chapter 4 experimental results and...
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79
CHAPTER 4
EXPERIMENTAL RESULTS AND DISCUSSION
4.1 INTRODUCTION
Results of laboratory model tests conducted on pipes embedded in
narrow trench backfilled with dry sand of loose (15 kN/m3), medium dense
(16.4 kN/m3) and dense conditions (17 kN/m3) are presented and discussed in
this chapter. The main focus in this chapter is a comparison of the behaviour
of pipe embedded at different depths. The parameters varied are cover depth,
unit weight of sand and position of geogrid reinforcement. Tests were
conducted for the cover depth ratios of 1, 2 and 3 and bed relative densities of
13.2% and 77.8% conditions. A limited test was conducted in the case of
medium dense condition (RD = 52%). In this chapter the results are discussed
in the following sequence.
1. Load-displacement response of the plate.
2. Deformation response of the pipe under surface loads.
3. Strain at the crown and springline of the pipe
4. Stress variation on the PVC pipe due to surface loads.
In the results reported, the recorded deflections and strains of pipe due to
weight of the backfill are negligibly small hence not included. Such a
behaviour is attributed to shallow burial depth (i.e. shallow cover).
80
4.2 LOAD-DISPLACEMENT RESPONSE OF THE PLATE
The behaviour of plate, which simulates the surface load on the
backfill of buried pipe embedded in sand backfill of different densities and
three cover depth ratios (H/D where H is the depth of cover of backfill above
the pipe crown and D is the diameter of pipe) with and without geogrid
reinforcement under axial compression load is reported. The performance of
pipe under surface loads in terms of diametric strain and hoop stresses is also
presented.
4.2.1 Load-displacement response of the plate with and without pipe
As a reference test the surface load is applied through a rigid plate
placed on the sand backfill directly without the pipe to know the variation in
the cover thickness (i.e. settlement response of backfill material between the
surface and pipe) if the pipe is buried in the backfill and tested under identical
conditions.
-16
-14
-12
-10
-8
-6
-4
-2
00 50 100 150 200
Surface Pressure (kN/m2)
Settl
emen
t in
mm
with pipe
without pipe
Figure 4.1 Settlement of the plate with and without pipe in loose sand
H/D = 2 ø = 32º
81
Figure 4.1 shows the settlement response of the plate tested in the
loose sand backfill without pipe and with a pipe of 200 mm embedded at a
cover depth of 600 mm. The settlement observed is more in the absence of the
pipe for the range of loads applied except for the initial load of 40 kN/m2 or
less in loose sand backfill. The difference in settlement between the two cases
increases with increase in load and the maximum difference is 3 mm for the
load intensity of 150 kN/m2 which indicates that the settlement of the plate on
the soil bed with the pipe is 75% of the settlement of the plate without the
pipe.
4.2.2 Load-displacement response of the plate without geogrid
reinforcement
The response of buried pipe is studied under surface loads. The
surface load is applied through a rigid plate placed on the sand backfill. The
effect of density of the backfill and the influence of cover depth ratio on the
settlement of the plate are reported.
4.2.2.1 Effect of density
Figure 4.2 shows the settlement response of the plate under loading
in two different densities of the sand backfill with pipe embedded at a cover
depth of 200 mm (H/D = 1). The settlement of the plate is increased with
increase in load in both loose and dense sand backfill and the rate of
settlement with load is higher in loose sand as expected. For the range of load
applied, the difference in settlement between the two density conditions is
increased with the load and the maximum difference is 5 mm for the test load
of 150 kN/m2. This is primarily due to the difference in the elastic moduli of
backfill materials at different densities. The observation reported above is
obvious and as expected. The narrow trench condition has not altered the
load-settlement response of the plate from the well established response.
82
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
00 50 100 150 200
Applied Surface pressure(kN/m 2)
Sett
lem
ent
in m
m
loosesandDensesand
Figure 4.2 Settlement of the plate in different densities of sand backfill
The ratio of the remaining cover to the original cover has been
plotted against the pressure applied on the surface of the backfill for the cover
depth ratios of 1 and 3 (Fig 4.3). Remaining cover is equal to the initial cover
less the plate settlement, plus the settlement of the pipe crown. The change in
cover height is more for the shallow backfill cover ratio (H/D) equal to 1 than
the backfill cover ratio of 3 irrespective of the intensity of applied load except
for the initial load intensities (i.e. < 30 kN/m2). For the backfill cover of 1, the
reduction in cover height with load is almost constant for the range of load
applied, whereas for the H/D = 3, this variation is reduced with the load and
tend to become asymptotic to load axis. Backfill cover height was reduced as
the loading progressed, the extent of settlement being dependent on the level
of loading, height of initial backfill and the degree of backfill compaction.
