50

th

IGC

50th

INDIAN GEOTECHNICAL CONFERENCE

17th

– 19th

DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

NUMERICAL STUDY ON THE BEHAVIOUR OF A RIGID RETAINING WALL

WITH RELIEF SHELVES

V. B. Chauhan1, S. M. Dasaka

2, Rizwan Khan

3

ABSTRACT

Rigid non-yielding retaining walls are made usually as gravity retaining walls. These gravity retaining

walls are bulky in size. There may be situations where high retaining walls are required to resist the

lateral earth pressure. However, massive gravity walls may not be viable due to economic and space

constraints. Also, in some cases, sufficient yielding of rigid cantilever retaining walls may not be

permitted due to site constraints, and these walls need to be designed for higher earth pressures, than the

active earth pressures. Earth pressure on a retaining wall decides the sectional dimensions of the wall, and

there have been several attempts in the literature to reduce the earth pressures on the retaining walls, by

using techniques such as using lightweight backfill, placement of compressible inclusions at the wall-

backfill interface, to name a few. A retaining wall with pressure relief shelves is one of the least explored

techniques to reduce the earth pressure on retaining walls. A few researchers previously proposed this

technique without systematic analysis and proper validation, and demonstrated that provision of relief

shelves can reduce lateral earth pressure on retaining walls. This area has never well researched to

understand the mechanical behaviour of these walls in terms of lateral earth pressure, because of its

particularity, complexity and existing variable factors. Such walls have been constructed in various parts

of the world for about a decade, but their behaviour was never well documented. Hence, the present study

is aimed at understanding the behaviour of such walls and to explore the effectiveness of these walls to

reduce earth pressure and lateral thrust and to get proper insight about the associated mechanisms

involved in the pressure reduction, if any. This work presents numerical analysis of rigid non-yielding

retaining wall retaining a dry cohesionless backfill with pressure relief shelves using FLAC3D

. A 6m high

rigid non-yielding (at-rest) retaining wall, retaining a dry cohesionless backfill, has been chosen for the

present study. Two cantilever relief shelves of thickness of 0.20m are placed at different heights of the

wall. Width of these relief shelves are varied as 0.5m, 0.6m, 0.7m and 0.8m, to conduct a parametric

study to understand the influence of width of relief shelves on the contact pressure below base slab,

surface settlement profile of backfill, deflection of relief shelves and reduction in lateral earth pressure.

Lateral earth pressure on the retaining walls studied is shown in Fig. 1. The present studies reveal that

1Ph. D. research scholar, Civil Engineering Department, IIT Bombay, Mumbai, India, chauhan.vinaybhushan@gmail.com

2Associate Professor, Civil Engineering Department, IIT Bombay, Mumbai, India, dasaka@civil.iitb.ac.in

3M. Tech student, Civil Engineering Department, IIT Bombay, Mumbai, India, rizwancivil99@gmail.com

V. B. Chauhan, S. M. Dasaka & Rizwan Khan

retaining walls with relief shelves can considerably reduce the thrust on wall in the range of 10.56-12.5%

when relief shelves are used with retaining wall, compared to that of retaining wall without relief shelf.

Deflection of relief shelves has marginally increased backfill surface settlement by 0.7-1 mm, which

might not affect the serviceability of the structure. Provision of relief shelves attributes towards a

redistribution and reduction of total contact pressure below the base slab considerably. Total contact

pressure below the base slab is reduced by around 13% for walls with relief shelves of 0.5-0.6 m with

width, thereby making these walls much safer against bearing capacity failure.

Fig. 1 Lateral earth pressure on the wall for various retaining walls

Amongst all the cases studied, relief shelves of width of 0.5m proved effective in reducing lateral earth

pressure and total contact pressure below base slab by 10.56% and 13.4%, respectively, without leading

to excessive deflection of relief shelves.

