i o n a l c a n t i l e v e r w a l l w h i c h g i v e s r e l a t i v e l y l e s s d i me n s i o n s f o r a s s u m e d s l a b b e a m m e c h a n i s m t h a n c o n v e n t i o n a l d e s i g n a p p r o a c h .
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Design Principles
Design principles for various component parts are discussed below in brief. T he procedu re of analysis is sa me as cantilever retaining wall but their preliminary dimensi ons given will be based on load distribution assume d for actual analysis. Like any other analysis and design this will be Iterative ( trial and error) method, the preliminary d imensions ma y be approximately gi ven as half of that for purely cantilever wall with so me exiting thumb rules.
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Fixation of base width
I n t hi s ca s e i t i s no t ne c e s sar y t ha t t he b a se wi d t h o f wa l l i s s o c ho s e n t ha t t he re s ult a nt o f fo rc e s r e ma i n wi t h i n mi d dl e t hird a nd the mi ni mu m ( up l i ft) pre s s ur e at t oe i s z ero b ut t hes e d i me ns i o ns c a n b e c ho se n a ppro xi ma t e l y wi t hout t he s e c he c ks.
-
Design of stem
The vertical stem is designed as cantilever for triangular loading but reinforcement will be pro vided from actual modified pressure diagram due to restoring force developed by concrete steps. Distribution reinforcement may be provided as per standards.
-
Design of Toe slab
It is also designed as a cantilever slab/beam. Reinforcement is provided at lower face. There will major reduction in depth and steel reinforcement in toe and heel slab due to reduction in the active pressure and addition in self -weight of wall. This will effectively economize the wall construction. Thickness is checked for the maximum cantilever moment.
-
Design of Heel slab
It is also designed as a cantilever. Reinforcement is provided at the upper face. Thickness is checked for the maximum cantilever moment.
-
Design of concrete steps
The concrete steps will be plac ed along length at suitable spacing L. The mechanism of friction generation is fully dependant on overburden load i.e. depth of step from top of wall hence the step provided at more depth will give better results. The one more effective element in friction development is embedment length and width of step. The overlaying
or overlapping of steps and embedment in various pressure zones like passive or rest will also be important. These steps will act as free cantilevers spanning from stem or somewhat like pla tes supported on spring or elastic media depending upon degree of compaction of backfill. These assumptions dominate its design or depth t stem and free end. If steps assumed as slab strips supported on elastic media then their depth and steel reinforceme nt for moment will be less than its minimum depth as per standards and steel required for tensile forces developed due to frictional resistance.
-
Calculation of frictional resistance offered by plate
The concrete plates are inserted in compacted backfill. They will develop frictional force along contact planes of concrete and soil due to overburden pressure and compaction. This frictional force will act as indirect stabilizing force for overturning retaining wall and will pull wall inside.
Mechanism
The concrete plate separated from stem inserte d in soil is as shown in figure 4.
L
Displaced stem Active state zone
Le Effective length of plate
Fig.6: Mechanism of step
The effective frictional p ressure=
Coefficient of friction x height of backfill on plate x dry density of backfill.
Effective length of plate =
Length of plate beyond active zone.
Effective frictional force =
Width of plate x effective length of plate x 2
x Effective frictional pressure .
-
Finalization of Step location
For actual analysis to decide location of step along length and along height of wall is most important task as it may hamper most of assumptions. Hence the length of step immersed in backfi ll was kept constant and the location of plate along length of wall was fixed from number of trails for stability. For finalizing the location of step along height of wall, the number of trials is taken starting from half of height and with interval of 500 mm. The stability analysis of each wall is done and concret e quantity, steel reinforcement are compared. The most economical wall is selected for final comparison as alternative with other retaining wall types.
The following table shows all aspects of stepped cantilever wall for various step heights from top of wall. The comparison is also shown graphically by subsequent graphs for each height.
1. Stepped retaining wall of height 6m
Assumptions
-
Back fill is enough compacted.
-
Step length embedded in backfill – 3.5m 3.Step dimensions – 400 x 300 mm
Table 1: Stability analysis and cost comparison
Step from top m.