H/D = 1
83
-1
-0.998
-0.996
-0.994
-0.992
-0.99
-0.988
-0.986
-0.984
-0.982
-0.980 50 100 150 200
Applied Surface pressure(kN/m 2)
Cov
er h
eigh
t / In
itial
cov
er h
eigh
t
H/D = 1
H/D = 3
Figure 4.3 Relative settlement of rigid plate during loading in dense sand
4.2.2.2 Effect of different levels of embedment of the pipe
Figures 4.4 and 4.5 show the settlement of the plate under loading
for three different levels of embedment of the pipe both in loose and dense
sand backfills. It is observed that the settlement is more pronounced at deeper
burial than in case of shallow depth and found to increase with the increase in
the surface pressure. The settlement of the plate is found to be less in the
stiffer (dense sand) backfill than in a soft (loose) backfill owing to high soil
modulus. The profile of the load-settlement curve is found to change from
convexity to concavity with the increase in the depth of embedment owing to
the effect of arching and rigid side boundaries of the tank.
ø = 42º
84
-14
-12
-10
-8
-6
-4
-2
00 50 100 150 200
Applied Surface pressure(kN/m2)
Sett
lem
ent
in m
m
H/D=1
H/D=2
H/D=3
Figure 4.4 Settlement of the plate with loading for three different levels of embedment of the pipe in loose sand backfill
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
00 50 100 150 200
Applied Surface pressure(kN/m2)
Sett
lem
ent
in m
m
H/D=1
H/D=2
H/D=3
Figure 4.5 Settlement of the plate with loading for three different levels of embedment of the pipe in dense sand backfill
ø = 42º
ø = 32º
85
The settlement of the plate is also analysed in terms of non-
dimensional parameter known as settlement ratio. Settlement ratio is defined
as the ratio of the settlement of the plate with pipe to the settlement of the
plate without pipe. Figures 4.6 and 4.7 show the variation of settlement ratio
against the dimensionless surface pressure (p/γD) for three different levels of
embedment of the pipe in loose and dense sand backfills respectively. The
settlement ratio is less than unity for all the three depths of embedment in
loose sand and is found to be higher for deeper embedment irrespective of the
magnitude of dimensionless surface pressure (p/γD). For the cover depth
ratio, H/D = 1, the settlement ratio increases with dimensionless pressure and
tends to remain almost constant for the p/γD>30, whereas for the H/D=2 the
settlement ratio remains almost constant for the entire range of dimensionless
pressure. For the H/D = 3 in loose backfill, the settlement ratio decreases with
dimensionless pressure which shows an opposite trend while comparing with
the settlement response of the plate with H/D = 1. However the settlement
ratio tends to remain constant for the p/γD>30 as observed in H/D = 1. From
the results presented above, it can be inferred that the settlement of loose
backfill material under surface pressure is reduced effectively in presence of
the pipe. The response in dense sand is unlike loose sand. In dense sand
settlement ratio is increased with increase in dimensionless pressure
irrespective of the depth of embedment (i.e. H/D ratio) but decreasing rate
and tends to remain constant for p/γD>35 particularly for the H/D = 2 and 3.
The settlement ratio is higher for deeper embedment as observed in loose
sand. The settlement ratio is found to be higher in the case of the stiffer
backfill(dense sand) than the soft backfill(loose sand). This is due to the
combined effect of arching and the low elastic modulus of the soft backfill.
Further in the case of loose sand backfill the idealized narrow trench
condition, the stiffness of the pipe and the rigid wall boundaries tend to have
some influence on the load- settlement curve at the early stages of loading
but similar response is not seen in the case of stiffer backfill.
86
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10 20 30 40 50 60
Dimensionless surface pressure
Sett
lem
ent r
atio
H/D = 1
H/D = 2H/D = 3
Figure 4.6 Settlement ratio vs. Dimensionless surface pressure in loose
sand
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
0 10 20 30 40 50 60
Dimensionless surface pressure
Sett
lem
ent r
atio
H/D = 1
H/D = 2H/D = 3
Figure 4.7 Settlement ratio vs. Dimensionless surface pressure in dense
sand
ø = 42º
ø = 32º
87
4.2.3 Comparison of Load-displacement response of the plate with
and without geogrid reinforcement in two different densities of
sand
Figure 4.8 shows the settlement response of the plate with and
without geogrid reinforcement at a cover depth of 600 mm in loose sand
backfill. The provision of geogrid reinforcement directly on the crown of the
pipe does not show reduction in the plate settlement. However the provision
of single layer of geogrid reinforcement above the crown of the pipe reduced
the settlement of the plate and the settlement reduction is more for the geogrid
reinforcement placed at 1D distance (200 mm) above the crown than at a
distance of 0.5D (100 mm). The reduction in settlement for the load of 150
kN/m2 is 10% for the geogrid reinforcement placed at the distance of 0.5D
above the crown (Type I reinforcement). The presence of single layer of
geogrid reinforcement at 1D distance above the crown of the pipe (Type II
reinforcement) showed a reduction of 26% in the settlement of the plate.
