Frew19.4 Manual
Frew19.4 Manual
Frew19.4 Manual
Version 19.4
Oasys Ltd
13 Fitzroy Street
London
W1T 4BQ
Central Square
Forth Street
Newcastle Upon Tyne
NE1 3PL
Telephone: +44 (0) 191 238 7559
Facsimile: +44 (0) 191 238 7555
e-mail: oasys@arup.com
Website: http://www.oasys-software.com/
All rights reserved. No parts of this work may be reproduced in any form or by any means - graphic, electronic, or
mechanical, including photocopying, recording, taping, or information storage and retrieval systems - without the
written permission of the publisher.
Products that are referred to in this document may be either trademarks and/or registered trademarks of the
respective owners. The publisher and the author make no claim to these trademarks.
While every precaution has been taken in the preparation of this document, the publisher and the author assume no
responsibility for errors or omissions, or for damages resulting from the use of information contained in this
document or from the use of programs and source code that may accompany it. In no event shall the publisher and
the author be liable for any loss of profit or any other commercial damage caused or alleged to have been caused
directly or indirectly by this document.
This document has been created to provide a guide for the use of the software. It does not provide engineering
advice, nor is it a substitute for the use of standard references. The user is deemed to be conversant with standard
engineering terms and codes of practice. It is the users responsibility to validate the program for the proposed
design use and to select suitable input data.
Table of Contents
1 About Frew 1
1.1 General...................................................................................................................................
Program Description 1
1.2 Program...................................................................................................................................
Features 1
1.3 Components
...................................................................................................................................
of the User Interface 3
1.3.1 Working w ith the
.........................................................................................................................................................
Gatew ay 3
2 Methods of Analysis 4
2.1 Stability...................................................................................................................................
Check 4
2.1.1 Fixed Earth Mechanism
.........................................................................................................................................................
s 4
2.1.2 Free Earth Mechanism
.........................................................................................................................................................
s 5
2.1.2.1 Multi-propped ..................................................................................................................................................
w alls 5
2.1.3 Active and Passive.........................................................................................................................................................
Lim its 8
2.1.4 Groundw ater Flow
......................................................................................................................................................... 10
2.2 Full Analysis
................................................................................................................................... 11
2.3 Soil Models
................................................................................................................................... 12
2.3.1 Safe Method ......................................................................................................................................................... 13
2.3.2 Mindlin Method......................................................................................................................................................... 13
2.3.3 Method of Sub-grade
.........................................................................................................................................................
Reaction 14
2.4 Active and
...................................................................................................................................
Passive Pressures 15
2.4.1 Effects of Excavation
.........................................................................................................................................................
and Backfill 16
2.4.2 Calculation of Earth
.........................................................................................................................................................
Pressure Coefficients 16
2.5 Total and
...................................................................................................................................
Effective Stress 18
2.5.1 ......................................................................................................................................................... 18
Drained Materials
2.5.2 .........................................................................................................................................................
Undrained Materials and Calculated Pore Pressures 18
2.5.3 .........................................................................................................................................................
Undrained Materials and User-defined Pore Pressure 21
2.5.4 .........................................................................................................................................................
Undrained to Drained Exam ple 22
3 Input Data 26
3.1 Assembling
...................................................................................................................................
Data 28
3.2 Preferences
................................................................................................................................... 32
3.3 New Model
...................................................................................................................................
Wizard 33
4 Frew-Safe Link 77
4.1 Data Entry
................................................................................................................................... 77
4.2 Data Conversion
................................................................................................................................... 82
4.2.1 Stages/Runs ......................................................................................................................................................... 82
4.2.2 Geom etry ......................................................................................................................................................... 84
4.2.3 Restraints ......................................................................................................................................................... 84
7 Output 116
7.1 Analysis
...................................................................................................................................
and Data Checking 116
7.2 Tabulated
...................................................................................................................................
Output 119
7.2.1 Stability Check
.........................................................................................................................................................
Results 121
7.2.2 Detailed Results
......................................................................................................................................................... 121
7.2.2.1 Results Annotations
..................................................................................................................................................
and Error Messages 123
7.2.3 Sum m ary Output
......................................................................................................................................................... 124
7.3 Graphical
...................................................................................................................................
Output 125
7.4 Batch...................................................................................................................................
Plotting 128
Index 178
1 About Frew
1.1 General Program Description
Frew (Flexible REtaining Walls) is a program that analyses flexible earth retaining structures such
as sheet pile and diaphragm walls. The program enables the user to study the deformations of, and
stresses within, the structure through a specified sequence of construction.
This sequence usually involves the initial installation of the wall followed by a series of activities such
as variations of soil levels and water pressures, the insertion or removal of struts or ground anchors
and the application of surcharges.
The program calculates displacements, earth pressures, bending moments, shear forces and strut
(or anchor) forces occurring during each stage in construction.
It is important to realise that Frew is an advanced program analysing a complex problem and the
user must be fully aware of the various methods of analysis, requirements and limitations discussed
in this help file before use.
The program input is fully interactive and allows both experienced and inexperienced users to control
the program operation.
The geometry of the wall is specified by a number of nodes. The positions of these nodes
are expressed by reduced levels. The nodes can be generated from the other data (soil
interface levels etc.) using the Automatic Node Generation feature.
Wall stiffness is constant between nodes, but may change at nodes. The base of the wall
may be specified at any node, nodes below this are in "free" soil. The wall stiffness can be
changed or relaxed at the various stages of the analysis.
Soil profiles are represented by a series of horizontal soil strata that may be different each
side of the wall. The boundaries of soil strata are always located midway between node
levels. This constraint will be accommodated when using the Automatic Node Generation
feature.
Struts may be inserted and subsequently removed. Each strut acts at a node. If the
Automatic Node Generation feature is used, a node will be generated at each specified
strut level. A strut may have a specified stiffness, pre-stress and lever arm and may be
inclined to the horizontal. For inclined struts with a non-zero lever arm, a rotational
stiffness at the node is modelled.
Surcharges may be inserted and subsequently removed. Each surcharge comprises a
uniformly distributed load or a pressure load of a specified width.
Soil may be excavated, backfilled or changed at each stage, on either side of the wall.
Water pressures may be either hydrostatic or piezometric.
The program provides a selection of stiffness models to represent the soil.
1. "Safe" flexibility model.
2. Mindlin model.
3. Sub-grade reaction model.
Note: The sub-grade reaction model is currently not active, it will be added to Frew in the near
future.
All methods allow rigid (vertical) boundaries at specified distances from the wall. A rigid
base is also assumed at the lowest node for the "Safe" and Mindlin methods.
Soil pressure limits, active and passive, may be redistributed to allow for arching effects.
Any vertical distribution of Young's modulus may be specified, and each model provides an
approximate representation of this distribution. Alternatively the user may specify Young's
modulus as either constant for the Mindlin model or linearly variable for the "Safe" method
if desired.
The effect of summer expansion and winter contraction of integral bridges can be assessed
using the integral bridge feature.
Where appropriate the effect of seismic ground movement can be assessed using the
Wood's and Mononobe-Okabe methods.
Top level categories can be expanded by clicking on the `+´ symbol beside the name or by double
clicking on the name. Clicking on the `-´ symbol or double clicking on the name when expanded will
close up the item. A branch in the view is fully expanded when the items have no symbol beside
them.
Double clicking on an item will open the appropriate table view or dialog for data input. The gateway
displays data from the current stage under "Data for Stage ..." node. The data items which have
changed from the previous stage are indicated by bold font.
2 Methods of Analysis
Frew is used to compute the behaviour of a retaining wall through a series of construction
sequences.
A summary of the Frew analysis, for inclusion with the program results and project reports, is
included in Brief technical description.
These pressures are used to calculate the required penetration of the wall to achieve rotational
stability.
Support for partial factor analysis is now available in the program.The user may specify this in
"Partial Factors" dialog.
Two statically determinate mechanisms in the form of "Fixed earth" cantilever and "Free earth"
propped retaining walls can be solved. For either problem several struts with specified forces can be
applied.
Note : The user should be aware that other mechanisms of collapse may exist for the problem which
are not considered by the stability check. These include rotation of the soil mass, failure of the
props/anchors or failure of the wall in bending.
The mechanism assumes that the wall is fixed by a passive force developing near its base. The level
of the base of the wall is calculated to give equilibrium under this assumed pressure distribution.
The mechanism assumes rotation about a specified strut and calculates the level of the base of the
wall and the force in the strut required to give equilibrium.
The ground level on the retained side is assumed to be 1 cm above the rotation strut.
Any soil layers above this assumed ground level are treated as equivalent surcharges.
The ground water distribution is also applied starting from the assumed ground level. However, the
pore pressure from the level of rotation strut downwards are same as the original pore pressure
distribution. The pore pressure from the level of assumed ground level to the level of rotation strut is
assumed to vary linearly.
Tolerance is related to the assumed location of ground level above the location of lowest strut. This
is currently taken as 1 cm.
Any strip surcharges that are present above the location of rotation strut are modelled as
equivalent strip surcharges at the level of the lowest strut. The load intensity and width of this
equivalent surcharge are calculated using 2:1 rule for diffusion of vertical stress in soil.
Q' = W*Q/W'
where,
Generally speaking, the centrelines of the actual surcharge and the equivalent surcharge
coincide. However, if the extent of equivalent surcharge crosses the wall, then the equivalent
surcharge is assumed to have the same width calculated as above, but it is assumed to start from
the edge of the wall.
Note: The partial factors for user-defined surcharges are not applied to the equivalent surcharge due
to overburden above the lowest strut in this analysis of multi-propped walls.
The generation of intermediate levels ensures the accuracy of the calculation of bending moments
and shear forces. Intermediate levels will be generated where there is a change in the linear profile
of pressure with depth e.g.
at surcharge levels
The effective active and passive pressures are denoted by p'a and p'p respectively. These are
calculated from the following equations:-
where
c' = effective cohesion or undrained
strength as appropriate
'v = vertical effective overburden pressure
Note : Modification of the vertical effective stress due to wall friction should be made by taking
appropriate values of k a and k p.
Where
c w = wall adhesion
where
s
= unit weight of soil
u = pore water pressure
zudl
= vertical sum of pressures of all
uniformly distributed loads (udl's)
above depth z.
The effect on the active pressure of strip surcharges is calculated by the method of Pappin et al
(1986), also reported in Institution of Structural Engineers (1986).
Note : If the width of the load (B) is small, the diagram will become triangular.
The additional active pressure due to the surcharge is replaced by a series of equivalent forces.
These act at the same spacing of the output increment down the wall. Thus a smaller output
increment will increase the accuracy of the calculation.
Varying values of ka
If the active pressure coefficient k a varies with depth, the program chooses a mean value of k a
between any depth z and the level of the surcharge. Stawal then imposes the criterion that the
active force due to the surcharge down to depth z be equal to the force derived from the diagram in
above.
This is then subjected to the further limitation that the pressure does not exceed qk az.
where
q = surcharge pressure.
1. Carry out initial calculation using input water data to obtain the first estimate of embedment of the
wall (d).
5. Repeat steps 2 to 4 until d is consistent with the groundwater profile and Uf is balanced at the
base.
Note: This modification to water profile is only for stability calculations. It is NOT carried over to the
actual Frew analysis.
The initial stage (Stage 0) is used to calculate the soil stress prior to the installation of the wall.
Displacements computed in this stage are set to zero.
At each stage thereafter the incremental displacements, due to the changes caused by that stage,
are calculated and added to the existing displacements. The soil stresses, strut forces, wall bending
moments and shear forces are then determined.
The wall is modelled as a series of elastic beam elements joined at the nodes. The lowest node is
either the base of the wall or at a prescribed rigid base in the ground beneath the wall.
The soil at each side of the wall is connected at the nodes as shown on the figure.
a) The initial earth pressures and the out of balance nodal forces are calculated assuming no
movement of the nodes.
b) The stiffness matrices representing the soil on either side of the wall and the wall itself are
assembled.
c) These matrices are combined, together with any stiffness' representing the actions of
struts or anchors, to form an overall stiffness matrix.
d) The incremental nodal displacements are calculated from the nodal forces acting on the
overall stiffness matrix assuming linear elastic behaviour.
e) The earth pressures at each node are calculated by adding the changes in earth pressure,
due to the current stage, to the initial earth pressures. The derivation of the changes in
earth pressure involves multiplying the incremental nodal displacements by the soil
stiffness matrices.
f) The earth pressures are compared with soil strength limitation criteria; conventionally taken
as either the active or passive limits. If any strength criterion is infringed a set of nodal
correction forces is calculated. These forces are used to restore earth pressures, which
are consistent with the strength criteria and also model the consequent plastic deformation
within the soil.
g) A new set of nodal forces is calculated by adding the nodal correction forces to those
calculated in step (a).
i) Total nodal displacements, earth pressures, strut forces and wall shear stresses and
bending moments are calculated.
Note: The sub-grade reaction model is not currently active, it will be added to Frew in the near
future.
All use different methods to represent the reaction of the soil in the elastic phase.
This method uses a pre-calculated soil stiffness matrix developed from the Oasys Safe program.
The soil is represented as an elastic continuum. It can be 'fixed' to the wall, thereby representing
full friction between the soil and wall. Alternatively the soil can be 'free', assuming no soil/wall
friction, see Fixed or Free solution.
This method interpolates from previously calculated and saved results, using finite element analysis
from the Safe program.
The method gives good approximations for plane strain situations where Young's modulus is
constant or increases linearly from zero at the free surface.
For a linear increase in Young's modulus from non-zero at the free surface the results are also good,
but for more complicated variations in layered materials the approximations become less reliable.
In many situations when props or struts are being used, "fixed" and "free" give similar results. An
exception is a cantilever situation where the "fixed" method will give less displacements because it
models greater fixity between the soil and wall.
It must be noted that the case with interface friction ("fixed") is somewhat approximate because
Poisson's ratio effects are not well modelled. For example, these effects in a complete elastic
solution can cause outward movement of the wall when there is a shallow soil excavation.
For detailed information on the approximations and thereby the accuracy of the Safe method see
Approximations used in the Safe Method.
The Mindlin method represents the soil as an elastic continuum modelled by integrated forms of
Mindlin's elasticity equations (Vaziri et al 1982). The advantage of this method is that a wall of finite
length in the third (horizontal) dimension may be approximately modelled. It also assumes that the
soil/wall interface has no friction.
The method is only strictly accurate for a soil with a constant Young's modulus. Approximations are
adopted for variable modulus with depth and as with the "Safe" method the user can override this by
setting a constant modulus value.
The soil may be represented by a Sub-grade Reaction model consisting of non-interacting springs.
K = EA / L
where
A = distance between the mid-point of the elements immediately above and below the node
under consideration
It is considered that this model is not realistic for most retaining walls, and no assistance can be
given here for the choice of spring length, which affects the spring stiffness.
pa = [k a 'v - k ac c] + u
pp = k p 'v + k pc c + u
Where
Where
The use of redistribution can allow for the effects of arching in the soil.
If "no redistribution" is specified, the wall pressures at all points are limited to lie between pa and pp .
However, if "redistribution" is allowed, it is assumed that arching may take place according to theory
presented in Calculation of Active and Passive Limits and Application of Redistribution.
Note: It is considered that the "redistribution" option, while still being somewhat conservative,
represents the "real" behaviour much more accurately.
If surcharges of limited extent are specified above the level in question the active pressure is
increased in accordance with the theory presented in Active Pressures due to Strip Load
Surcharges.
However, strip surcharges are not included in calculating passive pressure (see Passive Pressures
due to Strip Load Surcharges).
'h = Kr 'v
Kr = / (1 - )
where
For undrained behaviour, the same approach is applied to total stress. In this case, the undrained
Poisson's ratio would normally be taken to be 0.5, where Kr = 1.0
When filling, the horizontal effective stresses in the fill material are initially set to K0 times the
vertical effective stress.
i.e. 'h = K0 'v
The equations presented below are taken from EC7 (1995) Annex G. They have been simplified to
account only for vertical walls, with a vertical surcharge on the retained side. The following symbols
are used in the equations:
where,
And
= mt + - mw
mt , mw and have units of degrees. However, must be converted into radians before
substitution into the above equation for evaluating Kh.
For calculation of active earth pressure coefficients, the angle of shearing resistance of the soil and
the wall/soil friction angle must be entered as negative values.
For calculation of passive earth pressure coefficients positive angles should be used.
For both active and passive earth pressure coefficients the value of is positive for a ground level
which increases with distance from the wall.
1. Pore pressure (u). This is prescribed by the user and is independent of movement.
2. Effective stress (Pe). This has initial values determined by multiplying the vertical effective
stress by the coefficient of earth pressure at rest (K0 ).
Thereafter its values change in response to excavation, filling and wall movement.
zs
'
v dz u zudl
z
where:
u = Prescribed pore pressure
g = unit weight
z = level
zs = surface level
zudl = vertical stress due to all uniformly distributed surcharges above level z.
Effective stress and pore pressure are used directly to represent drained behaviour.
Note: The pore pressure profile is defined by the user and is independent of movement.
The feature is available in the Material Properties table, and is activated by specifying for an
undrained material another material zone from which effective stress parameters are to be taken.
