Innovative Support Systems Ltd

RAMWALL

DESIGN METHODOLOGY

Submitted by:

SubTerra Engineering Ltd.

June 2005
 Innovative Support Systems Ltd
RAMWALL Design Methodology

CONTENTS

Page

1. INTRODUCTION 1

2. REFERENCED DOCUMENTS & ABBREVIATIONS 1

3 DESIGN METHODOLOGY / THEORY 2

3.1 General 2

3.2 Internal Analysis 4

3.3 External Stability 6

3.4 Other Design Applications 18

4. WORKED EXAMPLE 19

4.1 General 19

5. DURABILITY CONSIDERATIONS 38

5.1 General 38

5.2 Metal Corrosion 38

5.3 Design for Durability 39

6. CONCLUSIONS 41

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RAMWALL Design Methodology

1. INTRODUCTION

These calculations (RAMW/001 Rev.0) present a design methodology / theory and

numerical design calculations for a new retaining wall system, RAMWALL.

RAMWALL comprises a gravity retaining wall constructed from bent welded wire fabric
grid filled with crushed aggregate. The calculates will present basic gravity retaining
wall stability charts for various configurations and heights of wall, slope angles and
ground conditions, foundation bearing capacity calculations and internal wall stresses.

Finally an investigation and testing program will be recommended to verify the theories
given in these calculations.

2. REFERENCED DOCUMENTS & ABBREVIATIONS

Standards and Codes of Practice

BS 8002:1994 Design of Earth-retaining structures

BS 8004 Foundations
BS 8006:1995 Strengthened/Reinforced Soils
EN 1997-1:2004 - Eurocode 7: Geotechnical design
BS 1052 Welded Wire Fabric
BS 443 and BS 729 - Galvanising
BS 4102 - PVC Coating
BS 5390 - Backfill

Abbreviations used in the text and formulae, with typical values used in the illustrations
and worked example:
kN  1000newton
   10 rad    B  3.5m

2   80 rad H  6m c  0 kPa
kPa  1 kN m

MPa  1000kPa
   30 rad 3 1
  20 kN m N  100 kN m

rad    30 rad q  10 kPa
180

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3 DESIGN METHODOLOGY / THEORY

3.1 General

Internal forces in the wall can be calculated using standard soil mechanics theory as
follows.

Assuming a cohesionless fill material ( = Angle of friction of the soil); the vertical stress
in a block of soil at a depth h is given by: v = .h

At rest lateral stress in the soil is given by: h = ko..h

where ko = 1 - sin 


As the soil expands laterally the soil lateral stress reduces to the limiting value,
2
ka..h where ka = tan (45o - /2) this is represented graphically below using a Mohr circle

of stress diagram, Figure 3.1.

Figure 3.1

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The reinforcement in the RAMWALL can be represented by considering a block of soil,

Figure 3.2. Applying a vertical load to the soil, the block will strain laterally, h, as well

as compress axially, v. The reinforcement grids in the RAMWALL will restrain the

soil, provided there is adhesion or interlock between the soil and the reinforcement and
the reinforcement is stiff. The force transferred by the soil into the reinforcement is
equivalent to the at rest lateral stress, h = ko.v.

This general condition is valid for any value of vertical stress. Reference to Figure 3.1
shows that the reinforced condition always lies below the rupture line.

From Figure 3.2, the tensile stress in any unit of reinforcement = ko.v/ar,

where ar = cross sectional area of the reinforcement.

Figure 3.2

Therefore, the strain in the reinforcement equals r = ko.v/ar.Er, where Er = elastic

modulus of steel. This equates to the lateral strain in the soil (r) in the direction of the

reinforcement.

This argument is only valid if the effective stiffness (ar.Er) of the reinforcement is high

so that r tends to zero.

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This is the case with RAMWALL as the reinforcement panels are made out of closely
spaced high tensile welded wire fabric bent into a series of zig-zag panels stacked on top
of each other. Combined with a suitable sized and graded fill material they will form a
fully interlocked mass where the forces in the soil will be restrained by the reinforcement
grid.

Grids are effective reinforcement because of the increased resistance to pullout formed by
the longitudinal bars and the bent shape. However, as the mechanism of pullout
resistance is not fully understood it is recommended that tests are carried out to validate
the assumptions made.

Internal Analysis:- concerns all areas relating to internal behaviour mechanisms, stress
within the structure, arrangement and durability of reinforcement and backfill properties.

External Stability:- check stability against sliding, overturning, bearing capacity failure
and overall slope stability failure.

3.2 Internal Analysis

Unlike a standard gabion where part of the gabion's strength relies on the placement of
the backfill material, the presence of the grids in the RAMWALL act as internal strips of
reinforcement to the backfill. The overall pattern of a constructed RAMWALL has been
designed to form a solid interlocked reinforced mass gravity retaining wall with nominal
compaction of the infill material.

Initial trials have shown that with a suitably graded fill the RAMWALL can be backfilled
simply by tipping and requires no additional compaction. These initial trials require
laboratory confirmation with grading tests on the backfill and tests to confirm the mass
density of a constructed wall for use in design. The tests will also trial different grades
and types of backfill material.