Width of toe slab
Width of heel slab
Depth of base slab
Total base slab
Stem Thik
Top
Bottom
3
0.85
2.5
0.4
3.7
0.2
0.35
3.5
0.65
2.5
0.4
3.5
0.2
0.35
4
0.65
1.9
0.4
2.9
0.2
0.35
4.5
0.65
2.42
0.4
3.42
0.2
0.35
5
0.65
2.6
0.4
3.6
0.2
0.35
5.5
0.65
2.9
0.45
3.9
0.2
0.35
Upward soil pressure in KN/m2
Effective frictional force
Concrete m3
Steel quantity Kg/m
Pmax.
Pmin.
101.7
295.2
38.21
2.305
138.26
103.6
292
51.85
2.3625
143.3
88
296.5
67.56
2.26
141.38
94.7
299.1
85.36
2.6055
158.99
101.7
296.1
105.23
2.815
176.65
106.9
305.4
127.18
3.2675
202.55
Upward soil pressure KN/m2
Effective frictional
force KN
Concrete m3
Steel quantity
Kg/m
Pmax.
Pmin.
220.63
281.53
78.91
3.9555
294.49
213.15
299.95
100.46
4.2125
272.96
217.81
295.3
124.61
4.3
280.63
206.31
294.54
151.35
4.15
275.03
197.56
295.12
180.68
4.35
320.84
183.01
295.3
212.62
4.48
313.44
177.32
289.68
247.15
4.96025
295.81
172.75
286.56
284.28
5.5275
308.79
Graph 1: Step location Vs concrete m3 for wall Ht. 6.0 m
Graph 2: Step location Vs steel kg for wall Ht. 6.0 m
2. Stepped retaining wall of height 8m
Assumptions
-
Back fill is enough compacted.
-
Step length embedded in back fill – 4.5m 3.Step dimensions – 500 x 300 mm
Table 2: Stability analysi s and cost comparison for wall
ht.8m
Step from top
Width of toe slab
Width of heel slab
Depth of base slab
Total base slab
Stem thickness in m
at top
Bottom
4
1.3
3.95
0.47
5.65
0.25
0.4
4.5
1.2
3.9
0.5
5.5
0.25
0.4
5
1.1
3.85
0.5
5.35
0.25
0.4
5.5
0.95
3.9
0.45
5.25
0.25
0.4
6
1.15
3.4
0.45
5
0.25
0.45
6.5
1.25
3.2
0.45
4.9
0.25
0.45
7
1.35
3.12
0.45
4.995
0.25
0.525
7.5
1.45
3.15
0.45
5.2
0.25
0.6
Graph 4
:
Step location Vs concrete cum/m for wall Ht. 8.0 m
Graph 7: Step location Vs concrete cum/m for wall Ht. 8.0 m
Graph 5: Step location Vs steel kg/m for wall Ht. 8 m
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Stepped retaining wall of height 10m
Assumptions
-
Back fill is enough compacted.
-
Step length embedded in backfill – 5.5m 3.Step dimensions – 600 x 300 mm
Table 3: Stability analysis and cost comparison for wall
Step from top m.
Width of toe slab m
Width of heel slab m
Depth of base slab m
Total base slab m
Stem thickness in m
at top
Bottom
5
1.5
8.5
0.55
10.5
0.35
0.5
5.5
1.45
7.15
0.55
9.15
0.35
0.55
6
1.4
6.85
0.55
8.75
0.35
0.5
6.5
1.35
6.65
0.55
8.5
0.35
0.5
7
1.5
6.5
0.5
8.5
0.35
0.5
7.5
1.45
6.15
0.55
8.2
0.35
0.6
8
1.5
5.55
0.55
7.8
0.35
0.75
8.5
1.5
5.25
0.55
7.5
0.35
0.75
9
1.6
4.925
0.6
7.25
0.35
0.725
9.5
1.75
5.425
0.6
8
0.35
0.825
height10m.
Graph 8: Step location Vs steel kg/m for wall Ht. 10.0 m
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Stepped retaining wall of height 12m
Assumptions
1.Step length embedded in backfill – 6.5 M 2.Step dimensions – 650 x 400 mm
Table 4:Stability analysis and co st comparison for wall
ht.12m
Step from top
Width of toe slab m
Width of heel slab m
Depth of base slab m
Total base slab m
6
2.1
5.9
0.75
8.65
6.5
1.9
6.6
0.75
9.15
7
1.8
6.3
0.65
8.75
7.5
1.65
6.2
0.65
8.45
8
1.5
6.35
0.65
8.45
8.5
1.4
6.1
0.65
8.2
9
1.25
5.85
0.6
7.8
9.5
1.4
5.45
0.7
7.5
10
1.51
5.09
0.7
7.25
10.5
1.6
5.6
0.65
8
11
1.7
5.2
0.65
7.8
11.5
1.8
5.225
0.7
8.1
Upword soil pressure KN/m2
Effective frictional force KN
Concrete m3
Steel quantity Kg/m
Pmax.