A "shape factor" is also required, which controls the shape of the permitted effective stress path for
undrained behaviour. The default value for the shape factor is 1, which prevents occurrence of any
effective stress state outside the Mohr-Coulomb failure envelope, but it can optionally be revised to 0,
representing a Modified Cam-Clay envelope, or any value in between. [NB: values less than 1 have
not been validated and use of a value less than 1 is not recommended. The option is retained in the
program for experimental purposes. A spreadsheet 'undr_dr_calc.xls' is provided in the 'Samples'
sub-folder of the program installation folder. This allows the user to experiment with values for the
various parameters and with the shape factor, if wished.]
If reasonable values of pore pressure are not used during undrained behaviour, then on transition to
drained behaviour, the program may not calculate displacements with satisfactory accuracy. The
calculation in Frew aims to provide a reasonable set of undrained pore pressures. Given the relative
simplicity of Frew and the present state of knowledge of soil behaviour, they cannot be accurate
(although should be better than a user-defined pore pressure profile) and the user should check that
they appear reasonable. Guidance on warning messages is given below.
The process used in the program can be understood by studying the stress path plot below. Failure
in an undrained material occurs at the intersection of the ' and Cu lines. This point is derived from
the effective stress parameters of the "material number for effective stress parameters" specified by
the user for each undrained material. The envelope of possible total stress values is shown in red
(examples for shape factors of 1 and 0.75 are shown); this is taken to be elliptical except where
reduced by shape factors > 0. The calculated undrained effective stress path is shown in blue.
For each iteration in an undrained stage, the program calculates the total stress and the effective
stress, using the value on the blue effective stress path unless limited by the red envelope. The
undrained pore pressure is then the difference between the total and effective stresses.
The diagram shows that, if the shape factor is less than 1, it is possible for the effective stress
calculated to lie outside the limits of the effective stress parameters; this would lead to some
changes in total stress, and hence displacement, in the transition from undrained to effective stress
behaviour. This problem is avoided by following the recommendation to use the default shape factor
of 1.0.
Any pore pressures entered by the user will be ignored in an undrained material for which automatic
calculation of pore pressures has been requested (i.e. by setting a valid "material for effective stress
parameters" in the Materials table).
Warning messages
These appear as symbols in the node results tables for any stage which calculates undrained pore
pressures, and a brief explanation is added in a footnote to the table.
This situation should not occur and probably reflects a data error in which either the user has change
the effective stress parameters between stages, or, in the first stage, inconsistent values of Ko, Ka
and Kp have been specified.
It could possibly be detected on returning to use of effective stress parameters after an undrained
stage with FACTOR < 1.
At an earlier drained stage, probably at initialisation, the program has calculated a horizontal stress
which exceeds the undrained strength limits specified by the user, in relation to the vertical stress at
the node. This may be due to incorrect data, i.e undrained strength not increasing in a sensible
manner with depth, or too low a value of constant Cu .
For undrained or partially drained behaviour (where pore pressures change in response to
movements), a constant pore pressure component (u0 ) defined by the user, is thereby very unlikely
to represent the actual pore pressure in the soil. Approximate undrained pore pressures can be
calculated by the program by setting an extra material parameter, see Undrained Materials and
Calculated Pore Pressures . If this option is selected, any "data" pore pressure distribution entered
by the user is ignored in undrained materials.
There are two ways of representing undrained materials, if undrained pore pressures are not being
calculated:
A. Specified profile of pore water pressure
Here, the pore pressure considered by the program can usually be regarded as the initial
pore pressure before deformation, whilst
The apparent horizontal effective stress (Pe) becomes the sum of the true effective earth
pressures and the excess pore pressures due to deformation.
Pe = 'h + u
B. Zero pore water pressure profile
Here, the value of apparent horizontal effective stress (Pe) can then be equated to the true
total stress.
Pe = 'h + u
In both these cases the values of Ka, Kp and Kr should be set to unity (1.0), but with non-zero
undrained strengths (c) and coefficients Kac and Kpc .
Calculation procedure
Frew executes the following calculation procedure. This includes for a profile of pore pressures, if
specified, as indicated.
Note: Frew uses 'a as a lower limit on the horizontal effective stress 'h. 'h is used in the
equilibrium equations, for determination of the wall deflection, where 'h = h
+u
The wall loads are specified as either a point node at a given level or as a pressure between a top
and bottom level. In order to be used in calculations these are converted to be considered as a set
of point loads at all nodes at the specified level.
For point loads, the load is either applied directly at the specified node, or the specified level is used
when generating nodes to create a node at the correct level - to which the load is then applied.
For pressures, the load is applied as a series of point loads applied to all nodes affected by the
pressure. To achieve this each node is considered to have an associated length of wall extending
from halfway between the selected node below to halfway between the selected node and the node
above. The total lateral load acting on this part of the wall is calculated based on the elevations of
the node length and pressure as shown in the example below.
Note: due to the loads being applied as a series of point loads on the nodes, there may be slight
errors in the calculated moments at the affected nodes. This is due to the fact that although the total
lateral load acting on each node is correct, due to the spacing between nodes and in the case of
linearly variable pressures the distribution of the pressure the nett force would not apply at the exact
level of the node meaning that a small moment would also be generated. It is assumed that in most
cases this error will be small as any moments generated in this manner would likely be small and
may to some extent cancel each other out at different nodes. However, the user should be aware of
this potential error and consider the impact, particularly where node spacings are large and irregular.
This does not apply to point loads which apply directly to a node at the correct level.
Eurocode 7
CIRIA 580
AASHTO LRFD 7th Ed.
Direct Kp
For each set factors are divided into factors on loads, factors on soil parameters and factors on K
values (earth pressure coefficients). The relevant values will be either divided or multiplied by these,
as specified in the table.
When analysing, each factor set that is selected to be used in analysis (by specifying "Yes" in the
corresponding table) will be run.
It is to be noted that user can choose only one partial factor type from among the four types - EC7,
CIRIA 580, AASHTO LRFD and Direct Kp. Otherwise, the user has to select the "None" option in
which case the unfactored analysis is carried out.
2.7.1 EC7
Values factored within this code are loads and soil parameters. Loads are multiplied by the factors
shown, and soil parameters divided.
It should be noted that soil parameters are applied directly to the soil parameters input by the user
that are then used to calculate the earth pressures used in calculations. Where the user directly
inputs the earth pressure coefficient they would need to factor this value manually.
The Eurocode 7 DA1-C1 factor set is also frequently used in combination with the factor on effects
of actions, which is described in more detail here.
Factors are specified within this code for loads and for earth pressure coefficients.
All of the load factors specified within the code are applied to surcharges and loads applied by the
user, and set to the type corresponding to the relevant factor. The only exception to this is loads
due to water, for which the factors are applied to the defined water pressure. It is therefore noted that
none of the other values calculated by the program are factored by the load factors. Vertical earth
pressures for example, are not factored, as the load applied to the wall will be factored due to the
factor on the earth pressure coefficient.
For the earth pressure coefficient factors, these are applied either to K values entered by the user, or
calculated based on the soil parameters. It should be noted that the only factors used are the
maximum Ka and K0 factors. Although other factors are included for completeness, these are not
used by Frew.
The increased K0 value is applied to both sides of the wall, as is factoring of the Ka limit. This will
increase the initial pressure on the the passive resisting side, as well as the active disturbing side.
While not a conservative assumption, this is necessary numerically to ensure that the problem is
stable in the initial stage prior to installation of the wall.
2.7.4 Direct Kp
The direct Kp factor is applied to the passive limit earth pressure coefficient. This is specified
directly for the left and right side of the wall, so the user is required to consider whether increasing or
decreasing the passive limit on each side has a stabilising or destabilising effect, and apply factors
accordingly. This factor is applied to the passive earth pressure coefficient whether specified directly
by the user or calculated based on soil properties.
To work around this the factor on the effects of actions, applies a factor directly to the shear and
bending values calculated for the wall. This does not affect the overall stability of the wall, but does
allow the calculations of factored maximum values for shear and bending that may be used to
assess the structural integrity of the wall.
It should be noted that where the factor on effects of actions is selected to be used, the load factors
need to be reduced accordingly. Factoring the loads at source, when the resulting bending and
shear values are factored would effectively result in double factoring the effect of these sources. In
this case, the factors to be applied to other loads should be divided by the factor on effects of actions
- such that the nett result is the same. For example where a factor of 1.50 is required for a load, and
a factor of 1.35 is specified for the effects of actions, then the factor on the load should be 1.50/1.35
= 1.11.
The user defined partial factor sets can be specified in editable records under the greyed out records
in any of the four partial factor sets discussed above.
When reading "user-defined" partial factor sets from the older versions, the program maps this to
EC7 based user-defined partial factor set, as all the fields match between both versions in this case.
3 Input Data
Data is input via the Global Data and Stage Data menus, or via the Gateway. Some basic and global
data can be input to a new file using the New Model Wizard, but the following gives some
background on the way the data is organised and can be edited after initial entry.
Global Data
Stage Data
The Stage Operations window or the icon will allow individual stages to be modified. When
opened, the Stage Operations view shows a tree diagram, which allows access to all available
options for each stage. Ticks are placed against those options which have been changed.
This window also allows the creation of new stages of analysis and the deletion of stages that are no
longer required.
Note: Left click on the boxes and to open or close the tree diagram for each stage.
The user can also access the "Global Data" menu items and the current stage menu items using
the Gateway.
Whenever the data item in the current stage item is different from the previous stage, it is shown in
bold.
Sketches showing the wall, soil strata, surcharges, water pressure, strut and excavation levels
should be prepared for each Stage.
Examples of potential changes that can be applied during the construction stages are:
Stage 0 Set up initial stresses in the soil by adding the material types, groundwater
conditions and applying any surcharges required prior to installing the wall. All
materials should be set to drained parameters for this stage.
Use the relaxation option to model the long term stiffness of the wall.
Combined stages shown here to aid placement of the nodes, see Nodes.
The following shows the construction sequence separated into stages ready for modelling.
Note: Soils 1 and 3 are Clay and have been used to represent the modelling of undrained material
and the change to drained for long term conditions. Soil 2 is a sand and thereby fully drained
throughout the construction sequence.
The program recalculates the displacements and forces within the system at each stage.
Several activities can be included within a single stage provided their effects are cumulative. For
example it is appropriate to insert a strut and then excavate below the level of the strut in one stage,
but it is not correct to excavate and then insert a strut at the base of the excavation in one stage. If
in doubt the user should incorporate extra stages.
The computer model of the program geometry should be drawn with the wall node locations carefully
selected in accordance with the guidance given in inserting Nodes.
The nature of each problem will vary considerably and thereby the amount of data changes required
for each construction stage. Some information is compulsory for the initial stages. Thereafter full
flexibility is allowed in order to build up the correct progression of construction stages and long term
effects.
Node levels
Analysis Method
Convergence control
parameters
Water
3.2 Preferences
The Preferences dialog is accessible by choosing Tools | Preferences from the program's menu. It
allows the user to specify the units for entering the data and reporting the results of the calculations.
These choices are stored in the computer's registry and are therefore associated with the program
rather than the data file. All data files will adopt the same choices.
Numeric Format controls the output of numerical data in the Tabular Output. The Tabular Output
presents input data and results in a variety of numeric formats, the format being selected to suit the
data. Engineering, Decimal, and Scientific formats are supported. The numbers of significant figures
or decimal places, and the smallest value distinguished from zero, may be set here by the user.
A time interval may be set to save data files automatically. Automatic saving can be disabled if
required by clearing the "Save file.." check box.
Show Welcome Screen enables or disables the display of the Welcome Screen. The Welcome
Screen will appear on program start-up, and give the option for the user to create a new file, to open
an existing file by browsing, or to open a recently used file.
Begin new files using the New Model Wizard, if ticked, will lead the user through a series of
screens to enter basic data for a new file. For more details, see New Model Wizard.
Company Info allows the user to change the company name and logo on the top of each page of
print out. To add a bitmap enter the full path of the file. The bitmap will appear fitted into a space
approximately 4cm by 1cm. The aspect ratio will be maintained. For internal Arup versions of the
program the bitmap option is not available.
Page Setup opens a dialog which allows the user to specify the calculation sheet style for graphical
and text printing e.g. whether it has borders and a company logo.
The New Model Wizard is designed to ensure that some basic settings and global data can be easily
entered. It does not create an entire data file, and strut, surcharge and stage data should be entered
once the wizard is complete.
Note! The New Model Wizard can only be accessed if the "Begin new files using New Model
Wizard" check box in Tools | Preferences is checked.
Job Number allows entry of an identifying job number. The user can view previously
used job numbers by clicking the drop-down button.
Initials for entry of the users initials.
Date this field is set by the program at the date the file is saved.
Job Title allows a single line for entry of the job title.
Subtitle allows a single line of additional job or calculation information.
Calculation Heading allows a single line for the main calculation heading.
The titles are reproduced in the title block at the head of all printed information for the calculations.
The fields should therefore be used to provide as many details as possible to identify the individual
calculation runs.
An additional field for notes has also been included to allow the entry of a detailed description of the
calculation. This can be reproduced at the start of the data output by selection of notes using File |
Print Selection.
Problem geometry Enter the levels of the top node and the lower rigid boundary. This will set
the correct view range in subsequent graphical display.
Materials Add or delete materials. Clicking "Add material" opens a further dialog
allowing input of basic material data.
This data entry method will be sufficient in many cases, but some other
settings (for example, undrained pore pressure calculation parameters)
need to be set later in the normal Materials table.
Node generation "Automatic" will allow all data input to be specified by level and node
positions are generated by Frew.
"Manual" means that node positions must be entered by the user and
most other data must be specified by node number rather than level.
Wall toe level Selecting "Obtain from stability check" will enable the user to run a
stability check before full analysis, to estimate the required toe level. This
can be manually overridden if required.
To enter a known required toe level, select "Enter manually" and enter the
level.
Clicking "Finish" completes the wizard and creates Stage 0 with the input data. The graphical input
view will open to allow entry of node levels (if these are being created manually). If automatic node
generation was selected, the graphical input view will show a single soil zone extending the full depth
of the problem. More soil zones can be added as required to set up the initial ground profile for
Stage 0.
Strut and surcharge data is added separately, and additional stages created with the required stage
changes, before proceeding to run a stability check and full analysis.
Note: The location of the nodes can not be changed in a later stage.
It is useful to sketch out the problem from beginning to end to ensure that the correct parameters are
entered as global data, see Assembling Data.
Note: Tables are locked for editing in the program when results are available. To edit the data in the
tables, the user has to explicitly delete the results.
3.4.1 Titles
When a existing file is opened, or a new file created without the New Model Wizard, the first window
to appear is the Titles window.
This window allows entry of identification data for each program file. The following fields are available:
Job Number allows entry of an identifying job number. The user can view previously
used job numbers by clicking the drop-down button.
Initials for entry of the users initials.
Date this field is set by the program at the date the file is saved.
Job Title allows a single line for entry of the job title.
Subtitle allows a single line of additional job or calculation information.
Calculation Heading allows a single line for the main calculation heading.
The titles are reproduced in the title block at the head of all printed information for the calculations.
The fields should therefore be used to provide as many details as possible to identify the individual
calculation runs.
An additional field for notes has also been included to allow the entry of a detailed description of the
calculation. This can be reproduced at the start of the data output by selection of notes using File |
Print Selection.
To add a picture place an image on to the clipboard. This must be in a RGB (Red / Green / Blue)
Bitmap format.
The image is purely for use as a prompt on the screen and can not be copied into the output data.
Care should be taken not to copy large bitmaps, which can dramatically increase the size of the file.
3.4.2 Units
This option allows the user to specify the units for entering the data and reporting the results of the
calculations.
Default options are the Système Internationale (SI) units - kN and m. The drop down menus provide
alternative units with their respective conversion factors to metric.
Standard sets of units may be set by selecting any of the buttons: SI, kN-m, kip-ft or kip-in.
Once the correct units have been selected then click 'OK' to continue.
SI units have been used as the default standard throughout this document.
The properties for the different layers of materials, either side of the wall, are entered in tabular form.
Properties must be entered for all the materials which will be required for all construction stages. If
drained and undrained parameters of the same material type are to be used then each set of
parameters must be entered on a separate line.
Note: The user should understand the way Frew models undrained and drained behaviour and the
transition between the two. For further information see the section on Total and Effective Stress.
Brief descriptions for each of the material types can be entered here. This description is used when
assigning material types to either side of the wall, thereby creating the soil zones (see entering Soil
Zones).
Note: Material type 0 represents air or water - no additional input data is required by the user.
Material Description
Property
Earth Select from the drop-down list whether the earth pressure coefficients will be
Press. "Calculated" or "User Specified".
Coef.
see Calculation of earth pressure coefficients
Note: For "Calculated" the cells of Ka, Kp, Kac and Kap will be uneditable
and when values are entered into ', ', and Cw/c the earth pressure
coefficients will be calculated. For "User Specified" the cells for ', ',
Cw/c will be greyed out and the cells of Ka, Kp, Kac and Kap will be editable.
y0 Reference level for the gradient of cohesion (c) or Young's modulus (E) with
depth. Tab across the column if they are constant with depth.
Note: This level does not have to correspond to the top of the material layer.
It is a reduced level and is not referenced from the bottom of the layer.
c gradient The rate of change of cohesion with depth. A positive value means
cohesion is increasing with depth.
E gradient The rate of change of Young's modulus with depth. A positive value means
stiffness is increasing with depth.
Shape factor For undrained materials only: factor to use in weighting the failure envelope on
the dry side between Mohr-Coulomb and Modified Cam-Clay envelopes.
Default is 1. Used only in calculation of undrained pore pressures, see
Undrained Materials and Calculated Pore Pessures.