Initial designs can be carried out using a porosity, r, of 0.35 and the density, r, of the

fill material. For designs to BS8004:1994 a porosity of 0.4 should be used.

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In 3.1 above it was shown that the internal forces in the RAMWALL backfill are
transferred directly in to the reinforcement either by friction or more likely interlock
between the reinforcement grid and the angular backfill material.

Therefore, stresses in the reinforcement can be calculated from the known forces acting
within the RAMWALL as the reinforcement is considered to be axially stiff and capable
of absorbing tensile, shear and bending forces. The maximum tensile stress in the
reinforcement can be determined from:

max Hu
r  ko
ar

Where max is the maximum stress developed in the wall, taking into consideration the

forces acting on the RAMWALL can be obtained assuming a Meyerhof distribution:

Nv
max 
( B  2 e)

where Nv is the vertical resultant load, B is the width of the RAMWALL and e is the
eccentricity of the resultant load about the centre-line of the base width B equal to M/N;
-3 2
ar is the area of reinforcement, which is equal to 1.4e10 m for a Hu = 0.9m high
RAMWALL unit when 6mm diameter welded wire fabric is used.

For stability, r<=t/m where t is the ultimate tensile strength of the reinforcement and

m is a partial material factor. The partial material factor is dependent on the reliability

of the tensile strength values, manufacturing quality, the backfill material, levels of
installation damage and the design life. For short-term design life conditions a value
equal to 1.05 could be used. For long term design life conditions a value of 1.5 may be
more appropriate. Reference could be made to BS8006 with adoption of the partial factor
used for metallic soil reinforcement.

The average shear stress in the wall can be taken as = PAH/B where PAH is the

resultant horizontal force acting on the RAMWALL. Without test results it is difficult to

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quantify the allowable shear fore of a RAMWALL unit but provided the RAMWALL
passes the overall check in sliding the shear force within the wall should be within
allowable limits. This assumption will be reviewed following full scale testing of the
product.

3.3 External Stability

Coulomb analysis: General Assumptions

The RAMWALL is a permeable structure so porewater pressures at the back face of the
wall will be zero. Section 5 gives further information on design, wall layout and where it
may be necessary to install filter layers to prevent loss of fines through the wall.

Coulomb analysis: Theory c = 0 ' soil

Figure 3.3(a) shows a theoretical layout of a wall with a failure surface extending from
the rear toe of the wall to the ground surface behind the wall. This failed wedge of soil
exerts horizontal and vertical thrusts on the wall, which tend to push the wall forwards
away from the retained soil slope.

The known forces acting on the wedge are:

i) Unknown frictional force R acting on the failure plane in a direction  to the

normal and opposing the downward movement of the wedge caused by the wall
moving away from the retained soil.

ii) The active thrust PA inclined at an assumed angle  to the normal and in the

direction opposing the downward movement of the wedge.

iii) The total weight of the wedge W

1 2  sin      sin    
W    H 
 sin    sin       
2  2 

iv) The known surcharge forces Q and q.

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By force equilibrium the unknown forces PA and R can be determined. From the
polygon of forces, Figure 3.3(b), it can be seen that the vector W plus the surcharge is
statically equivalent to PA and R. Since the absolute direction of these forces are known
the triangle of forces can be computed. Repeating this procedure for different failure
surfaces the maximum value of PA can be determined.

Figure 3.3

The horizontal component of the resultant thrust can be expressed as,

csc     sin    
2

KHA  
  sin    
 sin     sin      
 sin      
 sin      

1 2
PHA     H  KHA
2
where:

csc     sin    
2

KHA  
  sin    
 sin     sin      
 sin      
 sin      
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KHA  0.346

KHA
NHA 
2
NHA  0.173

(for = 80o, = 10o, = = 30o).

Adopting the notation that the vertical component PAV is positive when it is acting
downwards on the wall,

NVA  NHA cot   

NVA  0.145

(for = 80o, = 10o, = = 30o).

Where a surcharge q is applied over the upper surface, the orientation of the failure plane
corresponding to the maximum thrust is not affected. The surcharge component of
horizontal thrust is

 2 sin   
PqH  q  H  NHA
sin     

and so,

 2 sin   
NqHA   NHA
sin     

hence, the value of NqHA can be readily obtained from the numerical values of KHA
quoted on Figure 3.5a-e.

Furthermore,

NqVA  NqHA cot   

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It is a reasonable assumption for RAMWALL that the angle of friction  between the line
of thrust and the back of the wall is equal to .

The resultant thrust along the soil-wall interface, PA, is given by;

PA  PHA csc   

1 2  csc     sin     
2
PA     H  
2 sin      sin     
 sin      
 sin      
and

  csc     sin      
2
KA   
sin      sin     
 sin      
 sin       ,

The force acts at the third height of the wall above the rear toe. Graphs given in Figure
3.5a-e can be used to obtain the thrust coefficient KHA for various combinations of slope

backfill angle, , wall angle, , and soil friction angle, . Or alternatively the equations
quoted above can be used to obtain the values of PAH and PAV for use in the stability
analysis.