-14
-12
-10
-8
-6
-4
-2
00 50 100 150 200
Surface Pressure (kN/m2)
Settl
emen
t in
mm
without geogridWith Type II reinforecement
with Type I reinforcementwith geogrid at the crown
Figure 4.8 Settlement of the plate in loose sand
H/D = 3, ø = 32º
88
The settlement of the plate without the pipe and with the pipe at a
depth of 600 mm (H/D = 3) from the surface of the dense sand backfill is
shown in Figure 4.9. The settlement of the plate is found to be lesser in the
presence of the pipe owing to the stiffness offered by the pipe to the
surrounding backfill. The settlement of the plate slightly increases when the
geogrid is directly placed on the crown of the pipe. But the provision of
geogrid reinforcement at 0.5D and 1D above the crown of the pipe reduced
the settlement of the plate as observed in loose sand backfill and the reduction
is 13% and 20% respectively. The effect of geogrid reinforcement on the
reduction of plate settlement in dense sand backfill was found to be
comparatively lesser than the loose sand backfill.
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
00 50 100 150 200
Surface Pressure (kN/m 2)
Sett
lem
ent i
n m
m without geogridwith Type II reinforcementwith Type I reinforcementWith geogrid at the crown
Figure 4.9 Settlement of the plate in dense sand
H/D = 3, ø = 42º
89
4.3 RESPONSE OF BURIED PIPE TO LOADING WITHOUT GEOGRID REINFORCEMENT
4.3.1 Effect of different levels of embedment of the pipe in loose and dense sand conditions
The diametric strain of the pipe, defined as the change in the internal diameter of the pipe divided by its original internal diameter measurements, has been calculated and expressed as a percentage in the horizontal(springline) and vertical(crown and invert line) directions from the measured displacements of the pipe wall. The diametric strain of the pipe both in the crown (vertical) and springline (horizontal) at mid section of the pipe (centre) has been plotted against the surface pressure as shown in Figure 4.10 for the pipe buried at different cover depths in loose sand. The buried flexible pipe shows reduction in the vertical diameter and increase in the horizontal diameter due to the pressure applied at the surface of the backfill. The horizontal movement into the soil develops a passive resistance that acts to support the pipe. It is observed that the crown and the invert of the pipe are in compression and springline (both ends) are in tension when subjected to surface pressures.
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
3.5
0 50 100 150 200Applied Surface pressure (kN/m2)
Dia
met
ric s
trai
n (%
)
H/D = 1
H/D = 2
H/D = 3
FC
Horizontal
Vertical
Figure 4.10 Deflection responses to loading of the pipe at its mid section with varying backfill cover in loose sand
ø = 32º
90
The lower half of the diagram demonstrates the negative diametric
strains or compression of the pipe at the crown and the upper half presents the
positive or extensions of the pipe at the level of the springline. The pipe
response to the applied pressure is almost linear leading to an elliptical
deformation. The pipe crown deflected most directly beneath the centre of the
loading plate. The mid section of the pipe within the embedded length showed
larger inward deformation of the pipe. This is an unavoidable phenomenon in
soil box testing as well as in the field situation of trenches with end restraints.
It can be seen in the plots of the pipe strain with applied pressure that the
vertical diametric strain was usually significantly higher than the horizontal
strain. This is due to the fact that the initial deformation sheds the applied
stress to the side fill, increasing its stiffness and confinement and thereby
limiting the potential for increased lateral expansion of the pipe under
subsequent applied stress. This observation is in agreement with studies
conducted by Chapman et al (2007) on flexible pipes buried in sand and
subjected to static stress. As observed graphically, excessive ratios of vertical
to horizontal strain indicate the local buckling of the pipe crown. The pipe
deformation becomes less elliptical as the vertical deformation increases.