Material no. for For undrained materials only: the number of the material from which to use
effective stress effective stress parameters in undrained pore pressure calculations.
parameters
Note: the user should set the last column to zero if undrained pore pressure
calculations are not required.
c = c0 + Grad(c)*(y0 - y)
E = E0 + Grad(E)*(y0 - y)
3.4.4 Nodes
The Node level entry data is only available if automatic node generation is switched off in the New
Model Wizard or the Node generation data dialog. Nodes can then be entered by using the
graphical or tabular display and are required at the following locations:
1. Strut levels.
2. Top and base of the wall and levels at which the wall stiffness (EI value) changes.
3. Levels either side of the ground surfaces during excavation back fill and the interfaces
between soil zones.
Note 1: Ground surfaces and soil zone interfaces occur midway between nodes. The exception is
the highest ground surface which can coincide with the top node.
Note 2: Where seismic analysis is undertaken, and the seismic force is applied as a point load,
struts will be generated at the location in which the forces are to be applied. As a result nodes are
also required at these levels.
In addition to placing nodes at key locations in the construction sequences, it is also important to
space them at reasonably regular, close intervals down the line of the wall and beyond to the base of
the problem. This allows the program to clearly model the flexibility of the wall and provide results of
the forces, pressures and bending moments which are given at each node location.
Note: As a guide it is recommended that the maximum separation between any two nodes must
never be greater than twice the minimum separation between any of the nodes. Frew gives a
warning if this rule is violated.
Frew may have difficulty if unusually short elements are used in combination with the SAFE method
for analysis. Where the node spacing is significantly less than the size of the elements used in the
Safe analyses from which the stiffness matrices are derived, there is potential for the results to
oscillate (see below) making them unreliable, and in many cases preventing convergence. Frew will
give a warning when generating nodes if fixed points (strut levels, wall section levels, rigid boundary
level) and intermediate points (soil boundaries) are close together and may result in nodes that are
too closely spaced. For both manually and automatically generated nodes, a further check is
undertaken prior to analysis and a warning given if nodes are potentially too close. Where these
warnings are given by the program the user may either continue regardless carefully checking results
carefully to confirm suitability, or regenerate nodes after increasing or removing the gaps between
fixed and/or intermediate points.
Note: Material properties must be defined before the program allows the node locations to be
selected.
If the correct level range is not shown on the graphical view, define the extent of the problem by
selecting the menu option Graphics | Scaling | Set Problem limits and then enter the maximum and
minimum levels of the nodes.
Note: When soil stiffness is represented using the "Safe" or Mindlin methods, it is assumed that
the lowest node specified in the data defines a horizontal rough rigid boundary.
The snap interval is also entered here. This provides the closest point onto which the cursor will lock
to mark a point. The snap interval is taken as the nearest interval in metres.
Adding nodes.
To add nodes select the Global data | Node levels menu option or select the nodes button on
the graphics toolbar. Nodes can then be added by entering their level directly in the table or
graphically by the following procedure;
1. Use the mouse to place the cursor over the location of the top node.
2. Click with left button on the location.
Note: If the scale of the diagram is too small to locate the nodes accurately, then maximise the
main and graphics windows to increase the size of the image.
2. As an alternative go to the table at the side of the diagram. Use the arrow keys and return
button or the mouse to select the appropriate node. Change the value and press enter.
Deleting nodes.
1. Placing the cursor over the correct node and then using the left mouse button whilst
simultaneously holding down the Shift key.
2. Highlighting the line number in the table using the left mouse button, then pressing the
Delete key.
Struts and anchors are modelled in terms of an "equivalent strut" which represents the total number
of struts present in a one m length of wall (e.g. for struts at 2m centres, input half the force and
stiffness of an individual one).
Note: More than one strut may be defined at a particular node, and not all struts need to act
simultaneously.
If a strut is inserted in Stage 0, prior to the wall being installed, only the horizontal pre-stress force is
modelled. The stiffness of the strut will be modelled in subsequent stages.
An applied moment or a moment restraint at a node can be modelled by using a strut with an
inclination of 90 degrees and a non-zero lever arm together with an applied pre-stress force or a
stiffness respectively.
In subsequent stages after the anchor is 'locked off' it is usually convenient to remove this strut and
insert a strut that models both the pre-stress and stiffness of the anchor.
Inclined anchors are modelled by specifying an inclination to the horizontal and if they are not applied
at the vertical axis of the wall a lever arm can be specified to allow for this, see Strut Properties.
3.4.6 Surcharges
Surcharges may be applied at or below the surface of the ground on either side of the wall.
These are always uniform pressures and may be in the form of;
Note: The chosen value of Kr to which Ks is equated, should correspond to the material type that is
most influenced by the transfer of the applied load to the wall. If the layers are relatively thin then an
average value should be taken. If the stages include a change between undrained and drained
materials then multiple surcharges should be entered to take the change of Kr (at the relevant stage)
into account.
The surcharge can be applied before the wall is inserted (Stage 0). If this is the case the program
computes the effects of the surcharge on the soil stresses before installation of the wall. In some
cases this may however prevent the program from converging as there is a discontinuity in the lateral
earth pressures at the top node. Where this occurs this can usually be worked around by applying
the surcharge at a level slightly below the ground surface.
To determine the elastic effect on the horizontal effective stress, udl surcharges are multiplied by K0
in Stage 0, whereas in later stages they are multiplied by Kr.
They are therefore treated in the same way as the weight of soil, both in the initial state (Stage 0)
and in later stages as excavation and filling takes place, see Effects of excavation and backfill. In all
stages, including Stage 0, strip surcharges are multiplied by the factor Ks described above.
Active and passive limit pressures are also modified using the values of Ka and Kp for each layer
beneath the udl.
1. For the case where the Young's modulus (E) for the soil is constant for a depth several
times greater than the width of the surcharge the Boussinesq equations may be used to
derive horizontal stresses in the ground.
The pressures therefore on a rigid (ideally frictionless) vertical boundary would be double
the Boussinesq values.
2. For the case where the stiffness (E) increases sharply at a depth less than the width of the
surcharge, the load will appear to the more flexible soil to act rather like a 'udl'.
For the stiffer soil the effect of the surcharge load will still appear as the Boussinesq
pressure.
For both cases the analysis calculates the change of pressure on the wall before further movement
using the equation
p = 2Ks phB
where:
phB
= the change of horizontal stress according to the Boussinesq equations
Ks = is a correction factor specified by the user. Where Young's modulus is constant with
depth, Ks should be taken as 1.0.
For the case where stiffness increases sharply Ks can have a large range of values, the evaluation of
which is beyond the scope of this text. However if the strip load is wide compared with its distance
from the wall and the depth of the deforming soil, a value of Ks = /(1 - ) will give results equivalent
to loading with a udl with Kr = /(1 - ).
The method described for the active pressure is automatically applied by the program, but the
method described for the passive pressure is not applied. The user must therefore manually
enhance the passive pressure coefficient Kp or the soil cohesion c, if this effect is to be incorporated
into the analysis, see Passive Pressures due to Strip Load Surcharges.
The user is recommended to study the graphical output and check whether the pressures adopted
by the program are acceptable.
These are global factors that are applied to material properties or surcharges input parameters. The
new material parameters affected by these factors will then be used in the calculations. A single set
of factors shall be selected and these will apply to all materials in all stages.
WARNING: Frew has features to simplify application of partial factors in line with Eurocode 7 and
AASHTO LRFD Bridge Design 7th Edition. However, there are alternative ways of complying with
these standards, including manual adjustment of certain values. The features in the program do not
automatically make a design code compliant and the user must continue to check the output
carefully to ensure the assumptions and adjustments to characteristic values are as they require.
Note that pore pressures and strut pre-stress are not factored. If a strut pre-stress is used to model
a structural force, and other effects of actions are being factored, the user may wish to factor the
input value of strut pre-stress.
The Code for partial factors drop down box allows the user to select which design code they wish
to base the analysis on. Options include direct factoring of Kp, Eurocode 7, CIRIA C580 and the
AASHTO LRFD 7th Edition, as well as user specified versions of the AASHTO and EC7 guides. The
selections for the codes automatically add in the design cases considered in those codes and the
corresponding factors, and the user can also add additional sets to be analysed to these. The user
specified options allow the user to create their own sets using the factor types allowed by the guide.
Use in Analysis drop down box allows the user to select 'Yes' or 'No', indicating whether or not the
file should analyse the factor set.
Factor Application can be set to multiple or divide and indicates how the factors of the given type
are to be applied to the values entered or calculated by the program. Note that there are three broad
types, loads, soils and K values - these apply factors to loads, soil strength parameters and earth
pressure coefficients. The table will only show the factor application options for those factor types
used in the selected code.
Soil Factors allow the user to set the factors to be applied to soil strength parameters.
Load Factors allow the user to set the factors to be applied to loads.
K Factors allow the user to set the factors to be applied to K values, i.e. earth pressure coefficients,
that have been either specified by the user or entered manually.
Factor on Effects of Actions allows the user to decide whether or not the effects of actions should
be factored and for the factor to be set. Where the effects of actions are factored, they are always
multiplied by the specified factor.
It allows setting of the node generation method (automatic or manual), some settings for automatic
node generation, and whether to calculate the wall toe level from a stability check. If a stability
check has already been carried out, this dialog will show the calculated toe level. This can be
overriden by the user.
This window also allows the creation of new stages and the deletion of those no longer required.
When "Add stage" is selected the new stage can be inserted after any existing stage.
Note: Left click on the boxes and to open or close the tree diagram for each stage.
As mentioned earlier, the user can access stage specific data of the current stage using the
Gateway.
Note:
The information must first be set for Stage 0 - the initial conditions before entry of the wall in Stage 1.
Stage 0 appears automatically in the summary tree diagram on creating a new file.
The individual data for each stage can be accessed by using the mouse double left click on the data
heading in the tree diagram.
This action opens the window for data input.
Struts
Convergence control parameters
Optional Water data
Note: The properties set in Stage 0 will be carried forward into subsequent stages unless otherwise
amended.
The number of the current stage is always displayed in the status line at the base of the main
window.
New stages can be added to the list by selecting Add Stage on the Stage Operations window. This
activates a 'New Stage Title' box.
The stage title is then entered and the number of the stage before the new stage. Once the OK
button is selected the new stage is added.
Note : The number that first appears in the Inserting after Stage window is the number of the stage
currently highlighted by the cursor.
Select the "Add stage" button on the stage operations tree diagram and follow the instructions as for
new stages.
Stages can be deleted by highlighting the stage title in the Stage Operation window and selecting
Delete stage. A check box will appear before the stage is deleted.
It is possible to step through the stages in order to access and edit the same data window for each
stage. Use the buttons on the tool bar to move up and down between the various stages.
The number of each stage is displayed on the status line at the base main window.
Once the correct stage has been reached. edit the data as normal.
To reach specific windows go to the Stage Operations tree diagram, highlight the required operation
at the required stage and then either
Note: Changes made in a stage will be copied through to subsequent stages until the program
encounters a specific change already made by the user. For example, changing the soil zones in an
early stage will update later stages which had the same soil zone specification.
The stage titles can be edited by left clicking on the title so that it becomes highlighted in yellow and
then clicking again to get the cursor before typing the amendments as required.
Surcharges can be applied and removed individually for each stage. Edit the Stage In/Out entries as
required in the table.
Struts can be inserted and removed individually for each stage. Edit the Stage In/Out entries as
required in the table.
Description
This sets the name used to identify the load.
Stage In
This sets the first stage in which the load will be applied. This cannot be left blank, and the earliest
stage in which it can be applied is stage 1 when the wall is created.
Stage Out
If the wall load is to be removed, the number in this field can be set to indicate the first stage in
which the load will no longer be applied. Note that if this is left blank, the load will be assumed to
apply in all stages from the 'stage in' up to and including the final stage.
Load Distribution
This determines the type of load to be applied to the wall. This may be either a point load, a
constant pressure, or a linearly variable pressure.
Node/Level
The node and level input boxes are used to determine where the load is applied. For all pressures
the top and bottom level will need to be used to determine where the load is applied. For point loads
in models with generated nodes the user must specify the level at which the load is to be applied.
For user specified nodes, the user must specify which node the load is being applied to.
Load
For point loads the load per m of wall should be specified here. Positive forces are assumed to act
from right to left, and negative forces from left to right.
Pressure
For pressures acting on the wall, these can be specified here. For constant pressures only one
value is entered, and this pressure is applied constantly throughout. For linearly variable pressures
the user may specify the pressure at the top and bottom of the loaded area. The pressure is
assumed to vary linearly between these points. As with the loads, positive pressures are assumed
to act from right to left, and negative pressures from left to right.
Load Type
This category is only shown where partial factors have been selected and are being applied in the
model. This allows the user to select the load type, which is used to determine which load factor to
use when factoring the load.
Note: The interfaces between the soil zones are set midway between nodes. If automatic node
generation is being used, the program will do this for you. Otherwise, the locations of soil zone
interfaces must be taken into account when defining the node positions.
To add soil zones select the soil zones button on the graphics toolbar or the soil zones option
from the relevant stage in the 'Stage Operations' window.
To add a soil zone: Left-click on the graphical input view at the required level of the soil zone
interface and choose the required material from the dropdown list in the dialog which appears.
Click OK and the graphical input will be redrawn with the new soil zone shown. Alternatively, the
data can be added to the Material Layers table which will open at the same time as the Graphical
Input view for this option.
To edit a soil zone's material, right-click in the zone and choose the new material from the dialog. To
change the level of a soil zone, or delete it, simply edit or delete the record in the Material Layers
Soil zone data can be specified using the table by highlighting a cell and selecting the material type
from the list presented in the drop down box..
Alternatively, soil zone data can be entered graphically using the procedure described below.
1. Place the cursor over the first node and select with the left button.
2. Hold down the Shift key.
3. Place the cursor over the last node (still holding down the Shift key) and select the area of
nodes with the left button.
Select the required soil from the combo box and select OK.
Note: The number of the soil comes from the list of material types created in the materials table,
see Material Properties. Air or water are designated as material type 0.
Once entered the soil zones can be edited using either of the methods given above.
When using automatic node generation, to specify excavation or backfill, click the button on
the toolbar. Right-clicking on the left or right side of the wall in the graphical input view will bring up
the Dig/Fill dialog.
Enter the required new ground level and click OK. If the new ground level is above the existing
ground level (i.e. filling), the uppermost material will be extended to the new ground level.
When using manual node generation, excavation is specified by changing the material to the
required side of one or more nodes to 0. This represents air or water. Backfilling is specified by
changing the material from 0 to the required material number for the backfill material. Digging and
Any dig/fill operations are carried forward to successive stages until they are changed.
Note: It is not permissible to dig to, or below the base of the wall. However, this could be modelled,
if required, by specifying a very low bending stiffness for the bottom section of the wall.
Note: Changes in wall stiffness between stages will not adjust the moment curvature relationship
that exists at the end of the previous stage. The use of wall relaxation must be used to adjust the
moment curvature relationship.
For automatic node generation, the top level and bending stiffness of the wall is specified in the
Wall Data table. Changes in bending stiffness down the wall can be specified by entering more than
one line in this table. The base of the wall will be as manually specified by the user, or as generated
by the stability check, as required.
For manual node generation, the wall bending stiffness (EI value in kN/m2/m length of wall) is
specified at each node location. This allows the stiffness to be varied throughout the length of the
wall. The stiffness given to each node applies from that node down to the next node.
The base of the wall is taken as the first node with a given
EI value of zero.
Wall stiffness can either be entered directly into the table or graphically using the procedure given
below.
1. Place the cursor over the first node and select with the left button.
2. Hold down the Shift key.
3. Place the cursor over the last node (still holding down the Shift key) and select the area of
nodes with the left button.
Note : The Wall stiffness extends to the top of the node below. The last node in the added list is
therefore not available in the wall window to prevent the wall being extended below the base of the
defined problem.
3.5.12 Groundwater
The profile of groundwater can be either hydrostatic or piezometric. These can be different on either
side of the wall.
For a hydrostatic distribution enter a single piezometer, with zero pressure, at the phreatic
surface. The profile of pressure with depth will be linear beneath this level and have a gradient
dependent on the specified unit weight of water.
Note: The specified unit weight of water is a single global value which is applied to all piezometers
on the same side of the wall.
The piezometric distribution is specified using a series of pressure heads. The water pressure at
any point is computed by interpolating vertically between two adjacent points.
Note: The highest specified point must have zero water pressure. Negative pore pressures can
be specified below the highest point to describe soil suction. The water pressure is assumed to
increase hydrostatically below the lowest specified point.
The water pressures are also assumed to be constant laterally from either side of the wall.
Adding piezometers
Piezometer data is entered by selecting the piezometer button on the graphics toolbar or the in
the 'Stage Operations' window. Water data on the left or right side of the wall can be viewed by
selecting the appropriate page tab at the bottom of the table.
A piezometric groundwater profile can be entered in the table or by placing the cursor at the
appropriate level on the graphical view and clicking the mouse button. This opens the piezometer
data box.
This allows the level of the piezometer to be confirmed or edited and the corresponding pressure to
be entered. The pressure (P) is given as:
P = (hp – hw) w
where:
hp = The level of the piezometer
hw = The level of the piezometric head at the piezometer
w
= Global unit weight of water.
Note: Any amendments to the global weight of water will automatically be applied to all piezometers
on the same side of the wall.