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
 

1.30

1.20

o o
1.10

1.00

0.90
o

0.80
KAH

0.70

0.60 o

0.50 o

0.40

0.30

0.20

0.10
10 15 20 25 30 35 40
Angle of Friction ()

Figure 3.5a

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
 
1.20

1.10

1.00
o o

0.90

0.80 o

0.70
KAH

0.60 o

0.50 o

0.40

0.30

0.20

0.10

0.00
10 15 20 25 30 35 40
Angle of Friction ()

Figure 3.5b

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
 
1.00

0.90

o
0.80

o
0.70
o

0.60
KAH

o
0.50

o

0.40

0.30

0.20

0.10
10 15 20 25 30 35 40
Angle of Friction ()

Figure 3.5c

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
 
1.00

0.90

o
0.80

0.70
o
o

0.60
KAH

o
0.50

o

0.40

0.30

0.20

0.10
10 15 20 25 30 35 40
Angle of Friction ()

Figure 3.5d

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
 
1.00

0.90

0.80
o

0.70
o

0.60 o
KAH

0.50 o

o
0.40

0.30

0.20

0.10
10 15 20 25 30 35 40
Angle of Friction ()

Figure 3.5e

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Stability Checks - General

Gravity retaining walls are designed using limit states, failure in sliding, failure in
overturning, bearing capacity failure and overall failure of the wall and ground.

In the UK the design of gravity retaining walls are covered by BS 8002:1994 Design of
Earth-retaining structures or the Eurocode 7 Geotechnical Design.

BS 8002 allows both methods of limit state design; partial factors on the material,
forces/actions and resistances or overall factors of safety against sliding and overturning.
The overall safety factors are normally set at 1.3 for sliding and 1.5 for overturning. The
only stipulations given in the BS 8004 are a factor should be applied to the 'reasonable'
soil parameters equal to 1/1.2 and a porosity of 0.4 is used for the design of gabion type
walls.

The Eurocode stipulates design methods for the stability of the wall, bearing capacity and
overall slope stability using partial factors on the materials, actions and resistances. For
retaining walls three design approaches have to be checked with each approach having
different combinations of partial factors on the three variables, Material (Xk),
Forces/Actions (Frep) and Resistances (R). For stability (equilibrium) the effect of the
actions, Ed should be less than or equal to the design resistances Rd.

Both approaches require checks on the stresses within the wall are within allowable
limits.

The checks on internal stresses in the wall are covered in Section 3.3 above.

Worked examples of both design methods are given in Section 4.

Check for Sliding ULS: In the horizontal plane, the destabilising force from the active
earth pressure has to be opposed by the stabilising forces - frictional resistance and
cohesion along the base of the RAMWALL.

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Stabilising Force Fs  N f for a c' = 0 soil

or Fs  N f  c B for a c' > 0 soil

The Normal Force, N, is the sum of all the vertical forces perpendicular to the sliding
plane, including the weight of the wall, the vertical component of the active thrust and
surcharge on top of the wall if present. The density, r, and the porosity, r, of the

backfilled units are required to calculate the density of the RAMWALL. Subject to tests
a porosity value  r  0.35 can be used.

The coefficient of friction is equal to f  tan  

Destabilising Force Fds  PHA

The factor safety against sliding is;

Fs
SFs   1.3
Fd s

The vertical component of active thrust may be ignored in favour of safety.

Check for Overturning ULS: Using basic statics and taking moments about the front
toe of the RAMWALL, the overturning moment caused by the active soil pressure acting
on the back of the wall is resisted by the restoring moment caused by the weight of the
retaining wall.

The check may be expressed as:

1
Mr  5 kN m m

1
Mo  5 kN m m

Mr
Sfo   1.5
Mo

where Mr is the restoring moment, Mo is the overturning moment and SFo is the factor of
safety against overturning. The moments can be obtained by summing the products of
the forces by their respective lever arms from the front toe of the RAMWALL.

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Generally, the active soil pressure normally acts at through the third point of the wall
height; any uniform surcharge will act through the mid point of the wall height. The
restoring moment comprising the RAMWALL weight and the vertical component of
active soil thrust multiplied by the respective lever arms. The level arms for the restoring
moments are dependent on the particular geometry of the wall analysed.

Again the vertical component of the active thrust may be ignored in favour of safety.

Check on Foundation Bearing Capacity ULS: Foundation bearing pressures beneath

the RAMWALL can be computed using the relevant values of M and N and the
eccentricity e of the vertical force from the mid point of the base thus:

B Mr  Mo
ebc  
2 N

where N is the overall vertical force component, Mr is the overturning moment

component, and Mo is the overturning moment component.

The maximum bearing pressure on the foundation can be obtained using:

N  6 ebc 
Pf   1  
B  B 

if -B/6 <= ebc <= B/6

where ebc does not comply with this rule, part of the section will be in tension and the
maximum bearing pressure can be obtained using:

2 N
Pf 
3 B
 ebc
2

The maximum pressure must not exceed the allowable soil bearing capacity as with the
other stability checks the calculation of the allowable bearing capacity is subject to the
relevant code of practice or recognised procedure, which is beyond the scope of these
calculations.
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Serviceability Limit State: RAMWALLs are a flexible structure capable of sustaining

large settlements without damage to the structure. Therefore, only the durability and the
suitability of the backfill material needs to be considered for the serviceability limit state
design.