The pipes were usually observed to regain their shapes after they
were recovered from the buried pipe installation. It is evident from the results
that increasing the backfill cover offered greater protection to the pipe. A
comparison of load deflection data for 200 mm (H/D = 1) and 600 mm (H/D
= 3) cover verifies that cover height is an important parameter in limiting pipe
deflection for a given load. As the cover height increased the stiffness of the
soil pipe system increased.
91
The diametric strain at the crown of the pipe embedded at 400 mm
depth in loose sand is found to have an average reduction of 54% than the
pipe embedded at 200 mm cover depth over a range of applied pressure. A
reduction in diametric strain along the springline was found to be 30%. The
diametric strain at the crown of the pipe embedded at 600 mm cover was
found to be 85% lesser than the pipe buried at shallow cover of 200 mm for a
surface pressure of 150 kpa. Similar observation was evident along the
springline with an average reduction of 88%.
The diametric strains at section near the edge of the pipe are
presented in Figure 4.11 and are found to be lesser than the diametric strains
observed at mid section of the pipe. Also the increase of diametric strain is
not exactly linear with the applied load.
-1.5
-1
-0.5
0
0.5
1
1.5
0 50 100 150 200Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)
H/D=1
H/D=2
H/D=3
Vertical
Horizontal
Figure 4.11 Deflection responses to loading at section near edge of the
pipe with varying backfill cover in loose sand
ø = 32º
92
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 50 100 150 200
Applied Surface pressure(kN/m2)
Dia
met
ric S
trai
n (%
)
H/D=1
H/D=2
H/D=3
Vertical
Horizontal
Figure 4.12 Deflection responses to loading at mid section of the pipe
with varying backfill cover in dense sand
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0 50 100 150 200
Applied Surface pressure (kN/m2)
Dia
met
ric S
trai
n (%
)
H/D=1
H/D=2
H/D=3
Vertical
Horizontal
Figure 4.13 Deflection responses to loading near edge of the Pipe with varying backfill cover in dense sand
Figures 4.12 and 4.13 show the deformation response at mid and
end sections respectively of the pipe embedded in three different levels of
ø = 42º
ø = 42º
93
dense sand backfill. Similar observations as in the case of loose sand were
noticed. The pipe deflections were found to be lesser in stiffer backfill than in
the case of loose sand backfill. The increase in soil density increased the
modulus of passive resistance for the soil thus resulting in lesser deflections
under applied surface pressure. This indicates that a greater proportion of the
applied surface pressure is transferred to the stiffer backfill which, as it
becomes even more stiffer reduces the potential for horizontal diametric strain
and hence the vertical diametric strains. The proportion of the transfer of
applied stress away from the pipe increased as the stiffness of the side fill
increased. Such a trend is consistent with the field trials described by
Spannagel et al (1974) and Adams et al (1989). The deformation of the pipe
decreased as the depth of embedment increased thus ensuring that a deeper
burial of the pipe offered better protection irrespective of the density of the
backfill material. The vertical and horizontal diametric strains observed at the
ends of the pipe were found to be lesser than the observed diametric strains at
the centre of the pipe for the three levels of embedment.
Figure 4.14 Comparison of vertical and horizontal diametric strains at
midsection and near edge of the pipe in loose sand
H/D = 3, ø = 32º
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 50 100 150 200
Applied surface pressure kN/m 2
Dia
met
ric s
trai
n %
Deflection at midsection
Deflection near theedge
Horizontal
Vertical H/D = 3, ø = 32º
94
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 50 100 150 200
Applied surface pressure kN/m 2
Dia
met
ric s
trai
n %
Deflection at centre ofpipe
Deflection at end of pipe
Horizontal
Vertical
Figure 4.15 Comparison of vertical and horizontal diametric strains at
midsection and near edge of the pipe in dense sand
Figures 4.14 and 4.15 show the comparison of vertical and
horizontal diametric strain at the mid section and end of the pipe in loose and
dense conditions of sand respectively for the cover depth ratio of 3. It is
observed that the difference in vertical deflection at the centre and the end of
the pipe is more pronounced. However the difference in horizontal deflection
is found to be marginal in the case of dense sand owing to the stiffness of the
backfill and the rigid sidewalls of the tank.