Pmin.
297.29
217.93
213.27
9.4875
780.71
295.99
229.29
252.98
10.1125
653.98
297.01
224.59
296.07
9.1875
664.01
299.91
240.15
342.53
9.055
602.19
295.05
249.66
392.37
9.2925
665.24
286.61
260.06
445.59
9.7925
704.89
270.77
280.76
502.18
9.405
855.36
255.28
289.2
562.14
10
856.7
240.75
294.08
562.14
10.075
861.16
245.75
283.49
692.2
11.2375
810.15
244.36
283.43
762.29
11.945
822.89
249.26
283.24
835.76
11.85125
877.55
Graph 10: Step location Vs concrete cum/m for wall Ht. 12 m
Upward soil pressure KN/m2
Effective frictional force KN
Concretem3
Steel quantity Kg/m
Pmax.
Pmin.
297.9
290.8
299.8
12.5625
928.64
298.52
284.82
348.86
11.8625
968.68
295.9
282.2
401
11.875
946
291.9
275
457.9
12.09
925.5
300
283.5
517.88
11.4255
967
292.9
272.8
581.5
13.156
1015.9
282
280.35
648.73
13.4625
1004
264.5
276.8
719.6
14.425
1111
238.88
283.5
794.12
14.925
1089
267.8
271.9
872.19
15.9
1233
234.5
286.35
954
16.1625
1167
223.5
290.75
1040
17.0835
1064
213
299
1128.5
18.3625
1077
225
300
1221
19.92
1350
246.25
300
1317.5
22.725
1511
Graph 11: Step location Vs steel kg/m for wall Ht. 12.0 m
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Stepped retaining wall of height 15m
-
Assumptions
1.Step length embedded in backfill 7.5m 2.Step dimensions – 700 x 450 mm
Table 5:Stability analysis and cost comparis on for wall
ht.15m
Step from top m
Width of toe slab
m
Width of heel slab m
Depth of base slab m
Total base slab m
Stem thickness in m
at top
Bottom
7.5
2.1
6.3
0.75
9.5
0.35
1.1
8
2.15 6.1
0.75
9.15
0.35
0.9
8.5
2.12
5.73
0.75
8.75
0.35
0.9
9
2.12
5.46
0.75
8.5
0.35
0.92
9.5
2
5.33
0.72
8.15
0.35
0.82
10
2
5.225
0.8
8.195
0.35
0.97
10.5
2
4.7
0.75
7.8
0.35
1.1
11
2.1
4.15
0.75
7.5
0.35
1.25
11.5
2.2
3.75
0.75
7.25
0.35
1.3
12
2.25
4.45
0.75
8
0.35
1.3
12.5
2.4
4.1
0.75
7.8
0.35
1.3
13
2.6
4.2
0.785
8.1
0.35
1.3
13.5
2.8
4.4
0.85
8.5
0.35
1.3
14
2.9
5.1
0.9
9.3
0.35
1.3
14.5
3
6.05
1
10.4
0.35
1.35
Graph 13: Step location Vs concrete cum/m for wall Ht. 15.0 m
Graph 14: Step location Vs steel kg/m for wall Ht. 15.0m
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-
RESULTS AND DISSCUSSIONS
1.Example
The example of analysis and design of stepped cantilever retaining wall are given below.
Data assumptions
Data assumed for the stability calculation of stepped cantilever retaining wall:
-
Free Board not necessary
-
The backfill is enough compacted to develop necessary friction.
-
Bearing Capacity of soil: 30 0 KN per Square meter
-
Water level is much below the level of base and effect of soil moisture is ignored.
-
Dry density of soil: 18 KN per Cubic meter
-
Angle of internal friction: 300
-
Coefficient of friction: 0.60
-
Stability is checked for sliding and overturning.
-
Factor of safety against sliding = 1.5
-
Factor of safety against overturning = 2.0
The moment and reinforcement provided for various heights are as shown in table
-
Counter fort Retaining wall
The structural analysis of counter fort Retaining wall is done as per routine analytical practices. Generally these walls a re use for span more than 6m, but here in order to compare the results analysis and design of these counter fort retaining walls is done for Heights 6m to 1 5m. The mechanism of this wall is different from cantilever wall and here Base slab is more important design aspect.