3.4 Other Design Applications

The anticipated excellent interlocking and pullout characteristics of the RAMWALL grid
should make it suitable for use as soil reinforcement in reinforced earth structures with
the standard RAMWALL acting as a fascia wall, 1m thick, with extended strips of
RAMWALL grid placed at suitable intervals extending into the backfill.

The design of this type of wall is covered by the appropriate codes of practice - BS8006
and Eurcode 7. Testing of the pullout characteristics of the RAMWALL grid is required
before the system can be adapted for reinforced earth so the design of this type of
RAMWALL will be covered by a subsequent report.

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4. WORKED EXAMPLE

4.1 General

Figure 4.1 shows two configurations of an example RAMWALL, stepped rear face and
3
stepped front face. Assuming the backfill slope material properties are   19.0kN
 m

and   32 deg the stability of the RAMWALL can be checked as follows:

Figure 4.1

Check against sliding: (Conventional Analysis SFs >= 1.3)

Stabilising Force:

Fs  Nw  PVAf
for a c'=0 soil
Where N is the weight of the Ramwall, from Figure 4.1:
Wall dimensions:
H  5.566m

Bb  3.4m


Bt  (3.4  2.0) m

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Wall properties:
r  0.35

3
 r  22.5 kN m

 Bb  Bt 
Nw     H  r  1   r
 2 
1
Nw  195.367kN m

From Figure 4.1:

  75 deg

  25 deg

  

q  5kPa

csc     sin    
2
KHA  
   sin    
 sin     sin      
 sin      
 sin      
KHA  0.497

KVA  KHA cot   

KVA  0.533

1 2 sin   
PVA     H  KVA  q  H  KVA
2 sin     

1
PVA  171.531kN m

Fs   Nw  PVA tan 

1
Fs  229.263kN m

Destabilising Force:
Fds  PHA

where :
1 2 sin   
PHA     H  KHA  q  H  KHA
2 sin     

1
PHA  159.955kN m

Fds  PHA

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The factor safety against sliding is:

Fs
SFs 
Fds

SFs  1.43

The stepped rear face wall passes in sliding with the configuration shown in Figure 4.1:

Check against Overturning: (Conventional Analysis SFo >= 1.5)

Restoring Moment:
Mr  Mrm  MVA

where:
Mrm  Nw dw

and:
MVA  PVA dVA

dw is the distance from the front toe of the Ramwall to the centre of gravity,
from Figure 4.1:
Element Height:
Reh  0.902m


Element Widths:
B1  Bb

B2  Bb  0.4m


B3  B2  0.4m


B4  B3  0.4m


B5  B4  0.4m


B6  B5  0.4m


Taking moments about the toe:

 B12   B22   B32   B42   B52   B62 
  Reh    Reh    Reh    Reh    Reh    Reh
d w 
 2   2   2   2   2   2 
B1 Reh  B2 Reh  B3 Reh  B4 Reh  B5 Reh  B6 Reh
dw  1.297m

Mrm  Nw dw

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Therefore;
1
Mrm  253.434kN m m

PVA can be split into the surcharge component which acts at the mid point along the rear
face and the active earth pressure component which acts at the lower third point along the
rear face. Therefore the distances can be calculated knowing the width of the base and
the angle of the rear face of the Ramwall.

MVA     H  KVA  Bb 
1 2 H   q H sin    K   B  H 
 VA  b 
2  3 tan     sin       2 tan    

1
MVA  494.313kN m m

Mr  Mrm  MVA

Giving a total Restoring Moment of:

1
Mr  747.747kN m m

Overturning Moment comprises the horizontal component of the surcharge acting

through the mid point of the rear face and the horizontal component of the active earth
pressure acting through the lower third of the rear face as follows:
sin   
Mo     H  KHA    q H  KHA  
1 2 H H
2  
3 
sin      2
1
Mo  309.365kN m m

The factor of safety against overturning is:

Mr
SFo 
Mo

SFo  2.42

The stepped rear face wall passes in overturning with the configuration shown in Fig. 4.1.
The maximum bearing pressures exerted by the Ramwall on the foundation can be
calculated as follows:
Bb Mr  Mo
ebc  
2  Nw  PVA
ebc  0.505m

As ebc is greater than Bb/6 then part of the base is in tension and the maximum bearing
capacity is obtained by:
 Nw  PVA
Pf  2
 3 Bb 
  ebc
 2 

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2
Pf  159.7kN m

For stability the maximum bearing pressure given above must not exceed the allowable
bearing capacity of the foundation. Standard bearing capacity analyses can be used to
obtain the allowable bearing capacity.

Check on Internal Stresses - Stepped Rear Face

As discussed in Section 3.2 the stresses acting in the reinforcement must not exceed the
allowable stress of the steel. The stresses in the reinforcement can be calculated using the
Normal loads and Bending Moments acting within the Ramwall. Assuming a standard
0.9m high Ramwall unit constructed using 6mm diameter welded wire fabric, the area of
reinforcement:
2
ar  0.0014m


Hu  0.9 m

The maximum stress developed in the wall taking into consideration the forces acting on
the Ramwall can be obtained assumming a Meyerhof distribution:

 Nw  PVA
max 
Bb  2 e
2
max  153.535kN m

ko  0.426

The stress in the reinforcement can be calculated from (assumming ko=0.426 for the
backfill):
max Hu
r  ko
ar

2 1
r  42047kN m m

For high tensile welded wire fabric:

2 1
t  420000kN
 m m

Therefore, the stresses in the Ramwall are well below the allowable stress in the steel.