Editing
Once the information for a piezometer has been entered then the data can be edited or deleted using
the tabulated information beside the graphical view.
The piezometers can also be deleted by placing the cursor over the location and clicking the left
button whilst holding down the Shift key.
The type of soil model to be used must be selected here. Further data is then requested depending
which model is selected.
Mindlin method The Global Poisson's ratio and wall plan length must be
specified.
When soil stiffness is represented using the "Safe" or Mindlin methods, it is assumed that the
lowest node specified in the data defines a horizontal rough rigid boundary.
For details on inserting Nodes. The rigid boundary should be set at a level where the soil strain, due
to excavation or loading is expected to have reduced to near zero.
The distances from the wall to rigid vertical boundaries to the LEFT and RIGHT are also required.
For the Safe and Mindlin methods the vertical boundaries can be used to represent;
Note: The specified distances can be different on either side of the wall.
By restricting the distance at which deformation can occur, the effects of an excavation of limited
length can be achieved. For further information see Modelling Axi-symmetric Problems Using Frew.
In the Sub-grade reaction method the vertical boundary distances are used to represent the length
of the soil spring at each node. Spring lengths may be specified for each node and different values
may be given on the left and right sides of the wall.
From stage 2 onward it is possible to specify a % relaxation, to model long term behaviour of the
wall. For further information, see Creep and Relaxation. The wall relaxation is set to zero in following
stages unless changed by the user.
When 'Free' is used, vertical displacement is permitted, and soil blocks and wall behave as though
the interface between them is lubricated, transmitting no shear. When 'Fixed' is used, the soil
blocks are constrained at the interfaces, with no vertical displacement.
Neither the vertical displacements in the 'Free' case nor the shear stresses implied in the 'Fixed'
case are explicitly calculated by Frew. However, the stiffness matrices, originally set up by Safe,
are different for the two cases. Simpson (1994) has shown that allowance for vertical shear stresses
reduces computed horizontal (elastic) displacements, and this is significant in some cases.
Therefore the 'Fixed' case will generally lead to smaller displacements, and users may consider that
it is closer to reality since there is generally little vertical displacement on the plane of the wall.
Neither case accurately represents the development of shear stresses on the plane of the wall in
response to vertical displacements of the wall and soil, which are largely related to non-elastic
movements.
The value of Young's modulus is given to each soil layer, (see Material Properties). The profile of
Young's modulus may therefore vary irregularly with depth.
However, a linear profile is needed in order to use the Safe and constant value of E to use the
Mindlin method.
Safe Model
When using the Safe Model Frew can generate a "best fit" linear profile through the stepped profile
created by the individual soil layers on either side of the wall. Alternatively, the user can specify a
profile by giving the value of Young's modulus at the lowest node and then a gradient of the line. A
positive gradient creates an increasing profile with depth.
When Frew generates the best fit line, it then makes further modifications to the stiffness matrix.
This attempts to fit the irregular profile of Young's modulus better.
For details on the Accuracy with respect to Young's modulus (E).
Mindlin Model
The Mindlin Model requires a constant value of E. The method can either generate a best fit value
or use a user specified value.
For details on the use of E in the Mindlin method see Approximations used in the Mindlin method.
For both methods, if the "Generate" option is used, an approximate modification is made to allow for
the irregular variation of E value with depth. If the "Specified" option is selected then the user must
define the required profile.
The use of redistribution can allow for the effects of arching in the soil.
If "no redistribution" is specified, the wall pressures at all points are limited to lie between pa and pp.
However, if "redistribution" is allowed, it is assumed that arching may take place according to theory
presented in Calculation of Active and Passive Limits and Application of Redistribution.
Note: It is considered that the "redistribution" option, while being less conservative is more realistic.
If it is required that the total active pressure on the wall at any depth below the ground surface should
not drop below a specified value, a Minimum Equivalent Fluid Pressure (MEFP) can be automatically
calculated by Frew. To use this feature, check the minimum equivalent fluid pressure box on the
Analysis Data dialog.
This will add an option to the Stage Operations which allows entry of MEFP parameters.
If the MEFP is checked then another option is added to the Stage Operations tree view for that
stage,called "Minimum Equivalent Fluid Pressure ".
Selecting the "Minimum equivalent fluid pressure" option, the MEFP parameters table appears.
This table has a record for each material with parameters for left and right sides.
The required MEFP is specified as a linear relationship with depth plus an optional constant value.
Note: The user should really set the values to zero where they judge they are not needed or would
incorrectly affect the results, e.g. on the passive side of the wall.
During analysis, the active pressure is set to a minimum of a*(y 0-y)+b, where y is the level of the
node. If this is the governing criterion on active pressure, an 'm' symbol is shown in the tabular
output. In the graphical output, the MEFP-derived pressure is just plotted as part of the normal
active pressure line.
The strength of all undrained material below a softening depth will be reduced to global softening (%)
of the value in the Material Properties table.
Note: Since either (or both) sides of the wall can be excavated, the user can specify separate
parameters for both sides of the wall.
Convergence control parameters may be varied from the default values offered to improve the speed/
accuracy of the solution, or to reduce the chance of numerical instability.
The maximum number of iterations for each stage can be specified. The stage calculations will
complete at this maximum number of iterations if this is reached before both the tolerance criteria
given for the displacement and pressure are satisfied.
If the tolerance levels are reached first then the stage calculations will also complete.
Note: The default value for the maximum number of iterations is given as 900.
The maximum change of displacement between successive iterations. The absolute error in the
result will be considerably larger (typically by a factor of 10 to 100). The default value is 0.01mm.
The maximum error in pressure (i.e. how much the pressure at any node is below the active limit or
in excess of the passive limit. This is an absolute value and the default value is 0.1 kPa.
The damping coefficient used in the analysis. If convergence is slow this can be increased. If
instability is apparent it may possibly be solved by reducing this. The default value is 1.0.
4 Frew-Safe Link
Frew analyses the soil structure interaction of the retaining wall. Frew calculates the pressures,
displacements etc. at the wall. However, if one is interested in the movements of soil beneath the
wall, Frew will not be adequate. However, the same problem can be modeled in Safe. The Frew-Safe
link feature enables the user to create a Safe model which is nearly equivalent to the Frew model.
This feature involves creation of a Gwa file. The Gwa file format is a text format used by Oasys Gsa
to transfer data across different programs.
On clicking the above mentioned button, a file save dialog opens up and prompts for the name of a
Gwa file to save the data.
After the user specifies the file name, the existing Frew data is validated. If there are any warnings or
errors, they are displayed in the wizard. Warnings can be ignored, but the data cannot be exported if
there are any errors. If the relevant checkbox on this page is checked, a log file which contains all
the errors and warnings during the export process will be created.
The user may also specify different boundary distances, than those input in the actual Frew file. This
is particularly useful in cases when large vertical boundary distances from wall have been
specified.For further information see Accuracy of modelling boundaries in Frew.
If there are no errors, the "Next" button will open the next page of the wizard, where the wall data
should be entered. This includes the wall thickness, density, Young's modulus and Poisson's ratio
for the wall material.
1. Export geometry and restraints only - If this option is selected, only the critical points, lines
and areas are exported, together with the boundary conditions at the ends of the model. No
mesh generation data is exported. Thus, data pertaining to surcharges, struts, etc. which are
dependent on the mesh data, are also not exported. This option is useful if the user wants to
add additional geometric entities in the model after importing into Safe data file.
2. Export only first stage data - This option enables the user to export the entire first stage data,
including mesh generation data, surcharges, struts etc. to Safe. This is useful if the user is
interested in replicating the same geometry and only the initial conditions of the Frew model in
the Safe model.
3. Export whole model - If the user selects this option, almost the whole data, barring some
unsupported features which will be detailed later, will be exported to Safe.
1. Export no groundwater data - In this case, groundwater data is completely suppressed during
the export process.
2. Export complete groundwater data - In this case, the whole groundwater data from all the
stages is exported.
3. Export selective stages- If this option is chosen, the user has to specify the comma separated
list of stages for which the groundwater data must be exported. This option may be used for
excluding stages involving transition from undrained behaviour to drained behaviour. In Frew,
the user has to calculate these transient pore pressures himself. However, in Safe different
approaches can be adopted for calculating the transient pore pressures. There may be cases
when the user calculate transient pore pressure data in Frew may not accurately model the
problem in Safe. In such situations, the user may want to filter out groundwater data from
certain stages.
On clicking "Finish", the following "Mesh Settings" dialog pops up if the user chooses "Export only
first stage data" or "Export whole model" options:
This dialog allows the user to bias the mesh along horizontal segments as desired. The biased
segments have more nodes towards the wall. The horizontal segments correspond to horizontal lines
running from the left boundary to right boundary. A horizontal segment typically joins points located
at the boundary with a point on the wall or any surcharge points, two surcharge points etc.
The user can also specify the maximum number of elements that can be generated along a
horizontal segment. This option may help the user to increase the number of elements if necessary.
The default value is 6. However, this does not affect the number of elements generated along the wall
width, which is always 2.
Then, the required Gwa file is created. The data from this file can be imported into the Safe file by
clicking "Import Gwa" menu button in the Safe program.
The user is then prompted to choose the required Gwa file. Upon selection, the data is transferred
from the Gwa file to Safe file.
Stages/Runs
Geometry
Restraints
Surcharges
Struts
Materials
Groundwater
Unsupported Features
4.2.1 Stages/Runs
Stages in Frew are roughly equivalent to Runs in Safe. All stages in a Frew model translate to a
sequence of runs following each other in Safe, without any branching.
Frew Stages:
Safe Runs:
4.2.2 Geometry
For a given Frew model, points are generated at locations corresponding to:
• Material layer boundaries
• Groundwater levels
• Surcharge levels
• Strut locations
• Wall end points.
• Rigid boundary intersections
A series of lines connect these points in the form of a grid. Areas are formed from these lines.
Once this geometry is created, mesh generator is called if required by the user.The node spacing is
dense towards excavation levels. Unlike in Frew, the wall in Safe is made up of Quad-8 elements.
4.2.3 Restraints
The following points should be noted regarding the export of data related to restraints:
1. All restraints in the model are of pin-type, and are applied at the rigid boundaries.
2. The restraints are constant across all stages. Variable boundary distances across different stages
not supported.
4.2.4 Surcharges
The surcharges are applied as element edge loads in the corresponding stages.
4.2.5 Struts
Struts in Frew modeled as springs in Safe, and act at nodes located on the wall axis.
Pre-stress is applied as a node load in Safe. The prestress along the spring axis direction is resolved
into components along the X and Y axes, and applied as a pair of node loads in Safe.
4.2.6 Materials
In Frew, material data is specified only for Soil strata. In the Safe model, the excavations are
represented using "void" material, the wall is modeled using a linear elastic material, and the soil is
modeled using Mohr-Coulomb materials.
The wall material data is supplied by the user during the export process.
The Frew material model has all the data required for Safe Mohr-Coulomb model, except for the angle
of friction f , and Poisson's ratio
Angle of friction is the average of values obtained from the following expressions for coefficients of
active and passive pressure:
When a soil stratum is partially submerged, the 'g' parameter differs for the wet and dry part of the
stratum, even though all other parameters are identical. Hence two materials are needed to model
the partially submerged material in the first stage. These extra materials are generated and the
appropriate 'g' values for all the strata are calculated during the export process. The following figures
illustrate this situation:
4.2.7 Groundwater
Frew and Safe use different approaches for modeling pore pressure distribution. Following are a
couple of important differences.
Frew Safe
Piecewise linear interpolation of pore Radius of influence approach.
pressure.
All soil zone materials share the same pore Each material has its own pore pressure
pressure distribution data. distribution
In Safe, each data point is characterized by pore pressure value, its gradient, and a radius of
influence. The net pore pressure at a given point is the weighted average of the pore pressures
calculated at the given point using the existing pore pressure data points.
The weights for points which lie within a square defined by this radius of influence, the weights are
typically much higher compared to the weights for the points located outside the square.
In Frew, we can have different pore pressure gradients above and below a particular pore pressure
data point. However, this situation is not possible in Safe for a given data point, as only a single pore
pressure gradient is specified.
In order to generate a roughly equivalent pore pressure distribution in Safe, the pore pressures are
calculated at locations midway between the Frew pore pressure data points.
1. All the stages up to integral bridge analysis should be defined as before i.e. if there are 3 stages
before initial winter contraction, these 3 stages should be defined as usual.
2. The user should only define one stage as the integral bridge analysis stage, and this should be
the last stage. This is to be defined by the user at the end of all non-integral bridge stages.
3. The integral bridge stage can be added in the same way as the normal stage. However, to specify
a particular stage as integral bridge analysis stage, the user should open the "Analysis Options"
dialog for a particular stage, and check the "Perform Integral bridge calculations" check box.
This would cause more items to be available in the Gateway. These new items are "Integral bridge
data" "K*d vs d'd/H' curves" and "RF,G vs d'd/H' curves". The user should enter the necessary data in
these dialogs and tables.
4. The user can choose between "legacy" option and "Full" option for performing integral bridge
analysis. For the legacy option, the analysis is performed only one side of the wall. The user has to
specify whether the integral bridge analysis needs to be done at the left/right of wall. The user needs
to specify the strut index which models deck contraction and expansion. Preferably, this strut should
have only prestress, and no stiffness. During the integral bridge analysis cycles of contraction and
expansion, it will apply the prestress in this strut with appropriate sign.
For the "Full" option, the analysis is performed on both sides of the wall in the same file, as outlined
in PD6694-1 document.
5. Once the data has been entered, the user can go for the analysis in the regular way. When the
user clicks the "Analyse" button, the program performs normal analysis for all the non-integral bridge
stages. If these previous stages are analysed successfully,integral bridge analysis is started.
For the "Legacy" option, when the user specifies the analysis on the left side of the wall, the program
performs the following in each iteration:
apply initial summer expansion (about half the prestress specified for the deck strut),
full winter contraction (full prestress force), and
full summer expansion (full prestress force.)
However, when the user specifies analysis on the right side of the wall, following is the sequence of
integral bridge analysis stages:
apply initial winter contraction (about half the prestress specified for the deck strut),
full summer expansion (full prestress force), and
full winter contraction (full prestress force.)
The above iterations are repeated until convergence in d'd/H' values is achieved.
For the "Full" option, following sequence is first performed in each iteration to get the d'd/H' values to
the left of wall:
apply initial winter contraction (about half the prestress specified for the deck strut),
full summer expansion (full prestress force)
The above iterations are repeated until convergence in d'd/H' values is achieved on the left side of the
wall.
Subsequentlty, using the converged d'd and H' values on the left side of the wall, the program
The above iterations are continued until convergence in d'd/H' values is achieved on the right side of
the wall.
6. After analysis, the user can view the actual material properties used in integral bridge stages in
the results output as shown below:
These results are printed for each stage below the deflection, bending moment, shear forces results.
Also, the "At-rest" earth pressure profiles are plotted in the graphical output along with actual
pressures to visualize H' i.e. intersection of "At-rest" earth pressure profiles, and actual earth
pressure profile. It will also help in identifying any potential issues with intersection of earth pressure
profiles.
When entering material data the user can choose to enter a granular or cohesive material.
Where the granular option is chosen the material parameters are calculated as described in
Appendix A of PD6694-1. The user is required to enter suitable stiffness curves (RF,G vs d'd/H') and
passive pressure (K*d vs d'd/H') curves. The Seed and Idriss (1970) curve for small strain stiffness of
granular soils with 90% densification as shown in Appendix A of PD6694-1 is included as a standard
curve for the calculation of small strain stiffness 'S&I 90% Densification' and this may be used if
appropriate. Likewise there is an inbuilt option for K*d v d'd/H' 'Standard 6N/6P' that calculates the K*d
value using the formula shown in section 9.4.3 of PD6694-1.
Where the cohesive option is chosen the material parameters specified in the materials table are
used directly in the integral bridge analysis.
The success of the iterative procedure depends on determination of H’ and subsequently d’d. In the
PD 6694-1 algorithm, the parameter H’ is determined by the intersection of the actual earth pressure
profile and K0 (At-rest) earth pressure profile.
In cases where there are convergence issues, the following advanced options have been provided to
overcome these issues. However, these options are not specified in the PD6694-1 document, and
these are deviations from the original algorithm specified in this document. The user should exercise
caution when making use of these options.
The types of convergence issues, and the possible workarounds for overcoming these issues are
outlined below:
Cyclic non-convergence: In this case, the d’d/H’ vary between two well defined sensible values as
shown below:
In cases such as this, convergence may usually be achieved by increasing the number of nodes in
the model. If you are using “Automatic” node generation, this may be achieved by reducing the ratio
of maximum to minimum node spacing as shown below:
However, it is generally better to avoid generating too many nodes – greater than 200-250.
Cyclic non-convergence and stability failure due to non-intersection of earth pressure profiles: This is
same as above but one of the values having H’ equal to the full depth of the model (to rigid boundary
level) and is related to the non-intersection of the earth pressure profiles.
For convergence issues relating to non-intersection of earth pressure profiles(which usually happens
on the right side of the wall), there are two options provided in the program:
o Increasing K0 value based on OCR – which is obtained from vertical effective stress history. In
this case, K0 obtained from Jaky’s formula i.e. K0 = 1 – sin(phi’) is multiplied with (OCR)^0.5.