4.3.2 Comparison of deflection response of the pipe with and without
geogrid reinforcement above the crown of the pipe in two
densities of sand
The effect of geogrid reinforcement on the vertical and the
horizontal diametric strain of the pipe is studied and presented. Since the
provision of geogrid reinforcement exactly on the crown of the pipe did not
have appreciable influence on the deflection response of the pipe, the results
H/D = 3, ø = 42º
95
are confined to Type I (i.e. 100 mm = 0.5D above pipe crown) and Type II
(i.e. 200 mm = 1D above pipe crown) reinforcements. Since the Type II
reinforcement could not be provided for the H/D ratio equal to 1 (i.e. 200 mm
from the surface of the backfill) the results obtained for other conditions are
presented. Typical results of the tests are presented to provide an insight on
the effect of Type I and Type II reinforcement on the vertical diametric strain
of the pipe embedded at different depths and densities of the sand backfill.
4.3.2.1 Geogrid reinforcement at 0.5D above the crown of the pipe
(Type I reinforcement)
Figure 4.16 Geogrid reinforcement at 100 mm above the crown of the
pipe (Type I reinforcement)
The Figure 4.16 shows the provision of single layer of geogrid
reinforcement at 0.5D (100 mm) above the crown of the pipe in loose sand
backfill. The effect of reinforcement on the vertical and horizontal
deformations of the pipe is illustrated graphically below.
Cover Height
H Geogrid at 100 mm above pipe Crown
Trench Width
Springline
Backfill
Loading Plate
Bedding
D/2
D
96
-1.5
-1
-0.5
0
0.5
1
0 50 100 150 200
Applied Surface pressure(kN/m2)
Dia
met
ric S
trai
n (%
)At mid section w ithoutGeogrid
At mid section w ithGeogrid (Type 1)
Horizontal
Vertical
Figure 4.17 Diametric strain vs. Applied surface pressure at midsection
of the pipe with Type I reinforcement
The Figure 4.17 shows the behaviour of the pipe under the
influence of geogrid reinforcement embedded at 0.5D above the crown of the
pipe in loose sand backfill. It is observed that the diametric strain at the crown
of the pipe is reduced on the average by 16% and along the springline by 29
% over the range of applied surface pressure. The deflection response is also
found to depict a linear behaviour. It is clear that the influence of geogrid
reinforcement is predominant with increase in the surface pressure.
The vertical diametric strain (%) obtained for the embedment ratios
of 1 and 3 at the mid section of the pipe in loose sand backfill are presented in
Table 4.1. It is evident that the presence of geogrid reinforcement at 0.5D
above the pipe crown has reduced the vertical diametric strain by around 17%
for surface pressures ranging from 50 kPa to 150 kPa. Similar observation is
obtained with the pipe embedded at H/D = 3 condition and the reduction is
found to be around 16% for the surface pressures applied.
H/D = 2, ø = 32º
97
Table 4.1 Vertical Diametric strains (%) at mid section of the pipe in
loose sand with Type I reinforcement
Surface pressure (kN/m2)
H/D=1 H/D=3 Without geogrid
With geogrid
Without geogrid
With geogrid
50 -0.745 -0.603 -0.145 -0.117 100 -1.770 -1.48 -0.265 -0.220 150 -2.720 -2.31 -0.380 -0.323
The influence of geogrid reinforcement on the vertical diametric
strain at the mid section of the pipe embedded at H/D ratios of 1, 2 and 3 in
dense sand backfill is presented in Table 4.2. The presence of geogrid
reinforcement reduces the vertical diametric strain by 20% for the embedment
ratios of 1 and 2. In the case of pipe embedded at H/D = 3 condition the
percentage reduction is found to be 52% for the surface pressure of 50 Kpa
and this marginally reduces to 50% for the surface pressure of 150 kPa.
Further it is also observed that the influence of geogrid reinforcement is more
pronounced in the case of dense sand backfill than in loose sand for the range
of applied surface pressures and the embedment ratios studied owing to the
stiffness offered by the backfill and the geogrid reinforcement.
Table 4.2 Vertical Diametric strains (%) at mid section of the pipe in
Dense sand with Type I reinforcement
Surface pressure (kN/m2)
H/D=1 H/D=2 H/D=3 Without geogrid
With geogrid
Without geogrid
With geogrid
Without geogrid
With geogrid
50 -0.233 -0.186 -0.132 -0.105 -0.065 -0.031
100 -0.510 -0.418 -0.295 -0.244 -0.150 -0.100
150 -0.770 -0.646 -0.445 -0.372 -0.240 -0.120
98
The Figure 4.18 shown below gives the influence of geogrid
reinforcement on the deflection observed near the edge of the pipe say, 250
mm from the mid section of the pipe. The presence of single layer of geogrid
reinforcement at 0.5D above the crown of the pipe has reduced the diametric
strain of the pipe by 23% at the crown and 5% along the springline. It is also
observed that the presence of geogrid reinforcement does not show
considerable reduction in the diametric strain along the springline at the
section near the edge of the pipe.