4.3 Stepped Front Face

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Check against Sliding: (Conventional Analysis SFs >= 1.3)

Stabilising Force:
1
Nw  195.367kN m

same as stepped rear faced wall.

From Figure 4.1:
  95 deg

  25 deg

  

q  5kPa

H  5.391m


csc     sin    
2

KHA  
  sin    
 sin     sin      
 sin      
 sin      
KHA  0.339

KVA  KHA cot   

KVA  0.173

1 2 sin   
PVA     H  KVA  q  H  KVA
2 sin     

1
PVA  53.057kN m

Fs   Nw  PVA tan 

1
Fs  155.232kN m

Destabilising Force:
Fds  PHA

where:
1 2 sin   
PHA     H  KHA  q  H  KHA
2 sin     

1
PHA  104.13kN m

Fds  PHA

The factor safety against sliding is:

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Fs
SFs 
Fds

SFs  1.49

Therefore the stepped front face wall passes in sliding with the configuration shown in
Figure 4.1. The calculation above indicates that the stepped rear faced wall is more
reliant on the vertical component of the active earth pressure acting on the rear of the
Ramwall.

Check against Overturning: (Conventional Analysis SFo >= 1.5)

Restoring Moment:
Mr  Mrm  MVA

where
Mrm  Nw dw

and
MVA  PVA dVA

dw is the distance from the front toe of the Ramwall to the centre of gravity, from Figure
4.1:
Element Height:
Reh  0.902m


Element Widths:
B1  Bb

B2  Bb  0.4m


B3  B2  0.4m


B4  B3  0.4m


B5  B4  0.4m


B6  B5  0.4m


Taking moments about the toe:

 B12   B22   B32   B42   B52   B62 
 
 Reh   
 Reh   
 Reh   
 Reh   
 Reh    Reh
d w 
 2   2   2   2   2   2 
B1 Reh  B2 Reh  B3 Reh  B4 Reh  B5 Reh  B6 Reh
dw  B  dw

dw  2.203m

Mrm  Nw dw

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Therefore
1
Mrm  430.349kN m m

PVA can be split into the surcharge component which acts at the mid point along the rear
face and the active earth pressure component which acts at the lower third point along the
rear face. Therefore the distances can be calculated knowing the width of the base and
the angle of the rear face of the Ramwall.

MVA     H  KVA  Bb 
1 2 H   q H sin    K   B  H 
 VA  b 
2  3 tan     sin       2 tan    

1
MVA  189.155kN m m

Mr  Mrm  MVA

Giving a total Restoring Moment of:

1
Mr  619.504kN m m

Overturning Moment comprises the horizontal component of the surcharge acting

through the mid point of the rear face and the horizontal component of the active earth
pressure acting through the lower third of the rear face as follows:
sin   
Mo     H  KHA    q H  KHA  
1 2 H H
2  3 sin       2
1
Mo  196.567kN m m

The factor of safety against overturning is

Mr
SFo 
Mo

SFo  3.15

The stepped front face wall passes in overturning with the configuration shown in Figure
4.1.
The maximum bearing pressures exerted by the Ramwall on the foundation can be
calculated as follows:
Bb Mr  Mo
ebc  
2  Nw  PVA
3
ebc  2.487 10 m

As ebc is less than Bb/6 the base is in compression and then the maximum bearing
capacity is obtained by

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 Nw  PVA  6 ebc 
Pf   1 
Bb  Bb 
2
Pf  72.745kN m

For stability the maximum bearing pressure given above must not exceed the allowable
bearing capacity of the foundation. Standard bearing capacity analyses can be used to
obtain the allowable bearing capacity.

This calculation also shows that the stepped front face configuration is a more stable and
exerts less pressure on the foundation.

Check on Internal Stresses - Stepped Front Face

As discussed in Section 3.2 the stresses acting in the reinforcement must not exceed the
allowable stress of the steel. The stresses in the reinforcement can be calculated using the
Normal loads and Bending Moments acting within the Ramwall. Assuming a standard
0.9m high Ramwall unit constructed using 6mm diameter welded wire fabric, the area of
reinforcement:
2
ar  0.0014m


Hu  0.9 m

The maximum stress developed in the wall taking into consideration the forces acting on
the Ramwall can be obtained assumming a Meyerhof distribution:

 Nw  PVA
max 
Bb  2 e
2
max  72.959kN m

The stress in the reinforcement can be calculated from (assumming ko=0.426 for the
backfill):
ko  0.426

max Hu
r  ko
ar

2 1
r  19980kN m m

For high tensile welded wire fabic:

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2 1
t  420000kN
 m m

Therefore the stresses in the Ramwall are well below the allowable stress in the steel.