Keywords: Retaining wall, relief shelf, earth pressure, numerical modelling, FLAC 3D

50

th

IGC

50th

INDIAN GEOTECHNICAL CONFERENCE

17th

– 19th

DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

NUMERICAL STUDY ON THE BEHAVIOUR OF A RIGID RETAINING WALL

WITH RELIEF SHELVES

V. B. Chauhan, Ph. D. student, Civil Engineering Department, IIT Bombay. chauhan.vinaybhushan@gmail.com

S. M. Dasaka, Associate Professor, Civil Engineering Department, IIT Bombay. dasaka@civil.iitb.ac.in Rizwan Khan, M. Tech student, Civil Engineering Department, IIT Bombay. rizwancivil99@gmail.com

ABSTRACT: This paper presents numerical study on a 6m high retaining wall with 2 relief shelves having varying

width of relief shelves ranging 0.5-0.8m to understand the influence of width of relief shelves on the contact

pressure below base slab, surface settlement profile of backfill, deflection of relief shelves and reduction in lateral

earth pressure. It is found that retaining walls with relief shelves can considerably reduce the lateral thrust on wall

in the range of 10.56-12.5%. Among all the cases studied, relief shelves of width of 0.5m proved effective in

reducing lateral earth pressure and total contact pressure below base slab by 10.56% and 13.4% respectively,

without leading to excessive deflection of relief shelves.

INTRODUCTION

Retaining walls are an integral part of almost all

infrastructure projects, to support vertical or near

vertical backfills. Rigid non-yielding retaining

walls are made usually as gravity retaining walls.

These gravity retaining walls are bulky in size.

There may be situations where high retaining walls

are required to resist the lateral earth pressure.

However, massive gravity walls may not be viable

due to economic and space constraints [1]. Also, in

some cases, sufficient yielding of rigid cantilever

retaining walls may not be permitted due to site

constraints, and these walls need to be designed for

higher earth pressures, than the active earth

pressures. One alternative to tackle such issues is

to reduce the lateral thrust on the wall. As far as

structural design is considered, estimation of lateral

thrust on retaining walls plays a major role

affecting the cost of project [2, 3]. So, by reducing

lateral earth pressure, sectional dimensions of

retaining wall as well as cost of project can be

reduced. There are many methods available to

reduce the lateral earth pressure, such as use of

geo-inclusion materials such as expanded

polystyrene (EPS) [4], glass-fiber insulation [5]

and cardboard [6], light weight backfill, to name a

few. One such technique, which is least explored,

is retaining wall with relief shelves. Relief shelves

are horizontal platforms, which are constructed

monolithically with the stem of wall, and extend

into the backfill at right angles, throughout the

length of the retaining wall. Number of such

shelves is constructed at regular spacing along the

height of the wall. A few researchers previously

proposed this technique without systematic

analysis and proper validation, and demonstrated

that provision of relief shelves can reduce lateral

earth pressure on retaining walls. This area has

never well researched to understand the mechanical

behaviour of these walls in terms of lateral earth

pressure [7-10], because of its particularity,

complexity and existing variable factors. Such

walls have been constructed in various parts of the

world for about a decade, but their behaviour was

never well documented. Hence, the present study is

aimed at understanding the behaviour of such walls

and to explore the effectiveness of these walls to

reduce earth pressure and lateral thrust and to get

proper insight into the associated mechanisms

involved in the pressure reduction.

LITERATURE REVIEW

Effect of provision of relief shelves was studied

and noted that extending the relief shelves beyond

V. B. Chauhan, S. M. Dasaka & Rizwan Khan

the rupture surface in soil can considerably reduce

the lateral earth pressure and increase the stability

of retaining wall [7]. It was suggested that for walls

with greater heights, more than one relief shelf

could be a viable solution (Fig. 1). In the case of

counterfort retaining walls, the relief shelves can

be provided spanning the length of counterfort.

Fig. 1. Counterfort wall with relief shelves [7]

Researchers have demonstrated the benefit of

single relief shelf on the reduction of total lateral

thrust on a cantilever wall, through stability

analysis of wedges [8]. Through small-scale

physical model tests, it was showed that the

maximum height of sand that could be retained by

wall just prior to the incipient overturning is higher

in case of walls with relief shelf than that of walls

without relief shelf [8]. A possible solution for

earth pressure reduction on retaining walls was

suggested for high retaining walls [10], as shown

in (Fig. 2). Through an analysis, it was

demonstrated that contribution of the relief shelf to

the overall stability of the retaining wall, in terms

of extra stabilizing moment. It was suggested that

the soil below the relieving shelf should not

provide any support to relief shelf to realize the

reduction in earth pressure [11]. A similar

technique, named Graviloft, which is a

combination of gravity retaining and reinforced

concrete loft, was illustrated [12]. In such walls, a

loft was provided perpendicular to non-prismatic

section of stem.