This may work if there are excavation stages before the integral bridge analysis stage.
o Sometimes, the earth pressure profiles on the right side do not intersect even if there are no
excavations, and the situation does not change even if the wall depth is increased indefinitely. In
such a case, there is an option to use the earth pressure profile from the stage from the integral
bridge stage with backfill, but no thermal load, as the At-rest profile.
o Lastly, the earth pressure profiles come very close but do not intersect, leading to non-
convergence issues later. To overcome this, an option has been added to specify tolerance for
intersection of earth pressure profiles. This is helping in achieving convergence in some cases.
For example, in the model below, the two earth pressure profiles, do not strictly intersect, but
come close to within 5% of each other. Treating this as an intersection can sometimes help
achieving convergence in a later iteration. Following is an illustration:
Before tolerance (i.e. tolerance set to default 0.0), pressure profiles come close but do not intersect:
After tolerance set to 5%, convergence is subsequently achieved. It can be possible that the
pressure profiles actually intersected in a later iteration:
In this case, the higher values of H’ may extend beneath the toe of wall. This causes stability
issue as the soil zones till the depth H’ have low value of Kp.
The primary issue in the case is the assumption of a uniform value of rotational strain
parameter over the full height of the affected zone. This may not be correct for deeper values
of H’, as the deflection profile is mostly concentrated over the shallower depths and using the
deflections from the mid height of the affected zone H’, may give very low values of d’d
leading to very low values of Kp.
To overcome this issue, instead of using a single value of d’d/H’, the program evaluates this
value for each element based on the deflection at the element’s top node and its bottom
node ( i.e. (d’ at top of element – d’ at bottom of element)/ element length). For intermediate
nodes in the model, which are shared between successive elements, the program calculates
the average value of rotational strain coming from the top element and bottom element.
For intermediate nodes, (d/H) mentioned above is averaged between values for upper
element and lower element.
Further, the program avoids applying modified soil properties to those nodes whose rotational strain
is less than a threshold value. The default value of threshold nodal rotational strain is zero. However,
the user may give other non-zero values.
NOTE: When using the nodal rotational strain option, if the automatic calculation of K*d is selected,
the program uses a modified C factor in the equation given in section 9.4.3 of PD6694-1. This is due
to the fact that the C values given in this section 9.4.3 are based on average rotational strain and not
nodal rotational strain. For this option, the C values used in Prof. England et. al. are used - which are
essentially half the values given in section 9.4.3.
However, if the user specifies K*d vs d'd/H', and also in the case of RF,G vs d'd/H' curves, the program
uses average nodal rotational strain instead of d'd/H' when this option is selected. The user would
need to modify these input curves i.e. K*d vs d'd/H' and RF,G vs d'd/H' as necessary.
In addition, there is an option to calculate H' based on threshold nodal rotational strain i.e. this option
does not take into account the intersection of earth pressure profiles. The values of H' is calculated
by finding the depth at which the average nodal rotational strain drops to a low threshold value,
described above.
1. The iteration process starts with initial assumed values of d’d and H’ defined by the user in the
“Integral bridge analysis data” dialog.
The program updates the material properties at all nodes which are within a depth of H’ – on the
left side or right side or both sides of the wall as specified by the user in the “Integral bridge
analysis data” dialog.
Based on the initial d’d/H’ ratio, the program evaluates K*d and RF,G values for only granular
materials at all nodes which are within a depth H’.
The values of Kac and Kpc are calculated using the formulae :
Case 1 (“User-specified” earth pressure coefficients option is selected for the original material):
Kac a
) and Kpc p
)
Case 2 (“Calculated” earth pressure coefficients option is selected for the original material):
Kac a
*(1+Cw/C)) and Kpc *(1+Cw/C))
p
When in-built option is used for calculating K*d, the equation in section 9.4.3 of PD6694-1:2011
is used to calculate K*d from the value of Kp calculated above. However, if the user-defined K*d
versus d’d/H’ curves are used, then the program directly calculates the value of K*d from d’d/H’.
Revised value of Young’s modulus, E is calculated using the value of RF,G using the equations in
section A.3.2 of PD6694-1:2011 document:
v
is the vertical effective stress, and
m
is the mean effective stress.
Note: RF,G itself is calculated based on d’d/H’ ratio using the user-defined RF,G versus d’d/H’
curve.
The unit weight of the material is replaced with γ120 value as entered in the Integral bridge
analysis data dialog.
The above calculated values of material parameters for nodes with in a depth of H’ are shown in
the detailed results in italics:
2. Once all the relevant material parameters have been calculated as discussed above, the program
performs analysis in the usual manner for the three generated integral bridge analysis sub-stages:
"Legacy" option:
Case 1: Initial summer expansion, full winter contraction and full summer expansion.
Case 2: Initial winter contraction, full summer expansion, and full winter contraction.
"Full" option:
Left side iterations - Initial winter contraction followed by full summer expansion.
After left side iterations have converged, right side iterations are performed appending full winter
Based on the results of analysis from the last 2 sub-stages, H’ and d’d values are found.
H’ value is computed from the intersection of K0 earth pressure profile, and actual effective lateral
earth pressure, as discussed earlier:
d’ (d'd in the above figure) is the movement of the wall at a depth H’/2.
3. If the differences between d’assumed/H’assumed value, and the corresponding values calculated above
are within tolerance limits, then the program stops further analysis. However, if the difference is
greater than tolerance limits, then the calculated values of d’d and H’ are used to repeat the
calculations in steps 1 to 3 discussed above.
In "Legacy" option, integral bridge analysis can be performed on only one side of the wall i.e. "Left"
or "Right", in a single file. However, for the "Full" option, the program performs calculations on both
sides of the wall in a single file as outlined in PD6694-1 document.
The pressure coefficient envelope as shown in Figure 6 of PD6694-1 is complied with explicitly in
the "Full" method. There is no "redistribution of pressures" for the "Full" option for the integral
bridge analysis stages. However, for the "Legacy" option, the redistribution of pressures is allowed
in the integral bridge analysis stages, but the pressure coefficient envelope is not explicitly
checked.
In the calculations of Ka and Kp explained later below, for the "Full" option, the program first
identifies whether active or passive condition exist at the node in order to apply the envelope in
Figure 6 of PD6694-1.
"Legacy" option:
K0 = 1 - sin( 'max-triaxial,superior)
"Full" option:
When the user inputs the earth pressure coefficients directly, the same value of K0 is used.
For the "Full" option, the program first checks whether the soil at the node is tending to
active or passive condition. The soil on the left side during winter contraction or the soil on the right
side during summer expansion is treated as tending to active condition. The soil on the left side
during summer expansion or the soil on the right side during winter contraction is treated tending to
active condition.
K0 = 1 - sin( 'd,superior)
NOTE: In both the above equations, 'd values are derived from values entered by the user in
the "Material Properties" table, and NOT triaxial friction angle values.
Influence of OCR: When the user selects the OCR option under "Advanced Options", the
program multiplies the value of K0
Legacy option:
When the user specifies earth pressure coefficients directly in the "Material Properties"
table, same value of Ka is used.
On the other hand, if the user specifies angle of internal friction, delta/phi ratio etc., then Ka
is calculated using equations C.6 and C.7 given in Annex C of BS EN 1997-1:2004 with:
Angle of internal friction set to superior value of characteristic friction angle specified in the
"Material Properties" table.
Delta/Phi = 0.66,
Full option:
When the user specifies earth pressure coefficients directly in the "Material Properties"
table, same value of Ka is used.
As explained previously, the program first checks whether the soil at the node is tending to
active or passive condition.
When the user specifies earth pressure coefficients directly in the "Material
Properties" table, Ka is taken as K0.
Ka = 1 - sin( 'd,superior)
with 'd superior value derived from values entered by the user in the "Material
Properties" table.
When the user specifies earth pressure coefficients directly in the "Material
Properties" table, the same value of Ka is used.
On the other hand, if the user specifies angle of internal friction, delta/phi ratio etc.,
then Ka is calculated using equations C.6 and C.7 given in Annex C of BS EN 1997-1:2004
with:
Angle of internal friction set to superior value of characteristic friction angle specified
in the "Material Properties" table.
Delta/Phi = 0.66,
If the user specifies a Kd* versus d'd/H' curve for the material, then the program evaluates Kd*
directly using the value of d'd/H'.
Otherwise, if "Automatic" calculation for Kd* is selected by the user, then the following
procedure is adopted.
Legacy option:
Kp is calculated using equations C.6 and C.7 given in Annex C of BS EN 1997-1:2004 with:
Angle of internal friction set to superior value of characteristic triaxial friction angle specified
in the material parameters table in "Integral Bridge Analysis Data" dialog.
Delta/Phi = 0.5,
Beta = 0, and
Cw/C ratio = 0
Full option:
As explained previously, the program first checks whether the soil at the node is tending to
active or passive condition.
When the user specifies earth pressure coefficients directly in the "Material
Properties" table, Kp is taken as K0.
with 'd inferior value derived from values entered by the user in the "Material
Properties" table.
Angle of internal friction set to superior value of characteristic friction angle specified
in the "Material Properties" table.
Delta/Phi = 0.5,
Beta = 0, and
Cw/C ratio = 0.
From the above value of Kp, the program calculates Kd* using the equation in section 9.4.3
of PD 6694-1.
6 Seismic Analysis
Frew can be used to perform seismic analysis of a retaining wall. This analysis is undertaken based
on Wood's method and the Mononobe-Okabe method. These are pseudo-static methods that
estimate the additional lateral dynamic soil load on the wall. In this analysis struts representing the
dynamic soil and groundwater loads are applied to the wall.
There are a range of methods available to assess the impact of seismic events on retaining walls,
and the methods used by Frew will not be suitable in all cases. As a result it is important to
confirm with a seismic analysis expert that the methods used are suitable before analysis is
undertaken. Additionally loads other than the dynamic soil and groundwater may be applied, if there
are likely to be other loads applied to the wall (e.g. due to adjacent structures) consideration will
need to be given as to how these are taken into account.
2. Via the stage tree dialog add a further stage for the seismic analysis - this must be the final stage
of the analysis.
3. Go to the 'Analysis method' dialog for the seismic analysis stage, and click on the 'Perform
seismic analysis' check box then click 'Apply'.
4. Having selected to perform seismic analysis option, the 'Seismic analysis options' dialog can now
be selected in the gateway. Select the analysis options dialog, then select the preferred analysis
method and method for load application. If you intend to use calculated Kh values it is also
necessary to input the S value, and specify the design ground acceleration and acceleration due to
gravity. Once the required data has been input click on 'Apply'.
Note: The analysis type and load application methods are described in more detail in the Seismic
Analysis Methods section. Calculated Kh values are determined using the methodology described in
Eurocode 8 (see Calculation of Seismic Coefficients), the S values for a range of stratigraphy types
are given in Eurocode 8 Part 1.
5. Having chosen to perform seismic analysis, the 'Seismic material parameters' option becomes
visible for the final stage in the gateway and stage tree dialog. Click on either of these to open the
seismic material parameters table and then input relevant parameters as described below. Note that
there is one entry in this table corresponding to each of the materials in the general material
parameters table.
Parameter Description
This a non-editable field and gives the material description as per the main
Description
material parameters table.
Dry unit weight Dry unit weight of the soil for calculation of lateral earth pressure.
Saturated unit weight Saturated unit weight of the soil for calculation of lateral earth pressure.
Select either pervious or impervious. Pervious indicates that the soil is highly
pervious to water flow and the load from the soil structure and water are
Pervious/Impervious
calculated separately. Impervious indicates that water will move with the soil
and that they will act together.
The lateral soil pressure coefficient. If user specified this must be entered
Kh
manually, otherwise the calculated value will be shown in this box.
Ess is the small strain stiffness of the soil. Where only small displacements
Ess of the retaining wall are anticipated an alternate small strain stiffness may be
entered by the user.
The rate of change in small strain stiffness with depth. A positive value
Gradient Ess indicates stiffness increasing with depth. Note that the reference level for
each material is as set in the general material parameters table.
6. Having set the seismic parameters next analyse the file. During analysis strut forces will
automatically be generated and applied to the final stage representing the seismic force due to the
soil movement. These strut forces can be reviewed in the Struts table following analysis, but will be
deleted when results are deleted.
Note: To analyse intermediate construction stages it is necessary to create additional files for each
stage that you wish to analyse. These files should be created as above, but with the final stage
being that for which the seismic analysis is required, and with all subsequent stages deleted.
Where the calculated Kh option is chosen, Kh will be calculated using the following formula:
Kh = αS/r
For which,
α is the ratio of the design ground acceleration to acceleration due to gravity,
S is the soil factor specified by the user,
and r a factor representing the ratio between the acceleration value producing the maximum
permanent displacement compatible with the existing constraints, and the value corresponding to
the state of limit equilibrium.
The vertical seismic coefficient is calculated using the ratio of Kv to Kh (Rk) and the horizontal
seismic coefficient, such that:
Kv = Rk x Kh
For which k h is the horizontal seismic coefficient, γ the soil unit weight and H the retained height of
the soil.
Wood's method is supported by the research detailed in Wood (1973) which presents the results
from a range of simulations calculating the maximum dynamic pressure on the back of rigid retaining
walls. The method is then described in later works, e.g. Wood & Elms (1990).
The simulations supporting this method assume a homogenous fully elastic retained soil and stiff
underlying material. As a result, where multiple strata are present behind the retaining wall a
weighted average is taken for the parameters k h and γ such that;
and
Where n represents the layer number and z the layer thickness, as shown in the following example
figure.
For which K is the combined static and dynamic earth pressure coefficient, γ the soil unit weight, Kv
the vertical seismic coefficient, H the retained soil height, Ews the static water force and Ewd the
dynamic water force.
Given that the strut force should only represent the additional dynamic loading from the soil ∆Pd and
not the total load applied to the wall, the previous formula can be amended to give;
The calculations in Frew are based on this, evaluating the additional force for each node along the
face of the wall, then taking the sum of these to determine the total additional seismic force. This
can be written as:
For which x denotes each node, σ'v xt is the effective stress at the mid-point of the element above,
σ'v xb is the effective stress at the mid-point of the element below, Kx is the combined static and
dynamic earth pressure coefficient for relevant soil layer, k ax is the active earth pressure for the soil
at node x, and z x is the distance from the mid-point of the element above to the mid-point of the
element below.
To calculate the value of the combined pressure coefficient first the value of θ is calculated as shown
below.
The combined earth pressure coefficient K can then be calculated based on the formulae shown
below.
Φd - θ
or if β > Φd - θ
Where the user has selected to use the reduced limit on the passive side, the passive earth pressure
coefficient is calculated as shown below.
For which Φd is the design shear angle of the soil, δd is the angle of friction on the soil/wall interface,
and the directions of the forces acting on the wedge and geometry of the wedge are as shown in the
following diagram.
The active earth pressure coefficient is calculated as described in Calculation of Earth Pressure
Coefficients.
In addition to any general limitations of the method, there are a number of points that the user should
be aware of when using the Mononobe-Okabe method in Frew. These points should be considered
and it should be confirmed that the assumptions made are valid for the model being assessed.
Frew only considers the active case, where the soil stress along the face of the wall is at
pressures greater than this then the loads generated will not be correct.
Because Frew uses the vertical effective stress to calculate the dynamic soil force, the calculated
force will be affected by any surface loads applied to the soil.
Frew only considers vertical walls, i.e. it uses a value of 90o for ψ.
Where partial factors are applied factored values of Φ and δ will be used.
Frew only considers the change in the active pressure on the wall across the retained height, if it
is required to increase pressures below this the user should manually adjust earth pressure
coefficients for soils at this level during the seismic stage.
Where the load is distributed it is applied as a strut load to each node along the retained soil (i.e. a
strut is created with stiffness of 0 and a prestress equal to the required force and is applied to the
relevant node). First the average pressure on the back of the retaining wall is calculated as;
The load at each node is then calculated. The load distribution is assumed to be linear and can be
set by specifying the % of the average load at the base. Frew will then calculate the corresponding
load at the top of the wall to ensure the the total load is unchanged. The force applied at each node
is taken as the sum of the pressure as described above from the mid-point of the element below to
the mid-point of the element above the node. Two example distributions are shown below, one with
100% average load at the base of the wall, i.e. constant pressure, and one with 50% of the average
pressure at the base of the wall, i.e. 0.5q at the base to 1.5q at the top.
Where the load is applied as a point load, a strut force will be generated and applied at the elevation
specified by the user. If nodes are generated automatically this will be taken into account when
generating nodes to ensure that a node is present at the correct level.
For which Kh is the horizontal seismic coefficient, γw the unit weight of water and H' the height of the
water table from the base of the wall.
If load application is specified as a point load, then the load is applied as a point load at a level of f x
H' from the base of the wall, where the factor 'f' is specified by the user. If the load application is
specified as a distributed load then it is applied as a pressure increasingly linearly from 0 at the
water table to the maximum pressure (pmax ) at the base.
Where there are multiple strata present with some specified as pervious and others as impervious,
the pressure profile is the same as that described above but with zero pressure applied along the
length of the wall adjacent to impervious soils.
7 Output
7.1 Analysis and Data Checking
For a stability check, to check or set a wall toe level, select Stability Check from the Analysis menu,
the button, or the Stability Check button on the Node Generation Data dialog.
For full analysis, select Analyse from the Analysis menu or the button.
Stability Check
A dialog will appear with default parameters for the stability check. The list of stages in the program,
for which the stability check will be carried out will be listed in a table.
Select the required collapse mechanism (for details, see Stability Check). For the free earth
method, the lowest strut is selected as the rotation strut. If automatic node generation is being used,
ticking the "Generate nodes..." box will create all required nodes for the Frew analysis on successful
completion of the stability check for at least a single stage.