Table 6: Dimensions of Counter fort Retaining Wall
Ht of wall
m
Total Base Slab
m
Width of Toe Slab
Width of Heel slab
Base slab Thk.
m
Stem Thk. m
Top
Botm.
6
3.5
0.3
3.0
0.28
0.2
0.2
8
4.25
0.5
3.45
0.35
0.3
0.3
10
5.6
1.0
4.25
0.45
0.45
0.35
12
7.75
1.25
6.05
0.5
0.45
0.45
15
10.0
2.75
6.70
0.77
0.55
0.55
Counter fort Details
Spacing
4.0
3.5
3.0
3.0
3.0
Thickness
0.3
0.375
0.4
0.45
0.55
T he a n a l ys i s o f B a s e s l a b fo r wa l l i s p r e s e n t e d i n t a b l e H e r e T o e s l a b i s d e s i g n e d a s c a nt i l e v e r s l a b s p a n ni n g f r o m s t e m. T h e up wa r d s o i l p r e s s ur e wi l l b e a c t a s ma j o r l o a d o n t o e s l a b . B ut t he he e l s l a b wi l l b e d e s i g ne d a s s i mp l y s up p o r t e d s l a b i n b e t w e e n t wo a d j a c e n t c o u n t e r fo r t s . S o me t i me s wh e n t o e p r o j e c t i o n i s l a r g e r a nd i f t he r e i s p o s s i b i l i t y o f s t r e s s r e ve r s a l i n s t e m, t he c o u n t e r fo r t s a r e a l s o p r o vi d e d o n t o e s l a b a t t ha t t i me T o e s l a b d e s i g n wi l l a l s o b e a s he e l s l a b d e s i g n . T h e ma j o r l o a d fo r he e l s l a b wi l l b e e f f e c t i ve l o a d fr o m a ve r a ge U p wa r d p r e s s ur e a nd R e t a i ne d s o i l l o a d o n h e e l s l a b .
The base slab depth is provided as per required for maximum Bending Moment while reinforcement is provided as per actual requirement for Toe and Heel slab.
Table 7: Structural Analysis of Counter -fort Retaining wall
(Base slab)
Height of
wall m
Bending moment (KN.m)
Depth of base slab required mm
Depth of base slab Provided mm
Toe
Heel
6
12.67
158.98
240.03
400
8
47.58
232.12
290.00
450
10
187.55
419.80
390.00
550
12
288.36
534.34
440.00
600
15
1152.18
1391.32
710.00
850
The reinforcement provided for base slab i.e. Toe slab and various locations is shown in table 8 .
Table 8: Design of Base slab of counter fort retaining wall
counter fort is done based on above assumptions. The Max. Depth of this cantilever beam is width of heel slab. The steel reinforcement is provided as per requirement for tensile stress induced in it due to soil load on stem.
The moments and connection of counter for t details for various wall h eights are as shown in table 10
Ht. Of wall m.
Base slab
Thick. Mm
Main Steel.
Toe slab
Heel slab
Ast.
mm2
Bar Dia.
& Spacing
Ast.
mm2
Bar Dia.
& spacing
6
400
168.73
10
@150mm
1172.70
20
@150mm
8
450
297.07
12
@150mm
1538.54
20
@150mm
10
550
981.27
16
@150mm
2317.76
25
@150mm
12
600
1399.52
20
@150mm
2724.55
25
@150mm
15
850
4183.46
25
@115mm
5194.55
32
@150mm
Table 10: Moment and Connections of counter fort with Heel
Stem m
Momen t
Bar Dia. And
Spacing
Connections of counter fort with Heel Slab
Hori zonta
Bar Dia.
Spacing of
6
864
20
@100m
144
8
100mm
8
1792
20
@100m
168
8
100mm
10
3000
25
@100m
180
10
100mm
12
5184
25
@100m
216
10
100mm
15
10125
32
@100m
270
12
100mm
slab
The mechanism of stem o f counter fort retaining wall and Cantilever retaining wall is not same. In cantilever retaining wall, stem was acting as free cantilever with span equal height of wall while in counter fort, stem acts as simply supported slab spanning in between two adjac ent counter forts. The effective span for this will be span of counter fort along length of wall. The dimensions of stem are reduced due to this mechanism. The bending moment of the vertical wall is maximum at the junction of stem (wall) with Base and redu ces to the zero at the top of the wall.