Fig. 2. Cantilever retaining wall with relief shelves

[10]

It is demonstrated that proper design and

placement of such lofts optimized the resources

leading to 40% cost saving. Graviloft technology

has been successfully implemented for guide walls,

wing walls and divides walls of maximum height

of 26m in various projects such as box culvert,

aqueduct and barrage in the state of Maharashtra,

India [12]. Such walls resulted in smaller cross

section area of stem and base slab than

conventional gravity walls.

A well-documented case study of failure of a 10-13

m high cantilever retaining wall with relief shelves

has been reported in Hyderabad, India. The above

structure had failed after few years of construction,

and cracks on the stem of retaining wall just below

one of the relief shelves were noted, as shown in

Fig. 3. The forensic studies reveal that quality of

concrete used in the wall construction was very

satisfactory, and construction defects were

completely ruled out. Though the reasons behind

the failure of the above structure are not known

yet, the authors are of the opinion that the lateral

earth pressures might have been estimated

wrongly. In spite of wide use of these walls, there

is no common consensus on the efficacy of these

walls in the lateral pressure reduction.

50

th

IGC

50th

INDIAN GEOTECHNICAL CONFERENCE

17th

– 19th

DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

Fig. 3. Cantilever retaining wall with relief shelves

in Hyderabad, India

Moreover, no design guidelines are available on

the selection of optimum number, sectional

dimensions, and location of relief shelves, for a

given height of retaining wall. Failure of such

structures has motivated the authors to critically

examine the rigid retaining walls with relief

shelves and possible mechanism beyond lateral

pressure reduction.

NUMERICAL MODELLING OF RELIEF

SHELF WALLS

A 6 m high rigid non-yielding (at-rest) retaining

wall, retaining a dry cohesionless backfill, has been

chosen for the present study, and conventional

retaining wall without relief shelves (Fig. 4a) is

hereafter referred to as RS 0.0. Finite Difference

numerical package (FLAC 3D) is used in the study

to understand the effect of relief shelves on the

contact pressure below base slab, surface

settlement profile of backfill, deflection of relief

shelves and reduction in lateral earth pressure, two

cantilever relief shelves of same widths placed at

different heights of the wall are considered, as

shown in Fig. 4b. Sectional dimension of retaining

wall with relief shelves is shown in Fig. 4b,

wherein width of relief shelf (B) is varied as 0.5m,

0.6m, 0.7m and 0.8m.

Fig. 4. Geometry of retaining walls with and

without relief shelves (all dimensions in m)

These walls are hereafter referred to as RS 0.5, RS

0.6, RS 0.7 and RS 0.8, respectively. The thickness

of relief shelves is taken as 0.20m, throughout the

study. The length of foundation zone is kept as 30

m, which is five times the selected wall height, as

shown in Fig. 5.

Fig. 5. Numerical model of rigid retaining wall

with relief shelves

Factors of safety of retaining wall (RS 0.0) in

sliding and overturning modes of failure are

estimated as 3.95 and 4.0, respectively. To model a

plane strain problem, the length of retaining wall is

V. B. Chauhan, S. M. Dasaka & Rizwan Khan

considered as 1m. Sectional dimensions of all

retaining walls studied are shown in Fig. 4.

The mesh of numerical model of retaining is

divided into 10695 zones of uniform size. Fig. 5

shows the numerical grid considered to simulate

the rigid retaining wall. Fixed boundary condition

at bottom of foundation and roller boundary

condition at vertical ends of soil are chosen to

represent field conditions. Wall is not allowed to

move away from backfill, as it is considered as at-

rest wall.

MATERIALS AND INTERFACE

PROPERTIES

The rigid wall is modelled as elastic material.

Backfill material is modelled as a purely frictional,

elasto-plastic material following Mohr-Coulomb

failure criterion. Backfill and foundation soil

properties considered in the analysis are obtained

from [13], as shown in Table 1.

Table 1 Material properties [13]

Property Backfill Foundation Retaining

wall Bulk unit weight (kN/m

3)

16.5 17.5 24.0

Bulk Modulus

(kN/m2)

5200 5500 3.16×107

Poisson’s

Ratio

0.33 0.33 0.2

Cohesion

(kN/m2)

0 0 -

Friction angle

(Degrees)

43.5° 45.0° -

Dilation angle

(Degrees)

22.5° 22.5° -

Interface between different materials is modelled

as linear spring-slider system with interface shear

strength, defined by the Mohr-Coulomb failure

criterion. The relative interface movement is

controlled by interface normal stiffness (kn) and

shear stiffness (ks). A recommended thumb rule is

that ks and kn be set to ten times the equivalent

stiffness of the stiffest neighboring zone [14]. The

suggested maximum stiffness value is as follows:

min3

4max10 zGKkk sn

(1)