The program initially uses the default calculation interval in the stability calculations. If the stability
calculations are not successful with the initial calculation interval, the program will appropriately
change the value of the calculation interval, and re-run the stability check. This process is repeated
at most three times.
Tip: If the stability check fails to find the toe depth within the specified number of iterations, try
increasing the calculation interval or the iteration limit.
Full Analysis
the calculations.
4. All essential data has been entered, e.g. wall plan length and global Poisson's ratio for the
Mindlin method; boundary distances for the Safe and Mindlin methods.
5. Nodes have been generated or specified.
If there are errors, these must be corrected before the analysis can continue. Any data warnings will
also be shown here. These should be reviewed and any required changes made. Sometimes these
warnings will relate to features which are not required for the current analysis and can be ignored (for
example, "NOTE: Missing material for effective stress params in undrained pore pressure calcs" is
only relevant if undrained pore pressure calculations are required).
If no errors are found then the calculation continues through each stage. To continue to analysis
when there are data warnings, click the "Proceed" button.
Note: The Tabular Output view will be shown once the calculations have been completed. It can also
be accessed via View | Tabular Output as shown below, or the item in the Gateway.
At the beginning of each stage's results, any surcharge or strut insertion or removal will be noted and
the progress of convergence through the iterations is shown in a table. After the final stage's results,
an additional table shows the "envelope" of the calculated displacement, bending moment and shear
force values at each node.
Lines of output can be highlighted and then copied to the clipboard and pasted into most
Windows applications (as shown below). The output can also be directly exported to various text or
HTML formats by selecting Export from the File menu.
The results table is quite wide so the default font size is condensed. If larger size print is required,
this can be set by clicking the Larger Font button on the toolbar. Note that the Page Setup
may need to be landscape to avoid the lines of the results table scrolling on to two lines.
Calculation details
E Profiles assumed for calculation (generated):
On the LEFT: E at ground level = 38000. E at bottom node = 53000. kN/m²
On the RIGHT: E at ground level = 39000. E at bottom node = 58000. kN/m²
Iter Inc Node Disp Node Press Node
no. max no. error. no. error no.
displ
[mm] [mm] [kN/m²]
1 0.0 1 6.1375 1 0.14 11
2 6.1 1 0.1587 3 10.77 3
3 6.3 1 0.1620 4 7.65 4
4 6.4 1 0.1570 5 6.01 5
5 6.5 1 0.1503 5 5.00 6
10 6.9 1 0.0971 5 2.71 8
15 7.1 1 0.0484 6 1.32 9
20 7.2 1 0.0187 6 0.55 11
23 7.2 1 0.0092 6 0.26 11
Stress Pore
Stress Pore
Node Level Disp Vt Ve Pt Pe Pressure Soil
Vt Ve Pt Pe Pressure BM Shear
[m] [mm] [kN/m²] [kN/m²] [kN/m²] [kN/m²] [kN/m²] Left Right [kN/
m²] [kN/m²] [kN/m²] [kN/m²] [kN/m²] [kNm/m] [kN/m]
1 50.00 38.93 5.000 5.000 1.026 1.026 0.0 3 0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
50.00
0.0 -144.5
2 49.00 42.05 20.00 20.00 29.42 29.42 0.0 3 0
0.0 0.0 0.0 0.0 0.0 144.0 -129.3
3 48.00 44.89 40.00 40.00 8.080 8.080 0.0 3 0
0.0 0.0 0.0 0.0 0.0 258.6 -110.6
4 47.00 47.21 58.75 58.75 11.87 11.87 0.0 A 3 0
0.0 0.0 0.0 0.0 0.0 365.2 -99.97
5 46.00 48.81 80.00 70.00 24.12 14.12 10.00 A 3 0
0.0 0.0 0.0 0.0 0.0 458.6 -81.35
6 45.00 49.50 100.0 80.00 36.08 16.08 20.00 A 3 0
0.0 0.0 0.0 0.0 0.0 527.9 -51.25
7 44.00 49.15 120.0 90.00 48.01 18.01 30.00 A 3 0
0.0 0.0 0.0 0.0 0.0 561.1 -9.205
8 43.00 47.69 140.0 100.0 59.92 19.92 40.00 a 3 0
0.0 0.0 0.0 0.0 0.0 546.3 44.76
9 42.00 45.16 160.0 110.0 71.85 21.85 50.00 a 3 0
0.0 0.0 0.0 0.0 0.0 471.6 110.6
10 41.00 41.71 180.0 120.0 83.78 23.78 60.00 a 3 0
0.0 0.0 0.0 0.0 0.0 325.0 188.5
... etc
The level of each calculation point. The separation of these points is specified in the Analysis
Options.
The Bending moment and shear force profiles down the wall.
If the "Balance water pressures" feature is switched on (see Analysis and Data Checking), two sets
of results will be shown - the original results with the water data input by the user, and the final
results obtained by the program after balancing the water pressure at the base of the wall.
Calculation details
Displacement
Vertical total and effective stress (Vt and Ve)
Horizontal total and effective stress (Pt and Pe)
Water Pressure (U)
Bending Moment
Shear Force
Note: For the undrained condition, if undrained pore pressures are not calculated by the program,
the values of Ve and Pe shown and the user's U value will be apparent effective stresses and pore
pressures rather than actual stresses and pore pressures. A note will be added to the foot of the
results table and the values shown in brackets. See Undrained materials for more background.
Indicator Meaning
A The effective earth pressure is less than 1.01 times the active limit, but within the
convergence pressure limit
P The effective earth pressure is greater than 0.99 times the passive limit, but within the
convergence pressure limit
a The effective earth pressure is less than the Coulomb limit but still greater than the
redistributed active pressure limit
p The effective earth pressure is greater than the Coulomb limit but still less than the
redistributed passive pressure limit
r The effective earth pressure is greater than the redistributed passive pressure, but not
sufficient to cause a failure to the surface (see Calculation of Active and Passive Limits
and Application of Redistribution on page 58).
m The earth pressure reported is the Minimum Equivalent Fluid Pressure (MEFP)
where this has been specified.
Note that a, p and r are only used when redistribution is used to calculate active and passive
pressure limits.
Warning or error messages will be shown in both the Solution Progress window and on the detailed
results, if any stage has failed to analyse or has high bending moments below the base of the wall.
Most are self explanatory but some additional detail is given below.
Try increasing the number of iterations in the Convergence Control dialog for the relevant stage.
This error may occur in Stage 0 where a surcharge is applied at ground level before the wall has been
installed. This occurs where it creates a discontinuity in the lateral earth pressures at the top node.
Where this occurs this can usually be worked around by applying the surcharge at a level slightly
below the ground surface.
This means the data is such that the pore pressure exceeds vertical total stress (see Total and
Effective Stress). This is usually caused by a data input error.
If the iteration number (j) is 1, this is probably due to soil properties (and surcharges of limited
extent) being prescribed such that the active pressure exceeds the passive pressure at the node
indicated. If j is equal to 2 or more, this message usually implies the solution is becoming
numerically unstable.
These warnings are output if the program obtains relatively high bending moments below the base of
the wall. This can happen if the displacement of the wall is large compared with the flexure so
curvature cannot be computed with sufficient accuracy (need to have several significant figures of
difference of displacement and gradient of displacement between adjacent nodes.) The problem is
generally caused by small stiff elements and can usually be overcome by increasing the distance
between nodes. If these warnings are given, they indicate that the wall is not in equilibrium and
the results are not reliable.
This output includes a summary of the peak results, indicating where these occur and in which factor
set, as well as the results envelope for the full analysis of each factor set analysed.
Set Scale : This allows the user to toggle between the default 'best fit' scale, the closest available
engineering scale. e.g. 1:200, 1:250, 1:500, 1:1000, 1:1250, 1:2500, or exact scaling. The same
options are available via the View menu "Set exact scale" command.
Save Metafile :allows the file to be saved in the format of a Windows Metafile. This retains the
viewed scale. The metafile can be imported into other programs such as word processors,
spreadsheets and drawing packages.
Copy : allows the view to be copied to the clipboard in the form of a Windows Metafile.
Zoom Facility : Select an area to 'zoom in' to by using the mouse to click on a point on the drawing
and then dragging the box outwards to select the area to be viewed. The program will automatically
scale the new view. The original area can be restored by clicking on the 'restore zoom' icon as
shown here.
Smaller/Larger font : allows adjustment of the font sizes on the graphical output view.
Toggle strata on/off: switches strata fill colour on or off (for example, if printing to a monochrome
printer you may prefer to switch the fill off)
Axes scaling : individual x-axis scales can be set for each plotted parameter. The same option is
available via the View menu "Change axis scale(s)" command.
Active and passive total and effective stress profiles on either side of wall. The default is to
show total stress. If effective stress is plotted, water pressure will also be shown.
Envelope : Whereas other graphical results are for single stages, envelope provides the envelope of
results for all stages in the calculation.
Primary factor set shown : this drop down box can be used to show a primary factor set. This is
shown as a solid line.
Show additional factor set : this can be checked to show an additional set of results in the
graphical output, the factor set to be shown can then be selected using the drop down menu. The
secondary factor set will be shown as dashed lines.
When the graphical output view is open the Graphics menu shows the following options.
This will show the Print Selection dialog. Choose Tabular or Graphical and the required data and/or
results to show. Enter the required stage list. "All" is the default, but individual stages can be
entered, separated by spaces, or ranges of stage e.g. "2 to 5".
For tabular output, the output view will be opened or updated with only the selected output shown.
The information can be sent to printer in the usual way.
For graphical output, the Print dialog will be opened allowing selection of a suitable printer. Note:
Graphical output can not currently be batch printed to PDF printer drivers - a warning message will
be generated in this case. To print to PDF, open the graphical view and print each stage individually.
The flexibility coefficients stored in Frew were determined from a series of finite element analyses
carried out using the Safe program.
The above figure shows the geometry and boundary conditions assumed for the mesh in the Safe
analysis. The mesh is divided into 101 elements in height. The length is 10 times the total mesh
height and is divided into a series of unequal elements, which increase in length away from the left
hand boundary AB.
The model acts in plane strain and the vertical free face AB represents the location of the retaining
wall in Frew.
The boundary AB is divided into 101 elements as shown. A unit force was applied to each element
in turn, distributed as a uniform pressure over the length of the element.
The horizontal displacement at all nodes in the middle of the side of each element was then
calculated, down the vertical free face AB. These displacements represent the flexibility coefficients
and were stored as the flexibility matrix.
Using the principle of superposition, the total horizontal displacement at all nodes due to any load
combination, can be estimated.
Two cases are considered - one with the nodes on the line AB free to move vertically and the other
with the nodes fixed vertically. These are referred to as the "Fixed" and "Free" cases respectively.
For each case there are two sets of flexibility coefficients stored within Frew. These apply to soils
having either:
For varying profiles of E the user can specify their best estimate of a linear profile to best describe
the variation with level. The program will combine and modify the matrices to accommodate this, see
Accuracy with respect to Young's modulus (E).
Alternatively, the program will select a linear profile of Young's modulus, based on the specified non-
linear profile; the program then applies further corrections as described in Irregular variation of E.
Scaling factors are used to map the flexibility matrices from the Safe model onto the user defined
model in Frew.
To carry out this 'mapping' the boundary AB is divided into "Frew elements".
The boundaries of the Frew elements are mapped onto the Safe model. The flexibility for a unit
pressure over the Frew element length can then be determined.
This is achieved by summing the contributions, at the Frew node position, from all Safe elements
which contribute directly to the Frew element.
Weighting factors are used to account for the effect for loading from a partial Safe element if Frew
element boundaries bisect a Safe element. Using this procedure, the equivalent total load acting on
the Frew node corresponds to the length of the Frew element, in multiples of the Safe element
length.
Since the Safe coefficients were derived for 'elastic soil', the calculated Frew coefficients can be
scaled by the ratio of the Safe element length to the Frew element length. This gives an equivalent
total load at the Frew node of unity.
In general the Frew node will not correspond directly with a Safe node, and in such circumstances a
second level of interpolation is implemented.
Two sets of Frew flexibility coefficients are calculated which correspond to the Frew element centred
on the Safe nodes immediately above and below the Frew node. The actual Frew flexibility
coefficients used in the calculations is then taken to be a weighted average of these two sets of
coefficients.
No precise theory is available to enable accurate matrices to be derived for other cases, and various
intuitive methods have therefore been adopted. These have been tested by comparing flexibility
matrices computed by Frew with the results of additional finite element computations using Safe.
The stiffness matrices for the two components are then added. No theoretical proof of this result has
been found.
This method calculates a best fit linear Young's modulus profile E*z to represent the actual variation
Ez .
Application of matrix
The flexibility matrix (F*), corresponding to the linear approximation, can then be derived from the
pre-calculated matrices as described in The Basic Safe Model. In order to adjust this matrix to
obtain the flexibility matrix (F) corresponding to the actual variation of Young's modulus each term in
row i of (F*) is multiplied by a coefficient Ai . To maintain symmetry, terms F*ij and F*ji are both
multiplied by the same coefficient, chosen as the smaller of Ai or Aj .
A number of alternative means of deriving coefficient Ai have been attempted based on consideration
of the different distribution of work done due to unit load acting on two elastic soil blocks with
Young's modulus profile E*z and Ez . The following expression has been developed for the
coefficient Ai acting at node i.
where *ij is the displacement at depth z of the elastic soil block with Young's modulus profile E*z
due to unit load at node i.
No rigorous theoretical justification for this expression is available. However, comparison between
finite element solutions and those produced by this approximation have been carried out and have
shown that for most practical situations errors will rarely exceed 20%. The following figure shows
one of the more severe cases that could be envisaged, (Pappin et al, 1985).
Comparison of Safe and Mindlin flexibility approximations with FEA, at three depths
Here the displacement of the elastic soil block, with Young's modulus profile Ez , due to unit load at
three different levels, is shown compared against rigorous finite element solutions.
The flexibility coefficients in the Safe model were derived for one specific geometric case
which represented a ratio of L/D of 10, where L is the distance to the remote boundary and D the
depth of soil in front of the wall.
Note : Clearly, as L/D changes the flexibility coefficients will change and hence the stiffness matrix.
The greatest difference will occur at small ratios of L/D ( i.e. large depth of soil in comparison to a
close boundary). In this case it may be more reasonable to use a sub-grade reaction type of
analysis where the spring length is well defined.
To allow for varying ratios of L/D the Safe method has been modified by adding a single spring at
each node point. For high ratios of L/D the spring stiffness is small due to the large spring length.
The results are then virtually identical to those of the elasticity method alone.
For small L/D ratios the single spring stiffness becomes dominant and controls and calculated wall
movements.
1. a constant or
2. linearly increasing stiffness with depth.
Changes in wall pressure computed by Frew and Safe were compared for the same wall movements
for varying ratios of L/D. The comparisons were achieved by calculating the wall movements due to
an excavation using Frew, and then using the calculated movements as input data for a finite
element analysis using Safe. The behaviour was fully elastic in both cases.
With the same specified horizontal wall movements the changes in stress calculated by Safe are
pSafe. A comparison between pFrew and pSafe gives an indication of the agreement between
the two methods of analysis.
The Model
In the Frew analysis the wall was taken as extending to a depth of 25m below ground level and the
rigid boundary was at a depth of 28m. The dig depth was 5m giving 20m of soil in front of the wall.
The distance to the remote boundary on the left side of the wall was taken as 1000m and on the right
side the distance was varied to give L/D ratios of 0.25, 0.5, 1.0, 2.0, 4.0 and 50.0.
Comparisons were made for soil which has a constant Young's modulus (E1) throughout its depth
equal to 40,000kN/m² and also for a soil in which Young's modulus (E2) increased linearly from
5,000kN/m² at ground level to 75,000kN/m² at a depth of 28m.
The soil is assumed to be dry and to have a unit weight of 20 kN/m³ and at rest coefficient of earth
pressure K0 = 1.0. For an excavation of 5m the change in horizontal stress is calculated as:
p = 5*20*Kr = 100Kr
therefore at some depth 'd' below the top of the wall the initial horizontal stress in the front of the wall
will be:
therefore
p0 = 20d - 43 kN/m3
Due to digging 5m the wall moves and the stresses in front of the wall increases to pf. The change
in stress is therefore defined as
pFrew = pf - p0
Summary of Results
The ratio of pFrew / pSafe is shown below for the two cases considered.
This shows how pFrew / pSafe varies with depth and the ratio L/D. Taking an average ratio
Safe model
These options select from the two sets of pre-stored flexibility matrices computed by Safe for the
nodes on boundary AB. The two sets represent nodes free to move vertically or fixed vertically
respectively.
An exception is a cantilever situation where the "fixed" method will give less displacements because
it models greater fixity between the soil and wall.
It must be noted that the case with interface friction ("fixed") is somewhat approximate because
Poisson's ratio effects are not well modelled. For example, these effects in a complete elastic
solution, can cause outward movement of the wall when there is a shallow soil excavation.
If there were no rigid base or vertical loading the equations could be used directly to determine the
flexibility coefficients of the nodal points due to horizontal pressures applied to the nodes, assuming
that the wall is at a plane of symmetry.
The flexibility of the soil, with each side of the wall taken separately, is equal to twice that of a half
space. The effect of the width (W), or out of plane dimension of the retaining wall, can also be taken
into account to some extent as the equations model the length of the pressure loaded rectangular
area in the out of plane direction. Clearly if this dimension is large a plane strain condition is
modelled.
