Technical Paper by A. Fakher and C.J.F.P. Jones WHEN THE ...

Technical Paper by A. Fakher and C.J.F.P. Jones
WHEN THE BENDING STIFFNESS OF GEOSYNTHETIC
REINFORCEMENT IS IMPORTANT
ABSTRACT: A numerical simulation has been undertaken to model a layer of sand
overlaying a layer of geosynthetic reinforcement and super soft clay. Details of the
model and the modelling procedures are described and the influence of the bending
stiffness (flexural rigidity) of the reinforcement on the bearing capacity of super soft
clay is discussed. Factors affecting the reinforcement mechanisms of geosynthetic
reinforcement of super soft clay are considered.
KEYWORDS: In-plane bending stiffness, Geosynthetic reinforcement, Super soft
clay, Primary stage construction, Reinforced soil.
AUTHORS: A. Fakher, Lecturer, Department of Civil Engineering, Tehran
University, Iran, Telephone: 98/21-649-8981, Telefax: 98/21-646-1024, E-mail:
afakher@ut.ac.ir; and C.J.F.P. Jones, University of Newcastle upon Tyne, Department
of Civil Engineering, Drummond Building, Newcastle upon Tyne, NE1 7RU, United
Kingdom, Telephone: 44/191-222-7117, Telefax: 44/191-222-6613, E-mail:
c.j.f.p.jones@ncl.ac.uk.
PUBLICATION: Geosynthetics International is published by the Industrial Fabrics
Association International, 1801 County Road B West, Roseville, Minnesota 55113-
4061, USA, Telephone: 1/612-222-2508, Telefax: 1/612-631-9334. Geosynthetics
International is registered under ISSN 1072-6349.
DATE: Original manuscript submitted 1 September 2001, revised version received 1
November 2001, and accepted 5 November 2001. Discussion open until 1 June 2002.
REFERENCE: Fakher, A. and Jones, C.J.F.P., 2001, “When the Bending Stiffness of
Geosynthetic Reinforcement is Important”, Geosynthetics International, Vol. 8, No. 5,
pp. 445-460.
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
1 INTRODUCTION
A clay with a very high water content behaves neither like a liquid nor like a solid, it
has very little shear strength and can be termed a super soft clay. In the current paper,
super soft clay is defined as a disturbed cohesive soil whose water content is higher
than its liquid limit; such materials display extremely low yield stresses and represent
difficult construction conditions (Fakher et al. 1999).
An established technique used to enable construction on super soft clays is the
introduction of a primary construction stage that is used as a working platform on
which the main construction can be founded. A working platform can be produced by
placing a layer of geosynthetic reinforcement over the super soft clay and covering this
with a layer of cohesionless fill (Figure 1) (Yamanouchi and Gotoh 1979). Although it
has been demonstrated that this construction technique is successful, there is no general
agreement with respect to the reinforcement mechanism and how the reinforcement
improves the bearing capacity of working platforms. The current paper is aimed
at providing insight into the reinforcement mechanism associated with a thin layer of
cohesionless fill supported on geosynthetic reinforcement layered on the surface of
super soft clays. The numerical modelling presented has been undertaken in parallel
with a number of physical model studies into construction over super soft clay (Fakher
and Jones 1996a; Fakher and Jones 1996b; Fakher et al. 1996; Zakaria 1994). A major
advantage of numerical modelling is that it enables parametric studies to be undertaken
that enhance the results and findings of physical models.
2 DETAILS OF THE ANALYSIS
2.1 Idealisation and Boundary Conditions
A representative super soft clay, overlain by a layer of sand with/without a layer of
0.5 B
Sand
D
Super soft clay
Geogrid
reinforcement
10 B
7 B
10 B
Figure 1.
The geometry of the problem.
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
reinforcement, was simulated in the current study. A surface load was applied by a
rigid, rough footing of width, B, placed on the surface of the sand layer (Figure 1).
The super soft clay and cohesionless fill were idealised as construction materials
and the reinforcement considered to be either formed as a cable or a row of simple
beam elements. The analyses were performed using the finite difference program
FLAC (Itasca 1991). Details of the analysis grid and the boundary conditions used are
shown in Figure 2. Because of the symmetrical geometry, each analysis was performed
on half of the model.