4.4 Stepped Rear Face (to BS8004:1994)

Check against sliding: (Limit State Analysis SFs >= 1.0)

BS8004 requires a reduction to the angle of friction equal to tan(d)=tan()/1.2

 tan   
  atan  
 1.2 
  27.507deg

Stabilising Force
Fs   Nw  PVA f

for a c'=0 soil

Where N is the weight of the Ramwall, from Figure 4.1:
Wall dimensions:
H  5.566m

Bb  3.4 m

Bt  ( 3.4  2.0)  m

Wall properties:
 r  0.4

3
 r  22.5 kN m

 Bb  Bt 
Nw     H  r  1   r
 2 
1
Nw  180.338kN m

From Figure 4.1:

  75 deg

  25 deg

  

q  5 kPa

csc     sin    
2
KHA  
   sin    
 sin     sin      
 sin      
 sin      

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KHA  0.684

KVA  KHA cot   

KVA  0.627

1 2 sin   
PVA     H  KVA  q  H  KVA
2 sin     

1
PVA  201.59kN m

Fs   Nw  PVA tan 

1
Fs  198.88kN m

Destabilising Force:
Fds  PHA

where
1 2 sin   
PHA     H  KHA  q  H  KHA
2 sin     

1
PHA  219.943kN m

Fds  PHA

The factor safety against sliding is

Fs
SFs 
Fds

SFs  0.90

The stepped rear face wall fails in sliding with the configuration shown in Figure 4.1
using the design methods given by BS8004:1994. Try increasing the width of the wall:
Wall dimensions:
H  5.566m

Bb  4.0 m

Bt  ( 4.0  2.0)  m

Wall properties:
 r  0.4

3
 r  22.5 kN m

 Bb  Bt 
Nw     H  r  1   r
 2 
1
Nw  225.423kN m

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From Figure 4.1:

  75 deg

  25 deg

  

q  5 kPa

csc     sin    
2
KHA  
   sin    
 sin     sin      
 sin      
 sin      
KHA  0.684

KVA  KHA cot   

KVA  0.627

1 2 sin   
PVA     H  KVA  q  H  KVA
2 sin     

1
PVA  201.59kN m

Fs   Nw  PVA tan 

1
Fs  222.356kN m

Destabilising Force:
Fds  PHA

where :
1 2 sin   
PHA     H  KHA  q  H  KHA
2 sin     

1
PHA  219.943kN m

Fds  PHA

The factor safety against sliding is:

Fs
SFs 
Fds

SFs  1.01

The stepped rear face wall passes in sliding with an increased base width of 4m using the
design methods given by BS8004:1994.
Check against Overturning: (Limit State Analysis SFo >= 1.0)
Restoring Moment:
Mr  Mrm  MVA

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where :
Mrm  Nw dw

and
MVA  PVA dVA

dw is the distance from the front toe of the Ramwall to the centre of gravity,
from Figure 4.1:
Element Height:
Reh  0.902m


Element Widths:
B1  Bb

B2  Bb  0.4m


B3  B2  0.4m


B4  B3  0.4m


B5  B4  0.4m


B6  B5  0.4m


Taking moments about the toe:

 B12   B22   B32   B42   B52   B62 
 
 Reh   
 Reh   
 Reh   
 Reh    Reh    Reh
d w 
 2   2   2   2   2   2 
B1 Reh  B2 Reh  B3 Reh  B4 Reh  B5 Reh  B6 Reh
dw  1.578m

Mrm  Nw dw

Therefore
1
Mrm  355.667kN m m

PVA can be split into the surcharge component which acts at the mid point along the rear
face and the active earth pressure component which acts at the lower third point along the
rear face. Therefore the distances can be calculated knowing the width of the base and
the angle of the rear face of the Ramwall.

MVA     H  KVA  Bb 
1 2 H   q H sin    K   B  H 
 VA  b 
2  3 tan     sin       2 tan    

1
MVA  701.891kN m m

Mr  Mrm  MVA

Giving a total Restoring Moment of:

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3 1
Mr  1.058 10 kN m m

Overturning Moment comprises the horizontal component of the surcharge acting

through the mid point of the rear face and the horizontal component of the active earth
pressure acting through the lower third of the rear face as follows:
sin   
Mo     H  KHA    q H  KHA  
1 2 H H
2  
3 
sin      2
1
Mo  425.384kN m m

The factor of safety against overturning is:

Mr
SFo 
Mo

SFo  2.49

The stepped rear face wall passes in overturning with the configuration shown in Figure
4.1, but with an increased width of 4m to pass the check on sliding.
The maximum bearing pressures exerted by the Ramwall on the foundation can be
calculated as follows:
Bb Mr  Mo
ebc  
2  Nw  PVA
ebc  0.52m

As ebc is greater than Bb/6 then part of the base is in tension and the maximum bearing
capacity is obtained by
 Nw  PVA
Pf  2
 3 Bb 
  ebc
 2 
2
Pf  155.831kN m

For stability the maximum bearing pressure given above must not exceed the allowable
bearing capacity of the foundation. Standard bearing capacity analyses can be used to
obtain the allowable bearing capacity.