Where (∆z)min, K and G are the smallest dimension

in normal direction, bulk modulus and shear

modulus of the continuum zone adjacent to the

interface, respectively. This approach gives the

preliminary values of the interface stiffness

components, and these can be updated to avoid

intrusion to adjacent zone and to prevent excessive

computational time [15]. The interface at the base

of the wall has been assigned a value of normal

stiffness, kn= ks=1.5×109

kN/m2/m, thus preventing

penetration of wall into foundation soil. The

interface between the backfill soil and wall is

assigned a value of normal stiffness kn=1.5×109

kN/m2/m and zero shear stiffness to ascertain the

smooth interface between backfill and retaining

wall [16].

RESULTS AND DISCUSSION

The results of numerical modelling (FLAC3D

) of

earth pressure distribution on the rigid non-yielding

retaining wall without relief shelves are compared

with experimental test results [13], as shown in

Fig. 6, and it is noted from the figure that

numerical pressure distribution matches well with

that of experimental findings.

Fig. 6. Validation of numerical model used in the

present study

50

th

IGC

50th

INDIAN GEOTECHNICAL CONFERENCE

17th

– 19th

DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

Hence, the same numerical model is extended to

study the behaviour of rigid retaining walls with

two relief shelves provided at different levels, in

terms of the lateral earth pressure distribution,

contact pressure below base slab, total lateral

thrust, backfill settlement and deflection of relief

shelves.

Selection of number of relief shelves for a given

height of retaining wall should be done in such a

way that width of relief shelves should not be very

large as well as sufficient gap should be available

between two successive relief shelves for proper

compaction of backfill during the construction.

Hence, for 6 m high retaining wall, 2 relief shelves

are chosen for the present analysis.

For a rigid non-yielding wall, contact pressure

below base slab is governed by weight of wall,

center of gravity of wall and lateral thrust of soil.

Variation of contact pressure below base slab for

all retaining walls considered in the present study

is shown in Fig. 7.

Fig. 7. Contact pressure below the base for various

retaining walls

Retaining wall with relief shelves is different in

shape compared to the conventional retaining wall

and addition of horizontal relief shelves have

increased the weight of wall and shifted the center

of gravity of such wall towards backfill. Reduction

of lateral thrust has also played a role in variation

of contact pressure at base. Total contact pressure

below the base slab for all retaining walls

considered in the study is tabulated in Table 2.

Total contact pressures below the base slab is

reduced by 13.4% and 13.7% in case of RS 0.5 and

RS 0.6 walls. However, contact pressure

distribution below the base slab of retaining wall

without relief shelves is more or less same as that

of walls with relief shelves, viz. RS 0.7 and RS 0.8.

This behaviour of contact pressure distribution

might be attributed to increased weight of wall due

to added weight of shelves, reduction of lateral

earth pressure and shifting of center of gravity of

wall. These parameters have played in such a way

that contact pressure below the base has not

changed significantly in case of RS 0.7 and RS 0.8

walls. So, it can be concluded that proper selection

of width of relief shelves can reduce total contact

pressure below the base slab significantly and

subsequently increase the factor of safety against

bearing capacity failure. Surface settlement of

backfill is a criterion of serviceability of retaining

walls. Excessive backfill settlement leads to

collapse of backfill soil and subsequently failure of

surrounding structures.

Table 2. Total contact pressure below the base slab

Wall type RS

0.0

RS

0.5

RS

0.6

RS

0.7

RS

0.8

Total

pressure

kN/m

240.9 208.5 202.8 242.9 233.2

% Change

in contact

pressure

----- -13.4 -13.7 +0.85 -3.1

Fig. 8 presents surface settlement of all retaining

walls considered in this study. Backfill settlement

near the wall is ranging between 2-5 mm and it

gradually increases up to a maximum value of 10

mm far away from the stem. Surface settlement of

retaining walls with relief shelves is higher than

that of walls without shelves by 0.7-1 mm in the

region 1.5-4 m away from face of stem. This

increased settlement of backfill is attributed to

deflection of relief shelves. Pronounced effect of

deflection of relief shelves on backfill surface

V. B. Chauhan, S. M. Dasaka & Rizwan Khan

settlement has continuously been diminished with

increasing distance from stem and achieved the

same profile, as that of walls without relief shelves

beyond 8m from stem.