2.2 Behaviour and Mechanical Parameters of Soils
Leighton Buzzard sand was used as the cohesionless soil in the parallel experimental
studies on construction over super soft clays, and the properties of this material were
assumed in the analytical study (Fakher and Jones 1996b). A friction angle, φ = 35°,
was determined from laboratory tests, and a value for Poisson’s ratio, ν = 0.37, was
chosen based upon the suggestion by Stroud (1971). A unit weight of 16 kN/m 3 was
assumed for the sand. The elastic modulus, E, of sand depends upon the confining
pressure and is not constant within a mass of sand. However, to simplify the analysis
the elastic modulus, E, of the cohesionless fill was assumed to be 32 MPa based upon
general values suggested for quartz sands (Lambe and Whitman 1979). The values for
the shear modulus, G, and the bulk modulus, K, of the cohesionless fill were derived
using the following relationships:
Figure 2.
The grid pattern used in the current study.
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
G
E
= ------------------- ( = 1.2 × 10
21 ( + ν)
7 Pa)
(1)
E
K = ---------------------- ( = 4.1 × 10 (2)
31 ( – 2ν)
7 Pa)
The elastic properties of super soft clays are difficult to measure; however, experimental
studies have shown that the elastic modulus of the super soft clay is not significant
in the problem (Fakher 1997). Based upon experimental findings the shear
modulus and bulk modulus of the super soft clay were assumed equal to 42 and 20
MPa, respectively. The shear strength of the super soft clay was assumed to be 50 Pa
for the majority of the analysis, but was increased up to a value of 1,000 Pa to illustrate
the influence of stronger and stiffer soil. An elastic-perfectly plastic behaviour was
assumed for the soils in order to simplify the analyses.
2.3 Geosynthetic Reinforcement
The reinforcements were modelled in two ways in order to investigate the effects of
reinforcement bending stiffness on the bearing capacity of the super soft clay:
1. As cable elements, with no bending stiffness. This method is frequently used to
model geosynthetic reinforcements when bending is considered unimportant. The
cable elements used in the analyses were one-dimensional axial elements described
in terms of cross-sectional area, elastic modulus, and yield strength of the cable.
2. As beam elements with elastic bending stiffness. The beam elements used in the
analyses were two-dimensional elements with three degrees of freedom at each
node providing displacement in two perpendicular directions and rotation. The
beam elements were described in terms of cross-sectional area, elastic modulus,
second moment of area (moment of inertia), and plastic moment. The moment
capacity was assumed to be infinite.
The reinforcements were fixed to the line of symmetry (Figure 1). However, they
were not fixed to any other vertical boundary so as not to cause an unrealistic pull-out
resistance. The length of the geosynthetic reinforcement was 2 × 7B, where B is the
width of the footing. In view of the low value of the shear strength of super soft clay, it
was assumed that perfect adherence existed between the clay and the reinforcement.
The elastic modulus and cross-sectional area of the reinforcement were assumed to
be equal to 1 × 10 5 Pa and 0.0033 m 2 , respectively. The second moment of area, I, of
the beam elements was assumed to be equal to 7.64 × 10 -7 m 4 . However, this value was
varied from 1 × 10 - 8 to 2.15 × 10 - 6 m 4 in order to study the effect of bending stiffness,
EI. The bond stiffness and the bond strength of the element-soil interface and the yield
strength of the cable elements were assumed to be 3 × 10 7 N/m/m, 4.5 × 10 4 N/m, and
6.8 × 10 3 N, respectively for all the analyses. Details of the material properties used in
the different analyses are shown in Table 1.
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
Table 1.
Variables used in the analyses.
Analysis
no.