Check on Internal Stresses - Stepped Rear Face

As discussed in Section 3.2 the stresses acting in the reinforcement must not exceed the
allowable stress of the steel. The stresses in the reinforcement can be calculated using the
Normal loads and Bending Moments acting within the Ramwall. Assuming a standard

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0.9m high Ramwall unit constructed using 6mm diameter welded wire fabric, the area of
reinforcement:
2
ar  0.0014m


Hu  0.9 m

The maximum stress developed in the wall taking into consideration the forces acting on
the Ramwall can be obtained assumming a Meyerhof distribution:

 Nw  PVA
max 
Bb  2 e
2
max  144kN m

The stress in the reinforcement can be calculated from (assumming ko=0.426 for the
backfill):
ko  0.426

max Hu
r  ko
ar

2 1
r  39495kN m m

For high tensile welded wire fabic:

2 1
t  420000kN
 m m

Therefore the stresses in the Ramwall are well below the allowable stress in the steel.

4.5 Stepped Front Face - to BS8004:1994

Check against Sliding: (Limit State Analysis SFs >= 1.0)

Stabilising Force:
1
Nw  225.423kN m

same as stepped rear faced wall.

From Figure 4.1:
  95 deg

  25 deg

  

q  5 kPa

H  5.391m

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csc     sin    
2
KHA  
   sin    
 sin     sin      
 sin      
 sin      
KHA  0.488

KVA  KHA cot   

KVA  0.202

1 2 sin   
PVA     H  KVA  q  H  KVA
2 sin     

1
PVA  62.117kN m

Fs   Nw  PVA tan 

1
Fs  149.729kN m

Destabilising Force
Fds  PHA

where :
1 2 sin   
PHA     H  KHA  q  H  KHA
2 sin     

1
PHA  149.911kN m

Fds  PHA

The factor safety against sliding is:

Fs
SFs 
Fds

SFs  1.00

Therefore the stepped front face wall fails in sliding with the configuration shown in
Figure 4.1.
Check against Overturning: (Limit State Analysis SFo >= 1.0)
Restoring Moment:
Mr  Mrm  MVA

where:
Mrm  Nw dw

and
MVA  PVA dVA

dw is the distance from the front toe of the Ramwall to the centre of gravity, from Figure

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4.1:
Element Height:
Reh  0.902m


Element Widths:
B1  Bb

B2  Bb  0.4 m

B3  B2  0.4 m

B4  B3  0.4 m

B5  B4  0.4 m

B6  B5  0.4 m

Taking moments about the toe:

 B12   B22   B32   B42   B52   B62 
  Reh    Reh    Reh    Reh    Reh    Reh
d w 
 2   2   2   2   2   2 
B1 Reh  B2 Reh  B3 Reh  B4 Reh  B5 Reh  B6 Reh
dw  B  dw

dw  1.922m

Mrm  Nw dw

Therefore
1
Mrm  433.313kN m m

PVA can be split into the surcharge component which acts at the mid point along the rear
face and the active earth pressure component which acts at the lower third point along the
rear face. Therefore the distances can be calculated knowing the width of the base and
the angle of the rear face of the Ramwall.

MVA     H  KVA  Bb 
1 2 H   q H sin    K   B  H 
   VA  b 
2  3 tan   sin       2 tan    

1
MVA  258.727kN m m

Mr  Mrm  MVA

Giving a total Restoring Moment of:

1
Mr  692.04kN m m

Overturning Moment comprises the horizontal component of the surcharge acting

through the mid point of the rear face and the horizontal component of the active earth
pressure acting through the lower third of the rear face as follows:

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sin   
Mo     H  KHA    q H  KHA  
1 2 H H
2  3 sin       2
1
Mo  282.99kN m m

The factor of safety against overturning is

Mr
SFo 
Mo

SFo  2.445

The stepped front face wall passes in overturning with the configuration shown in Figure
4.1 and the increased base width of 4m.
The maximum bearing pressures exerted by the Ramwall on the foundation can be
calculated as follows:
Bb Mr  Mo
ebc  
2  Nw  PVA
ebc  0.577m

As ebc is less than Bb/6 the base is in compression and then the maximum bearing
capacity is obtained by
 Nw  PVA
Pf  2
 3 Bb 
  ebc
 2 
2
Pf  106.053kN m

For stability the maximum bearing pressure given above must not exceed the allowable
bearing capacity of the foundation. Standard bearing capacity analyses can be used to
obtain the allowable bearing capacity.

This calculation shows that the stepped front face configuration is a more stable and
exerts less pressure on the foundation.

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Check on Internal Stresses - Stepped Front Face

As discussed in Section 3.2 the stresses acting in the reinforcement must not exceed the
allowable stress of the steel. The stresses in the reinforcement can be calculated using the
Normal loads and Bending Moments acting within the Ramwall. Assuming a standard
0.9m high Ramwall unit constructed using 6mm diameter welded wire fabric, the area of
reinforcement:
2
ar  0.0014m


Hu  0.9 m

The maximum stress developed in the wall taking into consideration the forces acting on
the Ramwall can be obtained assumming a Meyerhof distribution:

 Nw  PVA
max 
Bb  2 e
2
max  101.063kN m

The stress in the reinforcement can be calculated from (assumming ko=0.426 for the
backfill):
ko  0.426

max Hu
r  ko
ar

2 1
r  27677kN m m

For high tensile welded wire fabric:

2 1
t  420000kN
 m m

Therefore, the stresses in the Ramwall are well below the allowable stress in the steel.