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)
Near edge w ithoutGeogrid
Near edge w ithGeogrid (Type 1)
Horizontal
Vertical
Figure 4.18 Diametric strain vs. applied surface pressure near edge of
the pipe with Type I reinforcement
Table 4.3 Vertical Diametric strains (%) near edge of the pipe in loose
sand with Type I reinforcement
Surface pressure (kN/m2)
H/D=1 H/D=3 Without geogrid
With geogrid
Without geogrid
With geogrid
50 -0.349 -0.254 -0.045 -0.038 100 -0.705 -0.542 -0.080 -0.060 150 -1.105 -0.795 -0.110 -0.070
H/D = 2, ø = 32º
99
The vertical diametric strain (%) near edge of the pipe is obtained
with and without geogrid reinforcement in loose sand backfill and is
presented in Table 4.3. The percentage reduction observed is 27%, 23% and
28% for the surface pressure of 50 kN/m2, 100 kN/m2 and 150 kN/m2
respectively for the H/D ratio of 1. In the case of H/D = 3 condition, reduction
in the vertical diametric strain is found to increase with the increase in surface
pressure and reaches a maximum of 26% for the surface pressure of 150
kN/m2.
Similar observations are noticed in dense sand backfill for
embedment ratios of 1, 2 and 3 with Type I reinforcement and presented in
Table 4.4. The reduction observed in dense sand due to geogrid inclusion is
higher than loose sand. It is 3 to 5 % higher than that observed in loose sand
backfill due to the provision of geogrid.
Table 4.4 Vertical Diametric strains (%) near edge of the pipe in dense
sand with Type I reinforcement
Surface pressure (kN/m2
H/D=1 H/D=2 H/D=3 Without geogrid
With geogrid
Without geogrid
With geogrid
Without geogrid
With geogrid
50 -0.105 -0.074 -0.035 -0.024 -0.030 -0.024
100 -0.245 -0.186 -0.130 -0.095 -0.060 -0.045 150 -0.380 -0.266 -0.315 -0.220 -0.090 -0.067
4.3.2.2 Geogrid at 1D above the crown of the pipe (Type II reinforcement)
The Figure 4.19 shows the provision of single layer of geogrid
reinforcement at 1D (200 mm) above the crown of the pipe. The effect of
reinforcement on the pipe deformations at the centre and ends in different
100
densities of the backfill and depth of embedment is also shown graphically in Figures 4.20 to 4.22.
Figure 4.19 Geogrid at 200 mm above the crown of the pipe (Type II
reinforcement)
-1.5
-1
-0.5
0
0.5
1
0 50 100 150 200
Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)
At mid section w ithoutGeogrid
At mid section w ith Geogrid(Type II)
Horizontal
Vertical
Figure 4.20 Diametric strain vs. Applied surface pressure at mid section
of the pipe with Type II reinforcement
Geogrid at 200 mm above pipe
Crown
Trench Width
Bedding
Springline
Backfill Cover Height,
H
Pipe Diameter, D
Loading Plate
D
H/D = 2, ø = 32º
101
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Applied Surface pressure(kN/m2)
Dia
met
ric S
trai
n (%
)
Near edge w ithout Geogrid
Near edge w ith Geogrid(Type II)
Horizontal
Vertical
Figure 4.21 Diametric strain vs. Applied surface pressure near edge of
the pipe with Type II reinforcement
Figures 4.20 and 4.21 show the influence of geogrid reinforcement
provided at 1D above the pipe on the deformations observed on the pipe at
center and near edge of the pipe (at a distance of 25 cm from the mid section
of the pipe) respectively. The provision of geogrid reinforcement did not
show any significant reduction in the beginning but with the increase in the
applied surface pressure it is evident that the presence of goegrid
reinforcement reduces the diametric strain at the crown of the pipe by 26%
and 25% along the springline of the pipe at the mid section. A reduction of
30% and 19% was observed at the crown and springline respectively near the
edge of the pipe.
H/D = 2, ø = 32º
102
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 50 100 150 200
Applied Surface pressure(kN/m2)
Dia
met
ric S
trai
n (%
)Without Geogrid
With Geogrid (Type II)
Vertical
Horizontal
Figure 4.22 Diametric strains vs. Applied surface pressure at mid
section of the pipe with Type II reinforcement
Figure 4.22 shows the influence of geogrid reinforcement provided
at 200 mm above the pipe embedded at a depth of 600 mm (ie H/D=3) in
dense sand backfill. A significant average reduction of 55% was observed in
the crown deflection and 50% along the springline of the pipe at the mid
section of the pipe directly beneath the loading .Similar observation was made
at the end of the pipe with an average reduction of 64% on the crown
deflection and 58 % on the springline deflection of the pipe (Figure 4.23). The
reduction in the vertical diametric strain was found to be more than the
horizontal diametric strain owing to the stiff backfill.