When modelling each side of the wall the soil must still be considered as a half space and the
resulting flexibility matrix doubled.
Therefore to maintain symmetry at the plane of the wall additional nodes must be added to both
sides. The base nodes are restrained both vertically (Z-Z direction) and horizontally (X-X) whereas
the vertical boundary nodes are only restrained horizontally (X-X). As these nodes are on a plane of
symmetry (X-X, Z-Z) they will not move in the (Y-Y) direction.
Nodal restraints are achieved by modelling stresses acting on rectangular areas centred at each
boundary node to force the displacements of the boundary nodes to be zero. For a vertical boundary
node a horizontal pressure is considered to act on a vertical rectangle. For a base node two
stresses are considered, one being a horizontal traction and the other a vertical pressure, both acting
on a horizontal rectangle. In all cases the width of the rectangle is taken as being equal to the width
(W) specified for the wall.
The final soil stiffness matrix has been computed by eliminating the boundary nodes and inverting the
flexibility matrix of the central nodes only.
When W is small three dimensional effects will dominate and to approximate the fixity of a plane by
a single line of nodes becomes somewhat dubious. Additional nodes on the fixed planes away from
the plane of symmetry (X-X, Z-Z), or varying the width (W) of the loaded rectangle at the fixed nodes
would improve this approximation. Nevertheless using the Mindlin flexibility method provides an
approximate means of studying the importance of W.
A drawback of the Mindlin flexibility method is that Young's modulus is assumed to be constant
with depth. This is significantly different from the "Safe" flexibility method which can model
accurately a linearly increasing modulus with depth. Nevertheless the same ratios that are applied
to model modulus variations can still be used with the Mindlin method, see Irregular variation of E.
Comparison of Safe and Mindlin flexibility approximations with FEA, at three depths
It can be seen that Frew provides quite good results when used with the Mindlin equations.
An item of information may therefore be necessary, but may also not be sufficient on its own to
ensure a conservative solution. An ideal, accurate solution is both necessary and sufficient.
8.4.1 General
Approximations to the limiting pressures on a retaining wall may be calculated using either "lower
bound" or "upper bound" methods.
For the lower bound method, a set of equilibrium stresses which does not violate the
strength of the soil, is studied. The limits which are calculated by this approach are
sufficient for stability (ensuring a conservative solution), but may be unnecessarily severe.
Rankine used a lower bound method to calculate active and passive pressures in simple
solutions. He assumed that wall pressure increased linearly with depth.
In the upper bound method a failure mechanism is considered. The limits obtained are
necessary for stability, but may not be sufficient.
Coulomb used an upper bound method to study the simplest failure mechanism - a plane slip
surface - to derive the forces on a wall.
It is found that for the simplest case of all, a frictionless wall translated horizontally without rotation,
their analyses give compatible results. This result is therefore accurate – both necessary and
sufficient.
Note: For one slip surface Coulomb's method only yields the total force on the wall. In order to find
the redistribution of that force, i.e. the pressures on the wall, further assumptions related to the
mode of deformation are required.
For more complex problems, involving wall friction and complicated patterns of deformation,
Rankine's simple assumptions about the pressure distributions are obviously wrong and Coulomb's
planar slip surface is not the most critical. Many other researchers have therefore derived information
about active/passive forces by studying other failure mechanisms. In the absence of additional
assumptions, these methods yield the limiting force on the wall between the ground surface and any
given point on the wall, but they do not dictate the distribution of that force, i.e. the pressures on the
wall. They produce limits which are necessary, but not exactly sufficient. However, by seeking the
most critical slip surface a result which is nearly sufficient ( to ensure a conservative solution) is
found.
In Frew, elasticity methods are used to derive a pressure distribution on the wall, and this is then
modified so that forces on sections of the wall are approximately within the limits required by plastic
(strength) considerations.
The method used will first be described for dry, cohesionless soil, considering only the active limit.
For a uniform material, values of the coefficient of active earth pressure Ka have been derived by
various researchers by searching for critical failure surfaces. These give necessary limits of the
forces on the wall.
Strictly
where :
Pa = the minimum effective soil force on the wall between the free surface and depth z
' = effective unit weight of soil.
Only if it is assumed that the earth pressure increases linearly with depth is it valid to use the same
value of Ka in the equation for
Now define
or
in a non-uniform soil
Then, provided the value of Ka is a very good upper bound the condition, p pa at all depths, (E1)
will be sufficient (safe), but not 'necessary' since the necessary condition only considers force.
Referring to the figure, the criterion of p pa means that the pressure p cannot drop below the limit
of pa. This is the limiting condition used in Frew when "no redistribution" of the wall pressures is
specified. It is sufficient to provide a conservative solution, but may be unnecessarily severe.
If P is the force on the wall between depth z and the ground surface, an alternative condition would
be
z
pdz P Pa 0.5 K a 'z 2 in a uniform soil (E2)
0
z z' z z'
pa dz Ka ' dz ' dz in a non - uniform soil
0 z' 0 0
These equations would allow the type of stress distribution, indicated in the above figure, which
would occur, for example, at a propped flexible wall.
The equation E1 for a uniform soil is necessary, but the following example shows that it is not
sufficient.
Consider the section of wall zj zi in the above figure. Above zj the wall pressure p is in excess of Pa.
Equation E2 would therefore allow the pressure between zj and zi to fall to zero, or even to have
negative values, provided that the area indicated as 2 does not exceed area 1.
This is clearly wrong; it is not admissible to have zero pressure on a finite length of wall supporting a
cohesionless soil. If it were, the element of wall between zj and zi could be removed and no sand
would flow out. It would be possible however, to have zero pressure at a point, with zj and zi
coincident; it is admissible to have a very small hole in a wall supporting sand.
If zj zi is a finite length, sand would flow out because of the self-weight of the material between zj and
zi . Thus, there is another limiting line, indicated as P1 in the above figure. For depth z below zj this
limit is given by:
z
p Ka ' dz p1
zj
(E3)
However, there is also a more severe restriction. This occurs because at depth zj there must be a
non-zero vertical stress since the horizontal stress immediately above zj is pj pa. In order to
maintain this horizontal stress, the minimum vertical stress is approximately Ka pj . Thus, for points
below zj , the line p2 provides a limit:
z
p Ka ' dz K aj p j p2
zj
(E4)
Equations E2 and E3 are similar in form to p pa. It was argued in Application in Frew above that
p pa was sufficient but not necessary, whilst Equation E2 was necessary but not sufficient.
Similarly, Equation E4 is not necessary. By analogy with Equation E2, the necessary Equation
becomes:
zi zi zi z
pdz p 2 dz Ka ' dz K aj p j dz
zj zj zj zj
(E5)
When the redistribution option is specified in Frew, Equation E5 is enforced between all pairs of
nodes corresponding to depths zi and zj ( zi > zj ). In effect, this means that a large number of
possible failure mechanisms, involving both local and overall failure, are checked. It is considered
that this system provides a good approximation to limits which are both necessary and sufficient.
The same arguments for redistribution may be followed through for both active and passive limits for
soils with cohesion (c), pore water pressure (u) and effective wall pressure p' (where p' = p - u).
Between any two depths zj and zi ( 0 zj zi ) the limits may be expressed as:
(active)
zi z
u Ka u j u dz K aj p ' j c j K acj cK ac dz
zj zj
zi
u p ' dz
zj
(E6)
(passive)
zi z
u Kp uj u dz K pj p ' j c j K pcj cK pc dz
zj zj
(E7)
A further restriction is placed so that negative effective stresses are never used or implied. This is
achieved by substituting zero for negative values of the expressions in brackets in the above
inequalities.
In the passive pressure limit calculation it is generally not reasonable to impose the internal failure
mechanism implied by Equation E7. The program therefore only enforces the limit implied by
Equation E2, which states that the earth pressure integrated between the surface and depth z must
not exceed the Rankine passive pressure integrated over the same depth. If Equation E7 indicates a
failure however a small 'r' is included in the output table and the user must check that an internal
failure mechanism would not occur.
In order to ensure that active and passive limits are not violated "displacement corrections" are
computed for each node and added to the displacements derived from elastic analysis. They are
displacements associated with plastic strain in the body of soil. When displacement corrections are
used, the wall pressure at any node is still influenced, through the elasticity equations, by the
movement of nodes below it but may be independent of its own movement and of the movement of
nodes above it.
Suppose an active/passive failure occurs as shown above. The displacement corrections applied to
ensure that the limits are not violated at node q will cause a change of stress but no displacement at
node r, whilst at node p there will be a change of displacement but no change of stress. Effectively
this means that movement is taking place at constant stress on the failure surface, whilst elastic
conditions are still maintained, separately, in the blocks of material on either side of the failure
surface.
The following procedure is used to achieve an iterative correction for wall pressures in the program.
The procedure starts at the top of the wall and works downwards.
1. For node i, calculate the correction (FORCOR) to the force between soil and wall required
to return to the active/passive limit. If redistribution is specified, this correction will be a
function of the pressures mobilised at nodes j above node i (i.e. j < i).
2. For node i, calculate approximately the displacement correction DCII (i) that would cause
the force at i to change by FORCOR:
Where S(I,I) is the diagonal term of the soil stiffness matrix corresponding to node i.
3. For nodes j (j < i), calculate the displacement correction DCJI (i,j) that is required to
prevent change of pressure at j when the displacement at i is corrected by DCII(i).
i
DCTOT(i) DCII(i) DCJI(i, j)
j-1
6. Calculate the elastic soil force corrections from DCTOT x soil stiffness matrix, add these to
the initial forces and recalculate the displacements ([DISP]) using the overall elastic
system (the sum of the wall, strut and soil stiffness). The soil forces [F] acting at the
nodes can then be recalculated as
Parametric studies were carried out using straight line and log spiral shaped failure surfaces and
finite element work for soil that has constant properties with depth.
The results showed that the log spiral method, which is considered to be the best available
approximation, usually gave very similar results to the straight line method.
From theoretical considerations the approximation illustrated above was developed to represent the
increase in the active pressure limit, thus transferring the vertical pressure to a horizontal pressure
on the wall.
This shows the shape of the pressure limit diagram and the criteria for calculation.
It should be noted that if the width of the load (B) is small, the diagram will become triangular. This
pressure distribution is then used to modify the active pressure limit. Comparison of this distribution
with the parametric studies suggests that it is generally conservative.
If Ka varies with depth it is considered conservative to choose a mean value of Ka between any depth
z and the level of the surcharge and then impose the criteria that the active force due to the
surcharge, down to depth z be equal to the force derived from the above diagram. This is then
subjected to the further limitation that the pressure never exceeds qKaz at any depth, where Kaz is
the active pressure coefficient at depth z.
The program assumes that the passive pressure at depth z is equal to:
'
Pp Kp z 2c K p u
zudl
is the sum of vertical pressure of all udl surcharges specified above z.
For strip load surcharges the user must adjust Kp (by adding additional soil layers if necessary) to
allow for any increase in the passive pressure. This could be done using a series of trial failure
surfaces to determine the passive pressure at any location.
Alternatively the user should check through and calculate the following requirements detailed here to
derive the most suitable increase in the passive pressures.
Note : The problem becomes more difficult if Kp varies with depth. A simple expedient would be to
use equations specified in Requirement 4, with the appropriate value of Kp at each depth.
This can be unsafe, however, if a soil with high Kp overlies a soil with low Kp . Requirement 1, which
limits the total passive force effect to , could be violated for the less frictional soil.
8.5.2.1 Requirement 1
General passive wedge
Calculation
Consider a deep failure plane which will encompass the whole area of the strip load surcharge.
The following calculation assumes no wall friction. Assume that this is generally valid, even with wall
friction.
1 ' 1 2
W ' d 2 tan d Kp
2 4 2 2
Say the passive force due to the weight of the wedge (Pw) is
1
Pw 'd 2K p W Kp
2
Thus, if W is increased by the effect of the surcharge, qB, the passive force will increase by
qB K p
.
Therefore
Pp W qB Kp
8.5.2.2 Requirement 2
Check of the depth of influence of the load.
Calculation
'
d A cot
4 2
A
Kp
This depth will be smaller in the presence of wall friction. In this case it is probably reasonable to
use the same formula with a larger value of Kp.
'
d ( A B) cot( 45 0 )
2
( A B)
Kp
8.5.2.3 Requirement 3
For a uniform surcharge
A = 0 and B =
Pudl = qKp
It is unlikely that passive pressure increase for a strip load exceeds value for uniform surcharge, i.e.
qKp.
A
Pudl qK p A B Kp qB K p
Kp
8.5.2.4 Requirement 4
General Application
To be safe, the effect of passive pressures should be placed rather low. Therefore the stress block
shown below is considered to be generally suitable. The pressure can be expressed by the
following equations:
Calculation
( A + 2B)
<z ; pp = 0
Kp
The wall is modelled as a series of elastic beam elements, the stiffness matrix being derived using
conventional methods from slope deflection equations. Considering a single beam element of length
L and flexural rigidity EI spanning between nodes A and B, the moments (M) and forces (P) at nodes
A and B can be expressed as functions of the deflections and rotation at the nodes i.e.:
Where A , B and A , B, represent the deflections and rotations at nodes A and B respectively
referred to the neutral axis of the beam. The above equations can be re-written in matrix form as:
and
where [A], [B] and [C] are functions of the element lengths and flexural rigidity (EI), and [ ] and
[ ] are the nodal horizontal displacements and rotations.
Struts or anchors can be installed at any node at any stage during the analysis.
As shown above the struts are specified as having a prestress force Ps and a stiffness Ss in terms
of force/unit displacement.
A lever arm Ls and inclination s can also be specified to model the effect of a moment being
applied to the wall by a strut or anchor. This feature can be used to model the effect of an inclined
strut or anchor applying the force eccentrically to the wall section. If s is set 90Deg, it can also be
used to model a moment restraint and an applied moment.
Based on the geometry defined above the force P and moment M applied at the node by the strut is
given by
P = Ps cos s
+ Ss cos2 s
+ Ss Ls cos s
sin s
(G5)
M = Ps Ls sin s
+ Ss Ls cos s
sin s
+ Ss L2s sin2 s
(G6)
In these expressions d is the horizontal deflection of the node and q the rotation of the node since
the introduction of the strut.
These equations can be written in the form of matrices that represented all struts currently acting on
the wall as
The effect of the struts are incorporated into the analysis by matrix addition of the expressions given
above to those given in equations G1 and G2, see General. Elimination of [ ] gives the following
expression which is comparable to equation G3.
The new stiffness matrix for the wall [S] including the effect of the struts, and the effect of the
prestress [D] are given by
[S] = [C] + [Ssh] – [[A] + [Ssc ]]T [[B] + [Ssm]]-1 [[A] + [Ssc ]] (G13)
T -1
[D] = [Ps cos s
] + [[A] + [Ssc ]] [[B] + [Ssm]] [Ps Ls sin s
] (G14)
Of particular interest is the special case of a strut inclined at 90Deg to the wall for which equation
(G6) reduces to
M = Ps Ls + Ss L2s (G15)
Axi-symmetric problem
Many excavations are roughly square, and St John (1975) has shown that these can be modelled
approximately as circular. For an axi-symmetric analysis the results apply to mid-side of the
square.
Once props have been inserted into an excavation, it makes little difference to the behaviour of the
section being analysed whether the excavation is infinitely long or circular. This is because most of
the strains which cause displacements are concentrated close to the props, and vertical arching
within the soil governs the stress field. Furthermore, when the strength of the soil is fully mobilised
in active and passive wedges, deformations are again localised and the geometry in plan is not too
important.
However, situations can arise in which the plan geometry has a very significant effect on the
magnitude of the movements. This is the case in heavily overconsolidated clays, for which the
movements may be large before the strength is fully mobilised. As explained above, the effect is
particularly important in computing movements before the first props are inserted.
Consider a cylinder of soil, radius a, inside a circular excavation. Consider the simplified case in
which Young's Modulus, E, is constant with depth and the depth is large. To determine the
horizontal stiffness, compare this with a block of thickness, t, and the same Young's Modulus, E.
Let the Poisson's ratios of the cylinder and the block be c and b respectively. For the same
pressure p, the displacements d are:
pa
Cylinder : d 1 c
E
pt 2
Block : d (1 b )
E
(1 c )
t a 2
(1 b )
Note : In the "Safe" version of Frew, b = 0.3 and if the soil is undrained, take c = 0.5
Therefore for an undrained soil using the Safe model, the distance to the internal rigid boundary t;
The same simplifying assumptions can be made for the soil out side the excavation as for the soil
inside.
Poisson's ratios of the cylinder and the block are c and b respectively.
pa
Cylinder : d 1 c
E
pt 2
Block : d (1 b )
E
(1 c )
t a 2
(1 b )
Therefore for an undrained soil using the Safe model, the distance to the external rigid boundary t ;
The analysis for axi-symmetric problems assumes that Young's modulus remains constant to great
depth. In practice it usually increases with depth and the material becomes relatively rigid at a finite
depth.
It is not obvious how this will affect the formulae given above, but a comparison of Frew, with a finite
element run of Safe carried out for the British Library excavation, indicated that the formulae were
reasonable approximations, giving displacements roughly 20% too large. However, this may be very
dependent on the geometry of a particular problem; it is also dependent on the approximations used
in Frew to represent elastic blocks of soil of finite length (see, Approximations used in the Safe
Method).