Second moment of
area beam elements
I (m 4 )
Ratio of sand
thickness, D, and
footing width, B
D/B
Shear strength of
super soft clay
C (Pa)
Footing
width
B (mm)
Displacement
increment
(mm)
Grid
aperture
(mm)
f-20 7.64E-07 0.51 50 50.4 30 × 33
f-21 7.64E-07 0.51 500 50.4 1 30 × 33
f-22 7.64E-07 0.51 100 50.4 1 30 × 33
f-23 7.64E-07 0.51 250 50.4 1 30 × 33
f-24 7.64E-07 0.51 1000 50.4 1 30 × 33
f-26 2.00E-07 0.51 50 50.4 1 30 × 33
f-27 8.50E-08 0.51 50 50.4 1 30 × 33
f-28 1.00E-08 0.51 50 50.4 1 30 × 33
f-29 2.15E-06 0.51 50 50.4 1 30 × 33
f-30 7.64E-07 0.51 50 108 2 30 × 33
f-31 7.64E-07 0.51 50 252 5 30 × 33
f-32 7.64E-07 0.51 50 504 10 30 × 33
f-33 7.64E-07 0.51 50 1008 20 30 × 33
f-40 7.64E-07 0.17 50 50.4 1 30 × 31
f-42 7.64E-07 0.51 50 50.4 1 30 × 33
f-44 7.64E-07 1.54 50 50.4 1 30 × 39
f-45 7.64E-07 2.06 50 50.4 1 30 × 42
2.4 Applied Loading
At the start of the analysis, the model was switched to gravity to produce the initial
stress state. Following this, a surface load was simulated by exerting successive displacement
increments. The program was run for each displacement increment and an
out-put file for each increment was stored; following this, the next displacement increment
was exerted using the data in the stored file as the starting criteria.
The displacement increment used in the analyses was found to be critical. An increment
of 0.02B was found to be satisfactory for the analyses. A discussion on the effects
of different displacement increments and different methods of applying load using
FLAC is given by Fakher (1997).
3 RESULTS AND DISCUSSION
A plot of the vertical loading on the footing versus vertical displacement for each analysis
is shown in Figure 3. The results show no peak bearing capacity and the selection
of the point of ultimate bearing capacity is a subjective matter, which depends on engi-
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
Vertical stress under footing (N/mm)
2.4
2.0
1.6
1.2
0.8
0.4
0.0
f-29, I = 2.15e-6 f-20, I = 7.64 e-7
f-26, I = 2e-7 f-27, I = 8.5e-8
f-28, I = 1e-8 f-20, no reinf.
f-20, cable
0 5 10 15 20 25
Vertical displacement (mm)
Figure 3. The influence of the reinforcement bending stiffness on the displacement of the
footing under different loads (values of I are in m 4 ).
neering judgement. A constant value for the modulus of elasticity, E, was chosen for
the reinforcement and the bending stiffness, EI, varied by varying the second moment
of area, I. The results show that the higher the bending stiffness the higher the potential
bearing capacity (Figure 3). This confirmed the conclusion derived from previous unitcell
shear box studies and scale-model loading tests (Fakher et al. 1996; Fakher and
Jones 1996b; Zakaria 1994).
3.1 Effect of Bending Stiffness of the Reinforcement
The effect of the reinforcement bending stiffness on the bearing load is shown in Figure
4 (when the vertical displacement/load width ratio, s/B = 0.3). It can be seen that
the presence of any type of reinforcement, with or without bending stiffness, has an
influence.
The deformed shape of a geosynthetic reinforcing material modelled as a cable or a
beam element with different stiffnesses, EI, is shown in Figure 5. An explanation for
the deformed shape of the reinforcement is that, as the footing moves vertically, the
adjacent super soft clay moves laterally. This results in ground surface heave adjacent
to the footing. The displacement of the super soft clay and the heave is influenced by
the in plane stiffness of the reinforcement. When the bending stiffness of the reinforcement
is high the heave is reduced and distributed over a wider area.
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Vertical stress under footing (N/mm)
0.8
s /B = 0.3
0.7
0.6
0.5
Beam element
No reinforcement
0.4
Cable element
0.3
0 0.04 0.08 0.12 0.16 0.2 0.24
Bending stiffness, EI (Nm)
Figure 4. The effect of bending stiffness of geogrid reinforcement on the bearing load
(the bending stiffness is reported for one meter run and has units of Nm).