The moments and reinforcement provided for various heights are as shown in table 9
Table 9: Moment and Reinforcement details a long length of stem for counter fort wall
Ht. of wall m.
Moments (KNm)
Steel prov. In V ertical wall
Stem Thic kness
Dreq. Mm
Dprov. mm
Ast mm2
Bar Dia. &
Spacing
6
72
161.51
200
1130.09
10
@70mm
8
73.5
163.19
300
1736.00
12
@65mm
10
67.5
156.39
350
552.52
16
@150mm
12
81
171.31
450
510.83
20
@150mm
15
101.25
191.53
550
520.35
25
@150mm
The counter forts act as self -supporting structural elements for retaining wall. It takes reactions, both from the stem as well as Heel slab. The counter fort may be considered to bend as a cantilever, fixed at heel slab. The counter fort acts as an inverted T beam of varying rib depth. The structural analysis of
The main stress along counter fort is tensile. The connection of counter fort with base slab and stem is important for all assumed mechanism. The steel reinforcement provided is in the form of two legged stirrups of required diameter steel. The saving in steel reinforcement can be done as per curtailment / Reduction in number of stirrups from bottom to top side of wall.
-
Stepped Cantilever retaining wall
The stepped cantilever wall is new type suggested in this thesis. Here concrete steps are provided on stem projecting into backfill. T he pressure compacted backfill will anchor the concrete plate/step and will develop frictional resistance force; this will act as indirect support for cantilever retaining wall. In short stem will act as propped cantilever and thus will reduce the destruct ive forces on stem / retaining wall.
Table 11: Summary of Dimensions of Stepped Cantilever
Retaining Wall
Ht. Of wall
m
Total base slab
m
Width of Toe Slab
M
Width of
Heel
slab m
Base slab Thk.
m
Stem
Thickness
Top
Bot
6
2.85
0.65
1.9
0.4
0.2
0.3
8
5.25
0.95
3.9
0.4
0.2
0.4
10
6.5
1.5
4.4
0.60
0.25
0.6
12
8.5
1.65
6.2
0.65
0.3
0.65
15
10.5
2.0
7.3
0.9
0.5
1.2
Concrete Steps
Total
Spacing
From
Top
Width
m
Depth
m
3.5
2
4.00
0.45
0.3
4.5
2
6.0
0.45
0.5
6.0
2
8
0.6
0.5
6.0
1.5
8
0.6
0.65
5.75
1.25
7.75
0.75
0.7
There is reduced soil load on base slab of wall firstly due to decreased base slab width and secondly due to reduction in load of soil resting on concrete steps/plates in backfill. In this case of wall interestingly it was the case that, wall was stable at shorter dimensions but the stem was pulled inside backfill due to assumed frictional force hence the structural dimensions were not much reduced to keep balance between self weight and resisting forces.
The forces acting and analysis and design of base slab for this new stepped cantilever retaining wall are as shown in Table12.
Table 12: Structural Analysis of Stepped cantilever Retaining
wall (Base slab)
Ht. Of
wall m.
Bending moment
(KNm)
Thickness
Required mm
Thickness
Provided mm
Toe
Heel
6
72.03
105.00
195.05
400
8
205.34
800.88
538.68
650
10
581.84
987.57
598.18
750
12
656.00
1112.92
618.55
800
15
979.98
1553.13
750.15
900
Table 13: Design of Base slab of Stepped cantilever Retaining wall
Ht. of wall m.
Base slab
Thick. Mm
Main Steel.
Toe slab
Heel slab
Ast. mm2
Bar Dia. & Spacing
Ast. mm2
Bar Dia. &
Spacing
6
400
505.63
12
@150mm
741.68
16
@150mm
8
650
887.99
20
@150mm
3623.94
25
@135mm
10
750
2217.81
25
@150mm
3854.36
32
@150mm
12
800
2343.51
25
@150mm
4069.80
25
@150mm
15
900
3130.30
32
@150mm
5079.49
36
@150mm
Ast.
mm2
960
1560
1800
1920
2160
Bar Dia. &
Spacing
10
@80 mm
12
@75 mm
16
@100
mm
16
@100
mm
16
@90 mm
The R.C.C. steps / plates projecting in backfill are main key elements in this type of wall. The Resisting force developed due to these steps is function of depth of these steps below top of wall, surface roughness of concrete plates, degree of compaction of backfill and specific weight of backfill. The steps are developing frictional force due to their anchorage in backfill and steps are reinforce d with sufficient steel required for tensile stress developed in it due to pulling effect. Though these steps are standing as free cantilever in backfill, they will not be designed as cantilever as it is assumed as backfill is compacted.