The behaviour within the berm will be quasi-elastic until a failure plane develops. It will also be
elastically connected to the ground beneath, until a failure develops. In the elastic phase, there will
not be much difference in stress distributions between a berm and a uniform layer of the same
height. In both cases, horizontal forces at the wall are transferred downwards by shear. The elastic
behaviour, therefore can be modelled as if the berm were a complete layer of soil.
Berm Geometry
The figure shows three possible types of failure surface. These will develop at different stages,
depending on the types of soil in the berm and in the ground beneath. (A particularly critical case
occurs when a berm of frictional soil overlies frictionless ground.) It is possible, for example, that
wall pressure above failure surface A will cause failure on surface B whilst surface A is still intact.
The user should propose equivalent values of Kp, Kpc and c - call them K*p, Kpc and c* - from which
The values of K*p and c* should be chosen such that the forces transferred through the berm will not
be big enough to cause any failures, type A, B or even C.
The passive resistance of the ground beneath is also affected by the berm. At any depth a failure
surface type C needs to be examined and a total passive force calculated. This passive force
includes the horizontal forces transferred into the ground through the berm.
q* = - ' h
Note that Frew disregards the effect of strip surcharges on limiting passive pressures.
Therefore, this negative pressure does not change the limiting passive resistance of the
ground below. It will, however, cause some movement which corresponds to the elastic
effect of the excavation within the berm.
Also note that several surcharges could be used at various levels within the height of the berm.
This could give a somewhat better approximation.
4. For the soil beneath the berm calculate amended Kp and c value as follows:
choose various levels below the berm, eg, points i, j etc.
at i determine critical failure surface C by using method of wedges (or using Oasys
SLOPE) to give minimum passive force Fi . If straight-line wedges are used, the wall
friction should normally be set to zero in this process.
calculate passive pressure pi between base of berm (at level zb ) and point i (at level
zi ) as
pi = (Fi - Fb ) / (zb - zi )
where Fb is the passive force within the height of the berm
h
Fb ( K *p z 2c * K *p )dz
0
h+ zudl
+ ( / 2)(zb - zi ) - ui
where zudl
is the sum of all uniformly distributed surcharges above point i (usually
none present in this case).
pj = (Fj - Fi ) / (zi - zj )
K pj vj 2c j K pj pj uj
Berm strip load surcharge and calculation of passive pressure beneath berm
The above procedures may get the active pressures slightly wrong, but that is of little consequence
generally for berms. The procedures may cause the program to fail however with a message saying
the active pressure is greater than the passive pressure at a node under the berm. If this occurs the
active coefficient in the material under the berm should be reduced.
This method is considered to be conservative, but simpler to use than that presented above. It relies
on the fact that, in calculating passive (limiting) pressures, Frew only considers uniformly
distributed surcharges (UDLs) and ignores the beneficial effects of strip surcharges.
1. For contact stresses between the berm and the wall, proceed as for the Rigorous Method
above with Steps 1 and 2.
2. At the level of the base of the berm (the level of node b the figure above), apply a negative
UDL surcharge q* = - h
3. At the same level, apply a positive strip surcharge representing the berm itself. This will
have a pressure equal to h and width A*, as defined in the figure in Rigorous Method .
Below the berm, normal values of coefficients of active and passive pressure may now be used.
Possible slips of Type C and D should be briefly reviewed, though it is unlikely that these will ever
give a problem.
It is more likely that this method will be too conservative, especially in frictional materials ( > 0).
This is because the benefit of the weight of the berm has been disregarded in calculating passive
pressures below the level b. An allowance may be made for this by applying Steps 2 and 3 above at
a slightly lower level, above which the weight of the full depth of the berm will be experienced by the
ground. Better still, Steps 2 and 3 can be applied incrementally over a few depths, so that the
adverse effect of the restricted length of the berm is applied gradually with depth.
When using this procedure it must be remembered that the force Fb is the passive force experienced
within the height of the berm, which is transferred as an adverse horizontal shear force to the ground
beneath. Therefore the additional passive resistance (force) in the ground beneath the berm, due to
W Kp Fb
the presence of the berm, may be taken as , where W is the weight of the berm. This
formula will need refinement if Kp varies with depth.
Elastic moduli are defined as ratios of stress to strain. The stresses and strains used in this ratio
may be either cumulative values (starting from zero stress and zero strain), or incremental values.
The above shows these two possibilities for a point X on a non-linear stress-strain curve.
The modulus in terms of cumulative stress and strain is commonly referred to as a secant modulus,
whilst the modulus related to a small increment of stress and strain at point X is a tangent modulus.
Note : It is also possible to have an incremental secant modulus which approximates to the tangent
modulus for small increments.
In describing the change of stiffness from short-term to long-term as a change of stiffness modulus,
structural engineers are referring to secant moduli. But it is important to realise that Frew uses
tangent (incremental) moduli as its basic data. This means that merely changing stiffness
moduli, when nothing else is changed, will have no effect at all.
The following shows the type of stress-strain curve required for a change from short-term to long-term
stiffness.
The high short-term stiffness on OA is required to drop to the lower long-term stiffness on line OBC.
Consider an element of structure which in the short-term has been stressed to Point A. In the
course of time, its state will move to be somewhere on line BC. If it is in a situation in which there is
no change of strain during this change, stresses will simply relax and it will move to point B. If, on
the other hand, the load on the element can not change, it will creep and move to point C. Thus
relaxation and creep are different manifestations of the same phenomenon. It is easier to think about
the working of Frew in terms of relaxation than of creep.
In Frew, if an element is at point A and the only change made is to change the Young's modulus in
the data, further behaviour will proceed along line AD. This does not represent creep or relaxation.
Somehow the program must be informed that even if nothing moves, stresses will change from point
A to point B. If these new stresses are no longer in equilibrium, the program will then respond by
further strains and the stress state will move up line BC.
Creep effects on bending stiffness (EI) in Frew can be modelled directly by using wall relaxation.
Relaxation calculation
The relaxation percentage is defined as (AB/AE)*100. For example for a concrete, the short-term
and long-term stiffness' are taken as 30 and 20GPa respectively. The relaxation percentage would
be
Creep in supporting struts or slabs can also be modelled. Use two struts at the required level which
give the correct short-term stiffness when combined. Then remove one of them to obtain the long-
term effect.
Note : In Frew, when a strut is removed, the force associated with it is also removed.
The user must first calculate and specify the profile of undrained pore pressures, then change them
to the drained values.
Note: It is not sufficient merely to change to effective stress parameters and impose the final
(drained) distribution of pore pressure.
1. Tabulate the values of vertical and horizontal effective stresses given by Frew for Stage 0
or the previous drained stage, for both the left and right sides of the wall. Add the user
input values of pore pressure u to obtain the total stresses.
2. Tabulate the corresponding values for the final undrained stage in the analysis.
3. Calculate the change in total horizontal h
and vertical v
stresses between the two
stages.
4. Calculate the "actual" change in pore water pressure due to movement in the wall between
the two stages.
This demands an understanding of the undrained stress path. For soils which are at yield
in shear, Skempton's pore pressure parameter A would be useful if its value can be
assessed. If the soils have not reached yield, a modified value of A is required.
u=B h
+ A( v
- ) Skempton's equation.
h
In stiff clays, it may be assumed that the mean normal effective stress remains constant
during shearing. This assumption would not necessarily be appropriate to other soils and
should always be reviewed carefully. In the plane strain conditions of Frew, it amounts to:
u=( h
+ )/2
v
Three additional stages (A, B and C) are now required to complete the transition between
undrained and drained behaviour.
7. Stage A. The new pore pressure profile should now be introduced into the next stage,
without changing the (undrained) strength criteria of the soils and keeping Kr = 1. This
causes Frew to recalculate effective stresses, but total stresses are unchanged and no
movement occurs.
8. Stage B. The soil strength parameters should then be changed to drained values,
This provides a check as, if the above procedure has been carried out correctly, this step
should have no effect and could be omitted. However, movement will occur if the specified
pore pressures and effective strength parameters are not consistent with the computed
horizontal effective stresses. Since the horizontal stresses are consistent with the
undrained strengths, this would imply inconsistency between the specified pore pressures,
drained and undrained strengths.
In more complex analyses it is possible that assumptions made in the above process may
cause small amounts of movement to occur in Stage B. If this occurs the user should
review the modelling of the problem and the strength criteria to ensure that results are
reasonable.
9. Stage C. Finally, the pore pressure profile should be changed to its long-term (drained)
values with Kr < 1, as for drained behaviour. This will cause changes in horizontal total
stresses and movement will be needed to restore equilibrium.
The following provides an example of a manually applied transition between undrained and drained
materials.
Soil Properties
Stage Data
Calculation procedure
u=( v
+ h
)/2
Note: Users should be aware that as Ko is used to calculate Pe in stage 0, total horizontal stress in
this stage should be calculated by adding Ko*u to Pe. In any other undrained stage Ka / Kp are used
and are equal to 1, therefore total horizontal stress can be calculated by simply adding u to Pe.
Passive Pressures
Graphical Results
9 List of References
9.1 References
ARUP. Guidance on Integral Bridge Design and Construction. Commentary on PD 9994-1:(2011)
Ove Arup & Partners Ltd, 2012.
Broms B B (1972). Stability of flexible structures. General Report, 5th Euro Conf SMFE, Vol 2,
Madrid.
BSI. 2011. PD 6694-1:2011 Recommendations for the Design of Structures Subject to Traffic
Loading to BS EN 1997-1:2004, British Standards Institute, London, UK
Clayton, C.R.I., Xu, M. and Bloodworth, A. A laboratory study of the development of earth
pressure behind integral bridge abutments. Geotechnique, 2006, 56 (8), pp 561 – 571.
Denton, S.R., Simpson, B. and Bond, A. Conference paper on “Overview of Geotechnical Design
of Bridges and the provisions of the UK NA for EN1997-1”, presented at “Proceedings of Bridge
Design to Eurocodes – UK Implementation Conference. Edited by S. Denton. London: Institution
of Civil Engineers, 22 – 23rd November 2010.
Denton, S.R., Riches, O., Christie, T. and Kidd, A. Conference paper on “Developments in
Integral Bridge Design”, presented at “Bridge Design to Eurocodes: UK Implementation”. Edited
by S. Denton. London: Institution of Civil Engineers, 22 – 23rd November 2010.
England, G.L., Tsang, C.M., and Bush, D. Integral Bridges – a fundamental approach to the time
temperature loading problem. Thomas Telford Ltd. 2000.
Highways Agency/ Arup, 2009. Integral Bridges – Best Practice Review and New Research, Phase
2b - Review of Existing Data, Back-Analysis of Measured Performance and Recommendations
(Stages 1, 2 and 3)
Lehane, B.M. Predicting the restraint to Integral Bridge deck expansion. Geotechnical
Lehane, B.M., Keogh, D.L. and O’Brien, E.J. Simplified Model for Restraining Effects of Backfill
Soil on Integral Bridges. Dublin: Trinity College, 1999.
Pappin J W, Simpson B, Felton P J, and Raison C (1985). Numerical analysis of flexible retaining
walls. Proc NUMETA '85, University College, Swansea, pp 789-802.
Phillips A, Ho K K S, Pappin J W (1999) Long term toe stability of multi-propped basement walls in
stiff clays. Retaining Structures, pp 333-342
Poulos H G (1971). Behaviour of laterally loaded piles : I Single piles. Proc ASCE JSMFE, 97, 5,
711-731.
Rhodes, S. and Cakebread, T. Integral Bridges and the Modelling of Soil-Structure Interaction.
New York City: LUSAS, 2014.
Simpson B. (1994) Discussion, Session 4b, 10th ECSMFE, Florence, 1991, Vol 4, pp1365-1366.
St John H D (1975). Field and theoretical studies of the behaviour of ground around deep
excavations in London Clay. PhD Thesis, University of Cambridge.
Xu, M., Clayton, C.R.I and Bloodworth, A.G. The earth pressure behind full-height frame
integral abutments supporting granular fill. Canadian Geotechnical Journal, 2007, 44(3), pp 284
– 298.
changing soil or wall properties and applying or removing struts, anchors or surcharges. The
program models the soil as an elastic continuum and allows for soil failure by restricting the earth
pressures to lie within the active or passive limits and also includes the effect of arching.
Frew is a program to analyse the soil structure interaction problem of a flexible retaining wall, for
example a sheet pile or diaphragm wall.
The wall is represented as a line of nodal points and three stiffness matrices relating nodal forces to
displacements are developed. One represents the wall in bending and the others represent the soil
on each side of the wall. The soil behaviour is modelled using one of three methods:
1. "Safe" flexibility method - the soil is represented as an elastic solid with the soil
stiffness matrices being developed from pre-stored stiffness matrices calculated using the
"Safe" finite element program. This method is ideally limited to a soil with linearly
increasing stiffness with depth, but empirical modifications are used for other cases.
2. Mindlin method - the soil is represented as an elastic solid with the soil stiffness based
on the integrated form of the Mindlin Equations. This method can model a wall of limited
length in plan but is ideally limited to a soil with constant stiffness with depth but again
empirical modifications are used for other cases.
3. Subgrade reaction method - the soil is represented as a series of non interactive
springs. This method is considered to be unrealistic in most circumstances.
The program analyses the behaviour for each stage of the construction sequence. At each stage it
calculates the force imbalance at each node imposed by that stage and calculates displacement and
soil stresses using the stiffness matrices. If the soil stresses are outside the active or passive
limiting pressures correction forces are applied and the problem solved iteratively until the stresses
are acceptable. Allowance can be made for arching within the soil body when calculating the active
and passive limiting pressures.
The program gives results for earth pressures, shear forces and bending moments in the wall, strut
forces and displacements. These are presented in tabular form and can be plotted
diagrammatically. In addition the number of iterations, the displacement error between successive
interactions and the maximum earth pressure error are output.
Full details of the assumptions and analysis methods are included in the following paper.
11 Manual Example
11.1 General
The data input and results for the manual example are available to view in Frew data file (.fwd) format
or pdf format in the 'Samples' sub-folder of the program installation folder. The example has been
created to show the data input for all aspects of the program and does not seek to provide any
indication of engineering advice.
Screen captures from this example have also been used throughout this document.
This example can be used by new users to practise data entry and get used to the details of the
program.
Index Creep
D
165
A Damping coefficient 76
Data Checking 116
Active and Passive Limits 8 Data Entry 77
Active earth pressure Deflection
Axi-symmetric problems 158 Calculation 155
Limits 11, 12, 142, 144, 148 Graphical representation 125
Output 125
Direct Kp factors 50
Pressures 15, 37, 143
Displacement
Surcharges 48, 149 Maximum incremental 77
Surcharges: 149 Tolerance of 76
Tolerance 76
Drained materials 16, 18, 21, 28, 37, 47, 53, 168
Analysis
Methods of 1 E
Procedure 11
Anchors 47, 157
Earth pressure at rest 18, 37
Angle of friction 86
Effective stress 18
Assembling data 28
element edge loads 85
Axis
Example
Graphical output 125
Analysis procedure 11, 12, 13
Axi-symmetric Problems 158, 161 Manual 28
B Excavation
Effects of 16, 40, 48, 139
Modelling of 62, 158
Backfill Export 77
Effects of 16, 28
Modelling of 62 F
Batch plotting 128
Bending moments 11 Factors of safety 50
berm 161 File
berms 161 New FREW file 28
Bitmaps first stage material 88
In titles window 36
Fixed and Free solution 71, 138
Boundary 70 Fixed Earth Mechanisms 4
Distances 70
Fixed or Free solution 71
Horizontal rigid 40, 70
Free Earth Mechanisms 5
Vertical 70, 134
Frew Toolbar 3
boundary distances 70, 77
C G
'g' 88
Components of the User Interface 3
Gateway 3
Convergence Control 75
L Runs 82
S
Lever arm 85
linear elasttic 86 SAFE method 1, 12, 71, 129
Accuracy of 13
M Approximations 129
Fixed or free 71
Material Properties 37, 53 Save Metafile 125
Materials 86 Scale
Mesh 84 Engineering 125
Mindlin method Shear Force 1, 121, 125
Accuracy of 140 Soil strength factors 50
Application in FREW 139 Soil Zones 59
Basic model 13, 70, 139 Stage
Mohr-Coulumb 86 Changing titles 55, 56
Construction 1
N Data 52
Deleting 55
New Stages 52, 53, 54 Editing 54
Nodes 1, 11, 28, 40, 59, 63, 121, 129 Stage 0 11, 18, 28, 53
Stages 82
P Standard Toolbar 3
Strip Loads 47, 48, 151
Partial Factors 50 Active pressures 149
Passive pressures 151
Passive earth pressure 37, 151
Limits 11, 142, 144, 148 Struts 85
Output 37, 125 Levels 40
Properties 1, 45, 155, 157
T
Table View 3
Tabular Output 3
Tabulated Output 119
Titles 35, 56
Toolbar 3
U
Uniformally distributed loads 47, 48
Units 36
Unsupported features 91
User defined factors 50
User Interface 3
V
validation 77
void 86
W
Wall 1, 86
Data 11, 63
Deflection 125
Friction 13, 15, 138
Geometry 1, 28, 63
Relaxation 28, 63, 70
Stiffness 1, 40, 45, 47, 48, 52, 54, 55, 56, 57,
59, 63, 155
Stiffness: 53
wall data 77
Wall Friction 138
Y
Youngs modulus 71