Deformed geosynthetic reinforcement
Y d /B
0.18
0.12
0.06
0.00
-0.06
-0.12
-0.18
-0.24
-0.30
f-20, cable
f-28, beam, I = 1e-8
f-27, beam, I = 8.5e-8
f-26, beam, I = 2e-7
f-20,beam, I = 7.64e-7
7.0 5.4 4.2 3.4 2.7 2.2 1.7 1.2 0.7 0.2
f-29, beam, I = 2.15e-6
X/B
Line of
symmetry
Figure 5. The effect of bending stiffness on the deformed shape of geogrid reinforcement
at s/B = 0.3.
3.2 Effect of Thickness of the Sand Layer
The ratio between the thickness of the sand layer, D, and the width of the footing, B,
was varied from 0.17 to 2.06, and it can be seen that this has an influence on the bear-
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
ing capacity ratio (Figure 6). The bearing capacity ratio is defined as the ratio between
the bearing capacity of reinforced ground and the bearing capacity of the same case
without reinforcement. When D/B is small, the increase in the bearing capacity ratio,
due to bending stiffness, is significant. As the D/B ratio increases, the influence of the
bending stiffness of the reinforcement diminishes.
The deformed shape of geosynthetic reinforcements for different ratios of D/B is
shown in Figure 7. The maximum heave of the reinforcement modelled as a cable is
located close to the footing when values of D/B are small. When the value of D/B
increases, the reinforcement bending stiffness has little effect on the deformed shape
and the deformation of the reinforcement, modelled as a beam or a cable, are similar.
3.3 Effect of Size of Footing
The width of the footing, B, was varied to investigate the relative influence of the reinforcement
on the behaviour of footings of different dimensions. When, B, increases,
the effect of the reinforcement bending stiffness decreases sharply (Figure 8). This
conforms with the findings of a dimensional analysis study on model loading tests
(Fakher et al. 1996).
The effect of footing width, B, on the deformed shape of the reinforcement is
shown in Figure 9. The location of the point of maximum heave depends on the size of
the footing when cable elements are used in the analysis. This is not apparent when
beam elements are used to model the reinforcement.
3.4 Effect of the Yield Stress of Clay
A series of analyses were performed to investigate the influence of the shear strength of
the underlying clay, C, on the bearing capacity. As expected, the bearing capacity
increases when C increases. An interesting observation is that the positive effect of bend-
3.5
Bearing capacity ratio
3.0
2.5
2.0
1.5
1.0
No reinforcement
Beam element
Cable element
I = 7.64 e-7
s /B = 0.3
Figure 6.
0.5
0.0 0.5 1.0 1.5 2.0 2.5
D/B
The effect of D/B on the bearing capacity ratio.
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
Yd / B
0.18
0.12
0.06
0.00
-0.06
-0.12
-0.18
-0.24
f-44, D/B = 1.54,
beam, s/B = 0.3
f-44, D/B = 1.54,
cable, s/B = 0.3
f-42, D/B = 0.51,
beam, s/B = 0.3
f-42, D/B = 0.51,
cable, s/B = 0.3
f-40, D/B = 0.17,
beam, s/B = 0.3
f-40, D/B = 0.17,
cable, s/B = 0.3
Figure 7.
-0.30
0 1 2 3 4 5 6 7 8
X / B
The effect of D/B on the deformed shape of the geosynthetic reinforcement.
1.6
Beam elements
Bearing capacity ratio
1.4
1.2
1.0
Cable elements
No reinforcement
I = 7.64e-7
D = 25 mm
s /B = 0.3
Figure 8.
0.8
0 200 400 600 800 1000 1200
B (mm)
The bearing capacity ratio at different footing sizes.
ing stiffness of the reinforcement decreases when C increases (Figure 10). Thus, the reinforcement
bending stiffness has little importance when the clay is not in a super soft state,
and the reinforcement bending stiffness may be neglected in routine design practice.