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5. DURABILITY CONSIDERATIONS

5.1 General

The consideration of corrosion in the RAMWALL reinforcement panels and the

durability of the backfill material is dependent on the design life of the proposed
structure. For a short term design life, say 1 to 20 years the corrosion is only a minor
consideration and generally can be ignored provided the backfill and the surrounding soil
is reasonably inert. However, for a long term design life, say 50 to 120 years the
corrosion of the RAMWALL panels and the durability of the backfill material is a major
concern. Testing the soils' aggressiveness and design issues of the reinforcement panels
need to be taken into consideration.

5.2 Metal Corrosion

The RAMWALL reinforcement panels and fascia panels are made of metal and are,
therefore, subject to electrochemical corrosion. Different types of metal corrode in
different ways:-
Steel, galvanised or not, exhibit general corrosion,
Aluminum and stainless steel exhibit pitted corrosion.

Of the two types general corrosion is often preferred as it is predictable and strength
decreases can be quantified.

The factors that affect the rate of corrosion are the soil aggressiveness, water content,
metal type, protective coatings and installation damage.

The soil in contact with the RAMWALL and the backfill material can be classified and
scored against a series of criteria to classify its aggressiveness; non aggressive, weakly
aggressive, aggressive and strongly aggressive.

Assessment of soil aggressiveness towards buried metals can be assessed using four
criteria; Resistivity, Redox Potential, Normal Hydrogen electrode and Moisture Content.
We would also, recommend that soil pH and soluble salts are tested as well.
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As well as internal factors in the soil, external factors such as runoff of salts from roads
or buildings need to be considered.

Galvanising the steel slows the rate of corrosion as it is a poor cathode and if damaged
these sections corrode and seal the gaps between the galvanising so preventing further
corrosion.

Rates of corrosion can be estimated for steel, galvanising the steel slows the initial rate
until the zinc coating is used up and then the steel will corrode at the same rate as
ordinary steel. Of the normally used rebar steels, low tensile steel grades are less
susceptible to pitting and hydrogen embrittlement.

Cinders, carbon particles, coke and coal should be avoided in the backfill material as
these materials have deleterious effect and can cause serious corrosion.

Physical damage during the installation can be assessed using a site damage test, see
BS8006:1995.

5.3 Design for Durability

Long-term durability of buried or partially buried metal structures can be provided by

designing for a sacrificial thickness, values are given in the UK and France for all but
highly aggressive ground conditions. Reference to the relevant code of practice can be
made to obtain the allowable sacrificial depths for the various degrees of soil
aggressiveness.

Testing of the RAMWALL may be able to prove that the structure has sufficient
redundancy in the internal reinforcement so the only durability questions would relate to
the facure panels and the backfill material.

Other ways of providing durability is to physically protect the reinforcement by various

methods, for example galvanising and/or PVC coating, nominally 0.25mm thick coating
to BS4102.

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Also, all metallic components should be electrolytically compatible or otherwise effective

electrical insulation must be provided.

The design needs to consider the durability of the backfill material in relation to the
design life of the structure, its location in terms of weather and groundwater chemistry
and the internal forces acting within the wall.

Any backfill material used must be resistant to the weather, groundwater and not
susceptible to crushing under the anticipated loads within the RAMWALL. The
hardness, crushing strength and resistance to weathering of the backfill material can be
tested to BS5390.

The RAMWALL structure is free draining and provided migration of fines from the
adjacent soil mass in to the infill is prevented, seepage or pore pressure will not develop
within the RAMWALL. Fines migration from susceptible soils can be prevented using a
suitable graded filter behind the wall (see Section 6.4.4.5, BS 8004:1986) or a geotextile
separator. The latter option provides a fast and economic solution to fines migration in
most situations and geotextile manufacturers can provide specific guidance on selection
and installation of suitable material. Soils are unlikely to require protection against fines-
migration provided;

D15 RAMWALL/D85 Soil > 4.

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6. CONCLUSIONS

RAMWALL can be designed as a standard gravity retaining wall using the conventional
coulomb active wedge method of analysis. The choice of Safety Factors; whether global
factors on the external forces or partial factors on the parameters are dependent on the
design method or code of practice adopted. A worked example using both approaches is
given in Section 4.0 above. These worked examples show that using partial factors is the
more onerous method of analysis.

Calculations have also shown that the stepped rear face configuration of wall exerts
significantly more pressure on the foundation than the stepped front face configuration.

Internal stresses on the RAMWALL units can be obtained assuming a Meyerhof

distribution and the internal forces N and M. Assuming the effective stiffness of the
reinforcement is high the tensile stress in the reinforcement can be calculated and
checked against the allowable tensile strength. The allowable tensile strength is equal to
the maximum tensile strength of the reinforcement divided by a partial material factor.
This factor can consider the quality of steel manufacture, the reliability of the test results
and the durability required for the design life. Values of between 1.15 and 2.0 can be
considered for short and long-term designs.

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