Fig. 8. Surface settlement profile of backfill

Fig. 9. Vertical deflection profile of top relief shelf

Deflection profile of top and bottom relief shelves

are compared in Figs. 9 and 10, respectively, and

maximum deflection of such relief shelves is listed

in Table 3. Deflection of relief shelves were found

maximum at bottom relief shelf compared to top

relief shelf for all retaining walls with relief

shelves except RS 0.5. Deflection of relief shelves

has significantly increased, when width of relief

shelf is greater than 0.5m. This observation

highlights that for the wall under study, maximum

width of relief shelves should be restricted to 0.5m.

Large width of relief shelves are leading to

excessive deflection due to their own weight,

which may further increase due to creep.

Fig. 10. Vertical deflection profile of bottom relief

shelf

Table 3. Maximum deflection (mm) of relief

shelves for various retaining walls

Relief Shelf RS 0.5 RS 0.6 RS 0.7 RS 0.8

Top RS 3.5 7.69 10.87 14.49

Bottom RS 3.10 8.46 11.40 14.74

Distribution of earth pressure on all retaining walls

is shown in Figs. 11 and 12. Provision of two relief

shelves has made the whole retaining wall into

three small segments. From Figs. 11 and 12, it can

be observed that lateral earth pressures in top

segment of all retaining walls with relief shelves

are less than that of retaining wall without relief

shelf, but attain higher values in the middle and

lowermost segments. Earth pressure behind the

relief shelves are lower than that of retaining wall

without relief shelf at corresponding height. Earth

pressure in lower most region has attained a peak

which might be due to numerical instability arising

from the presence of three corners in wall

geometry (two at base slab and one at junction of

stem and base slab). Presence of such corners

makes interfaces complex in numerical analysis,

which is due to intersection and overlapping of two

interfaces at a point.

50

th

IGC

50th

INDIAN GEOTECHNICAL CONFERENCE

17th

– 19th

DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

Fig. 11. Lateral earth pressure on the wall for

various retaining walls

Fig. 12. Lateral earth pressure on the wall for

various retaining walls

Table 4 Total lateral thrust and reduction in thrust

on retaining walls

Wall

type

Total thrust kN/m % Reduction

in thrust

RS 0.0 196.93 --

RS 0.5 176.12 10.56

RS 0.6 174.83 11.2

RS 0.7 174.4 11.5

RS 0.8 172.0 12.5

Total lateral thrust is calculated for all the retaining

walls considered in the present study, as shown in

Table 4.

Fig. 13. Comparison of reduction of lateral earth

pressure on wall by various methods

In the present study, a significant amount of total

lateral thrust reduction in the range of 10.56-12.5%

is obtained by provision of two relief shelves.

A comparison of lateral earth pressure distribution

obtained in the present study and the method

suggested by Bowles[10] on 6m high retaining

wall with relief shelves is presented in Fig. 13.

Percentage reduction in total thrust is found to be

66.1% when compared with method suggested by

Bowles[10], while the same for RS 0.5 has been

found to be 10.56%. However, further studies in

this direction are warranted, to get more insight

into the retaining walls with relief shelves,

especially physical model tests with earth pressure

measurements.

CONCLUSION

The study involves comprehensive finite difference

numerical analysis to assess the effectiveness of

providing relief shelves to the retaining walls. This

technique of reducing earth pressure on retaining

walls may prove economical, if properly

implemented. A 6 m high retaining wall with two

relief shelves is analyzed in this study. The effect

of width of relief shelves on backfill surface

settlement, contact pressure below base slab,

V. B. Chauhan, S. M. Dasaka & Rizwan Khan

deflection of relief shelves and earth pressure

reduction are analyzed and following conclusions

are drawn.

1. Among all the cases studied, retaining walls

with relief shelves can considerably reduce

the lateral thrust on wall in the range of

10.56-12.5%.

2. Proper selection number, location, and

dimensions of relief shelf can considerably

reduce the total contact pressure below the

base slab and making the retaining wall

much safer in bearing capacity failure

mode.

3. Among all the cases studied, relief shelves

of width of 0.5 m proved effective in

reducing lateral earth pressure and total

contact pressure below base slab by 13.4%

and 10.5% respectively, without leading to

excessive deflection of relief shelves.

4. Deflection of relief shelves increased

backfill surface settlement by 0.7-1 mm,

which might not affect the serviceability of

the structure.

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