The details of forces acting and design of these concrete steps is as shown in Table 14
Table 14: Concrete Step analysi s and design d etails
Ht. of
wall m
Step
Dimensions
Location
Width
Depth
Depth below Top
In Fill Embed ment
6
0.4
0.3
4.0
3.5
8
0.5
0.3
5.5
4.5
10
0.6
0.3
6.5
5.5
12
0.65
0.4
7.5
6.5
15
0.7
0.45
9.5
7.5
Reinforcement Details
Step
spacing along
length
Frictional force
developed
Dia
No
12
4
2.0
67.68
12
6
2.0
151.47
12
8
2.0
244.30
12
12
1.5
342.23
16
10
1.25
517.10
In this type of wall the nature of moment variation will be similar as that of Cantilever retaining wall but there will be drastic change in moment at the point where concrete step is projected inside backfill. Up to this point the moment will be function of height of backfill but below this the moment will be algebraic sum of both resisting and destructive moments i.e. Destructive moment due to backfill and resisting moment of frictional force developed due to step.
The steel reinforcement will be provided not only adhering to moment values but with also consideration to minimum steel quantities and Practical site considerations also.
The table 15 and 16 shows the moment variation and steel reinforcement provided for this stepped cantilever wall
Table 15: Moment Variation Alo ng length of stem for Stepped cantilever Wall
6m
8m
10m
Moment KNm
D
Prod Mm
Moment KNm
D
Prod mm
Moment KNm
D
Prod mm
0-L/4
3.375
225
8.0
250
15.63
300
L/4-
L/2
27.0
250
64.0
300
125
400
L/2-
2L/3
91.12
275
216.0
450
421.87
600
2L/3-
L
35.52
300
310.04
550
674.27
750
12m
15m
Moment KNm
D
Prod mm
Moment KNm
D
Prod Mm
0-L/4
27.0
350
52.7
400
L/4-
L/2
216.0
500
421.9
700
L/2-
2L/3
729
750
1423.8
1000
2L/3-
L
1385.77
1000
2944.08
1400
Table 16: Reinforcement details along Height of stem
Ht. of wall m.
Moment (KNm)
Steel prov. In Vertical wall
Stem Thic kness
Dreq. mm
Dprov. mm
Ast mm2
Bar Dia. & Spacing
6
35.52
138.94
300
500.82
12
@150mm
8
310.04
410.49
500
2732.36
20
@115mm
10
674.27
605.35
700
4274.66
25
@115mm
12
1385.77
867.83
950
4238.38
25
@115mm
15
2944.08
1264.93
1350
9803.36
32
@80mm
-
Unit Cost per meter of wall
-
Counter fort Retaining Wall:
The cost of counter fort retaining wall includes cost of concrete for stem, counter fort and base slab is added, and the steel quantity is calculated from actual steel used with some provision for wastage also. For counter fort retainin g wall, the cost of wall is calculated for total spacing of counter forts and from this per meter cost of wall is calculated.
The cost per running meter fr counter fort retaining wall for various retain h eights is as shown in table
Table 17: Cost per Running Meter for Counter fort Retaining
Ht. of wall
6m
8m
Location
Concrete m3
Steel kg
Concrete m3
Steel kg
Stem
1.2
76.08
2.4
137.6
Base slab
0.98
66.16
1.49
80.08
Counter Forts
2.7
137.2
5.18
234.05
Total
4.88
279.44
9.07
451.73
Rate
3500
43
3500
43
Amount
17080
12015.9
31745
19424.39
Sum
29095.9
51169.4
29100
51170
10m
12m
15m
Concrete m3
Steel kg
Concretem 3
Steel kg
Concrete m3
Steel kg
3.5
156.8
5.4
251.52
8.25
439.7
2.52
139.86
3.9
229.82
7.7
475.28
8.5
527.98
16.34
765.5
27.64
1810.55
14.52
824.64
25.64
1246.84
43.59
2725.53
3500
43
3500
43
3500
43
50820
35459.5
2
89740
53614.1
2
152565
117197.79
86279.52
143354
269763
86280
143360
269770
-
Stepped Cantilever Retaining Wall
As like for counter fort retai ning wall, the cost of stepped cantilever retaining wall will be calculated firstly as per spacing of steps in backfill along length of wall and hence it is transferred to per meter cost. The construction practice for stepped cantilever wall will not be very special than cantilever wall hence except extra amount for backfill compaction, no any extra provision is made in cost calculation.