H/D = 3, ø = 42º
103
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 50 100 150 200
Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)
Without Geogrid
With Geogrid (Type II)
Vertical
Horizontal
Figure 4.23 Diametric strain vs. Applied surface pressure near edge of
the pipe with Type II reinforcement
The influence of Type II reinforcement on the vertical diametric
strain at the mid section and near the edge of the pipe for the embedment ratio
of 3 in loose sand and 2 in dense sand is presented in Table 4.5. It is evident
that the geogrid reinforcement has reduced the vertical diametric strain by
around 15% in loose sand for the cover depth ratio of 3 at the mid and end
sections of the pipe within the embedded length for the surface pressure of
50kPa. It is found that the percentage reduction gradually increases with
applied surface pressure. A reduction of 28% and 36% is observed in the
vertical diametric strain at a surface pressure of 150 kPa at the mid and end
sections of the pipe respectively. Similar observation is noticed in the pipe
embedded at H/D = 2 condition .The percentage reduction observed in the
dense sand backfill is more than the loose sand backfill for the embedment
ratios considered and the range of surface pressures applied.
H/D = 3, ø = 42º
104
Table 4.5 Vertical diametric strains (%) at mid section of the pipe in loose
and dense sand with Type II reinforcement
Surface pressure (kN/m2)
Loose sand (ø = 32º) Dense Sand (ø = 42º) H/D=3 H/D=2
Without geogrid
With geogrid Without geogrid
With geogrid
At mid section
Near edge
At mid section
Near edge
At mid section
Near edge
At mid section
Near edge
50 -0.145 -0.045 -0.123 -0.039 -0.132 -0.035 -0.088 -0.019
100 -0.265 -0.080 -0.198 -0.050 -0.295 -0.130 -0.162 -0.054
150 -0.380 -0.110 0.270 -0.070 -0.445 -0.315 -0.213 -0.141
Similar observations are made in the horizontal diametric strain
with Type II reinforcement. However the provision of geogrid above the
crown had lesser effect in reducing the springline deformation of the pipe.
4.3.3 Comparison of deflection response of the pipe with and without
geogrid reinforcement along the springline of the pipe in two
different densities of sand
The influence of providing single and two layers of geogrid
reinforcement along the springline of the pipe on the vertical and horizontal
diametric strains of the pipe are studied and presented. Typical results of the
tests showing the influence of Type III (Single layer of geogrid along the
springline), Type IV (Two layers of geogrid with loose sand packing between
the layers) and Type V (Two layers of geogrid with dense sand packing
between the layers) reinforcements on the horizontal diametric strain of the
pipe for different embedment ratios and densities of the sand backfill are
presented and discussed.
105
4.3.3.1 Single layer along the springline (Type III reinforcement)
Cover Height
H
Trench Width
Geogrid along springline
Backfill
Loading Plate
Bedding
Figure 4.24 Geogrid along the springline of the pipe (Type III
reinforcement)
Single layer of geogrid reinforcement provided along the springline
of the pipe is shown in Figure 4.24. The effect of geogrid reinforcement in the
reduction of deformations at the centre and ends of the pipe within the
embedment length is graphically illustrated below.
D
106
-1.5
-1
-0.5
0
0.5
1
0 50 100 150 200
Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)At mid section w ithoutGeogrid
At mid section w ithGeogrid (Type III)
Horizontal
Vertical
Figure 4.25 Diametric strain vs. Applied surface pressure at mid section
of the pipe with Type III reinforcement
Figure 4.25 shows the behaviour of the pipe at its mid section with
the provision of geogrid reinforcement along the springline of the pipe.
Variation of diametric strain is almost linear both in the horizontal and
vertical diameters of the pipe for the surface pressures applied. A reduction of
47% in the horizontal deflection was observed along the springline of the
pipe. However it was found that the provision of geogrid reinforcement along
the springline of the pipe did not have much influence on the crown deflection
of the pipe at its mid section.
The results obtained with Type III reinforcement provided for
embedment ratios of 1 and 3 in loose sand is presented in Table 4.6. The
reduction in the horizontal diametric strain is found to be 46% for the surface
pressure of 150 kPa for both the embedment ratios.