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0.18
0.12
0.06
0.00
Yd / B
-0.06
-0.12
-0.18
-0.24
f-20, B = 50.4 mm, beam, s/B = 0.3
f-20, B = 50.4 mm, cable, s/B = 0.3
f-31, B = 252 mm, beam, s/B = 0.3
f-31, B = 252 mm, cable, s/B = 0.3
-0.30
0 1 2 3 4 5 6 7
X/B
Figure 9. The effect of footing size on the deformed shape of the geosynthetic
reinforcement.
1.5
1.4
Ratio = Bearing capacity from analysis with beam elements
Bearing capacity from analysis with cable elements
1.3
Ratio
1.2
1.1
Figure 10.
1.0
0 200 400 600 800 1000
Shear strength of clay, C (Pa)
The influence of shear strength of the underlying clay on the bearing capacity.
3.5 Deformation and Displacement of the Continuum Materials
The deformed shape of the finite difference grid, representing the super soft clay, the
reinforcement, and the overlying sand, and the directions of the principal stresses are
shown in Figure 11. The data are derived from test f-20 at s/B = 0.3 (Table 1).
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
(a)
B / 2
4B
3.5B
(b)
B / 2
(c)
B / 2
Figure 11. The deformed shape of the grid and the principal stress directions at s/B = 0.3
(analysis f-20, Table 1): (a) no reinforcement; (b) reinforcement modelled as cable
elements; (c) reinforcement modelled as beam elements.
The influence of the reinforcement and the reinforcement stiffness on the behaviour
of the system can be seen in Figures 11b and 11c. It is apparent that, with stiff
reinforcement, a shallow zone of the super soft clay is loaded.
The deformed shape of the reinforcement with increased settlement is shown in
Figure 12. In the case of reinforcement modelled as beam elements, heave occurs
remote from the footing and increases and spreads further as s/B increases. When s/B
increases from 0.1 to 0.3, the distance between the centre line and the point with the
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Yd / B
0.18
0.12
0.06
0.00
-0.06
-0.12
-0.18
-0.24
-0.30
f-20, beam, s/B = 0.3
f-20, cable, s/B = 0.3
f-20, beam, s/B = 0.1
f-20, cable, s/B = 0.1
0 1 2 3 4 5 6
X / B
Figure 12.
settlement.
The deformed shape of the geosynthetic reinforcement with increasing
maximum heave increases from 1.8 B to 2.5 B for the case studied. If the bending stiffness
of the geosynthetic reinforcement is neglected, heave occurs close to the footing
and the horizontal location of the point of maximum heave is not influenced by an
increase in s/B.
3.6 Ground Surface Heave
Figure 13 shows the deformed shape of the ground surface. When beam elements are
used to model the geosynthetic reinforcement, a smaller heave occurs, and the location
of maximum heave occurs at a distance further from the footing than the case when
cable elements are used.
Contours of normalised vertical displacement, Y d /B, plotted over an area of
4B × 3.5B are shown in Figure 14. An interesting observation is that the maximum
heave (positive values of Y d ) does not occur at the ground surface when beam elements
are used (Figure 14c). The implication is that the reinforcement bending stiffness plays
a significant role in preventing heave of the super soft clay from being transferred to
the sand layer and ground surface.
3.7 Overall Discussion
When a footing overlying a layer of super soft clay settles, the clay beneath the footing
moves laterally to escape toward the ground surface resulting in heave. Control of the
resultant heave is a key factor to the successful construction over super soft clay and in
the bearing capacity mechanism. The reinforcement bending stiffness plays a significant
role in preventing the heave of the super soft clay being transferred to the sand
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0.15
0.10
0.05
Figure 13.
Yd / B
0.00
-0.05
-0.10
f-20, no-reinf., s/B = 0.3
-0.15
f-20, beam, s/B = 0.3
-0.20
-0.25
f-20, cable, s/B = 0.2
-0.30
0 2 4 6 8 10
X / B
The deformed shape of the ground surface.
layer. When the bending stiffness of the reinforcement is high, the heave is reduced
and distributed over a wider area. It can be concluded that the use of geosynthetic reinforcement
having a stiff three-dimensional structure, such as a geocell, is beneficial.