Table 18: Cost per running meter for Stepped Cantilever
Retaining Wall
Ht. of wall
6m
8m
Location
Concrete m3
Steel kg
Concrete m3
Steel kg
Stem
3
142.78
4.8
476.72
Base slab
2.28
84.91
4.2
370.71
Steps
0.25
8.2
0.39
16.63
Total
5.53
235.89
9.39
864.06
Rate
3500
43
3500
43
Amount
19355
10143.3
32865
37154.58
Sum
29498.3
70019.58
29500
70000
10m
12m
15m
Concretem3
Steel kg
Concretem3
Steel kg
Concretem3
Steel kg
8.6
972.2
11.52
602.65
25.5
1688.23
7.8
623.21
8.29
500
11.8
850.07
0.55
26.18
0.9
59.69
1.2
100.88
16.95
1621.59
20.71
1162.3
38.5
2639.18
3500
43
3500
43
3500
43
59325
69728.4
72485
49981
134750
113485
129053
122466
248235
129050
122470
248240
-
-
Cost Comparison :
The cost per meter for all these three proposed types is tabulated above. In table 19 the comparison of concrete quantity per meter for different wall heights and different wall types are shown.
Wall Ht. m
Counter fort wall
Stepped Cantilever wall
6
4.88
5.53
8
9.07
9.39
10
14.52
16.95
12
25.64
20.72
15
43.59
38.5
Table 19: Comparison of Concrete for Different Walls
Grapp6:Concrete Quantity Comparison
Table 20: Steel reinforcement per meter of w all
Wall Ht. m
Counter fort wall
Stepped Cantilever wall
6
279.44
235.89
8
451.73
864.96
10
824.64
1621.59
12
1246.84
1162.34
15
2725.53
2639.18
Graph 17: Reinforcement Qu antity Comparison
The table 21 shows final cost comparison of all these wall type s for same heights and graph 18 showing variation.
Wall Ht. m
Counter fort wall
Stepped Cantilever wall
6
29100
29500
8
51170
70000
10
86280
129050
12
143360
122470
15
269770
248240
Table 21: Final Cost Comparison
Graph 18 : Final Cost Comparison
[3]. At first instant, Stepped cantilever Retaining wall are economically best suited for wall heights from 11.0 M to 15.0 M. this is proving to be better alternative for large wall heights as more than11.0 M. Its mechanism is proven and used in many civil engineering structures.
REFERENCES
[1]. S.K Bhatia and R.M Baker, Difference between Cantilever and Gravity retaining walls under static condition, Indian Geotec hnical Journal, Vol.15, No.3, May 1985. [2]. Kaare Hoeg and Ramesh Murarka, Probabilistic Analysis and Design of a Retaining Wal , Journal of Geotechnical Engineering Division, Vol.100, March 1994. [3]. Swami Saran, Displacement Dependent Earth Pressure in Retaining Walls, Indian Geotechnical Journal, Indian Geotechnical Journal, Vol.20, July 1990. [4]. Leo Cassagrande, Comments on Conventional Design of Retaining Structures, Journal of the soil mechanics and foundation division, ASCE,, Vol.99, Feb2003.BIOGRAPHIES
Prof. Dr.Patil S.S.
It is clear from table that for heights from 8.0 M to 10.0 M counter fort retaining wall is giving economical results. Hence counter fort wall is better alternative for retaining heights up to 10.0 M. Other wall types may also be checked depending on actua l site conditions.
The stepped cantilever is giving best result for height more than 10.0 M, from this height counter fort retaining walls are being uneconomical.
-
-
CONCLUSIONS
-
B.E(Civil), M.E (Civil Structures), Ph.D.(B.U.Banglore), Chairman Indian Society of Structural Engineers Solapur Local Centre, Professor & Head of Civil Engineering Department, Walchand Institute of Technology, Ashok Chowk Solapur. (M.S) INDIA.
Mr. Bagban Aamir A.R
B.E (Civil), M.E (Civil Structures), M.E Student of Walchand Institute of Technology, Ashok Chowk Solapur (M.S) INDIA