The structural behaviour of the geosynthetic in this situation can be likened to a
plate that has bending stiffness (flexural rigidity) and tensile stiffness. The plate-type
behaviour of reinforcement, with bending stiffness, overlaying super soft clay provides
more than a large displacement mechanism, such as a membrane-type support
system (Burd 1995). The plate-type behaviour starts with a small vertical deflection of
the reinforcement and distributes the heave of the ground surface over a wider area as
the vertical deflection of the footing increases. It is seen that as the size of the footing
increases, the influence of the bending stiffness of the reinforcement decreases
sharply; this confirms the plate-type behaviour of the mechanism.
When a fill is being spread on the geosynthetic overlying the super soft clay, the
surface layer of the clay tends to move laterally, pushed out by the spreading layers of
soil. Consequently, a tensile force is developed in the geosynthetic reinforcement due
to lateral movement of the soil. This tensile force needs to be sustained by the anchorage
of the reinforcement; this is provided by the pull out resistance of the reinforcement
at the interface of the sand and clay. As the reinforcement tensile stiffness
increases, the required pull out displacement to mobilise the maximum pull out resistance
decreases. Hence, a geosynthetic reinforcement with a high tensile stiffness (as
opposed to high bending stiffness) provides a better anchorage in the soils resulting in
an increase in the bearing capacity.
4 CONCLUSIONS
The bending stiffness of geosynthetic reinforcement is neglected in most design prac-
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
(a)
-0.3
-0.2
B / 2
-0.05
+0.1
+0.05
Y d / B = 0
(b)
-0.3
-0.1
-0.05
+0.1
+0.05
Reinforcement
Y d / B = 0
(c)
-0.3
+0.1
Reinforcement
-0.1
-0.05
+0.05
Y d / B = 0
Figure 14. Contours of normalised vertical displacement, Y d /B : (a) no reinforcement;
(b) cable elements used to model the reinforcement; (c) beam elements used to model the
reinforcement.
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
tice, but it should be considered in the design of earthworks over super soft clay. The
current study suggests that the structural behaviour of the reinforcement over super
soft clay is like a plate supported by the vertical reaction force from the clay. If the
plate is anchored horizontally, it will present a high resistance to the vertical load. The
effect of the reinforcement pull-out resistance is to provide a horizontal restraint for
the plate. The following conclusions associated with the influence of the reinforcement
bending stiffness resulted from the current study:
1. The structural behaviour of the geosynthetic reinforcement with bending stiffness
used as a primary construction stage over super soft clays is like a stiff plate.
2. The higher the reinforcement bending stiffness, the higher the bearing capacity of
the system.
3. The use of reinforcement with high bending stiffness reduces the heave of the surface
which is distributed over a wider area.
4. With very stiff (in bending) reinforcement, the maximum heave does not occur at
the ground surface.
The relative importance of the reinforcement bending stiffness depends on the following
factors:
• When the D/B ratio is small, the increase of the bearing capacity ratio due to bending
stiffness is significant.
• When the footing width B increases, the effect of bending stiffness decreases
sharply.
• The reinforcement bending stiffness is not important when the underlying clay is
not in a super soft state.
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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important
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Apparatus”, Ph.D. Thesis, University of Cambridge, United Kingdom, 163 p.
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Capacity for Earthwork Method on Soft Clay Ground Using a Resinous Mesh”,
Technology Reports of Kyushu University, Vol. 52, No. 3, pp. 201-207. (in Japanese)
Zakaria, N.A., 1994, “Construction on Supersoft Soils Using Geogrids”, Ph.D. Thesis,
University of Newcastle Upon Tyne, United Kingdom, 230 p.
NOTATIONS
Basic SI units are given in parentheses.
B = width of footing (m)
C = shear strength of clay (Pa)
D = thickness of sand layer overlying reinforcement (m)
E = elastic modulus (Pa)
G = shear modulus (Pa)
I = second moment of area of reinforcement (m 4 )
K = bulk modulus (Pa)
s = settlement of footing (m)
X = distance from centre line of footing (m)
Y d = vertical displacement of the soil continuum (m)
ν = Poisson’s ratio (dimensionless)
φ = friction angle of sand (°)
460 GEOSYNTHETICS INTERNATIONAL • 2001, VOL. 8, NO. 5