H/D = 2, ø = 32º
107
Table 4.6 Horizontal diametric strains (%) at midsection of the pipe in
loose sand with Type III reinforcement
Surface pressure (kN/m2)
H/D=1 H/D=3
Without geogrid
With geogrid
Without geogrid
With geogrid
50 0.032 0.023 0.05 0.024
100 0.725 0.384 0.085 0.045
150 1.08 0.583 0.120 0.064
Typical results obtained with embedment ratios of 1, 2 and 3 in
dense sand are presented in Table 4.7. The geogrid reinforcement reduces the
horizontal diametric strain by 46% to 53% at a surface pressure of 50 kN/m2
for the H/D ratios of 1 to 3. However at a surface pressure of 150 kN/m2 a
constant reduction of 48% is observed in the horizontal strain.
Table 4.7 Horizontal diametric strains (%) at mid section of the pipe in
Dense sand with Type III reinforcement
Surface pressure (kN/m2)
H/D=1 H/D=2 H/D=3
Without geogrid
With geogrid
Without geogrid
With geogrid
Without geogrid
With geogrid
50 0.098 0.046 0.030 0.014 0.034 0.016
100 0.195 0.099 0.127 0.064 0.065 0.030
150 0.285 0.151 0.232 0.120 0.100 0.052
108
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Applied Surface pressure(kN/m2)
Dia
met
ric S
trai
n (%
)Near edge w ithout Geogrid
Near edge w ith Geogrid(Type III)
Horizontal
Vertical
Figure 4.26 Diametric strain vs. Applied surface pressure near edge of
the pipe with Type III reinforcement
Figure 4.26 shows the influence of geogrid reinforcement provided
along the springline on diametric strain at the section near the edge of the
pipe. At this section also, the diametric strain tends to vary linearly within the
applied surface pressure as seen at the mid section of the pipe. A comparison
between the magnitudes of diametric strains along the springline (horizontal)
and along the line joining crown and invert of pipe shows marginal
difference, which indicates that pipe deformation is almost elliptical at the
edge of the pipe. From the results presented it was found that an average
reduction of 40% was found in the diametric strain at the crown of the pipe
and the same was 38%was noticed at the springline of the pipe.
The observations made in loose and dense sand backfill near the
edge of the pipe are presented in Tables 4.8 and 4.9 respectively. It is evident
from the results presented that the springline deformation reduced by 35% to
37% over the range of applied surface pressures in loose sand backfill. In the
case of dense sand backfill the inclusion of geogrid along the springline has
H/D = 2, ø = 32º
109
reduced the horizontal diametric strain by 37% to 42% for the applied surface
pressure of 150 kPa irrespective of the cover depth ratios considered in this
study.
Table 4.8 Horizontal diametric strains (%) near edge of the pipe in loose
sand with Type III reinforcement
Surface pressure (kN/m2)
H/D=1 H/D=3 Without geogrid
With geogrid
Without geogrid
With geogrid
50 0.314 0.169 0.050 0.027 100 0.645 0.406 0.095 0.059
150 0.975 0.633 0.140 0.091
Table 4.9 Horizontal diametric strains (%) near edge of the pipe in
Dense sand with Type III reinforcement
Surface pressure (kN/m2)
H/D=1 H/D=2 H/D=3
Without geogrid
With geogrid
Without geogrid
With geogrid
Without geogrid
With geogrid
50 0.065 0.033 0.045 0.017 0.030 0.021 100 0.150 0.091 0.115 0.076 0.070 0.045
150 0.260 0.163 0.180 0.182 0.110 0.063
4.3.3.2 Two layers of geogrid with 50 mm loose sand packing (Type IV
reinforcement)
The Figure 4.27 shows the provision of two layers of geogrid
reinforcement with 50 mm of loose sand packing between the geogrid layers
along the springline of the pipe. The effect of above said reinforcement on
110
the pipe deformations at the mid section and the ends of the pipe is presented
below.
Figure 4.27 Two layers of geogrid reinforcement with 50 mm loose sand
packing (Type IV reinforcement)
-1.5
-1
-0.5
0
0.5
1
0 50 100 150 200
Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)
At mid section w ithoutGeogrid
At mid section w ithGeogrid (Type IV)
Horizontal
Vertical
Figure 4.28 Diametric strain vs. Applied surface pressure at mid section
of the Pipe with Type IV reinforcement
Cover Height
H
Trench Width
Two layers of Geogrid with 50 mm loose sand packing
Backfill
Loading Plate
Bedding
D
H/D = 2, ø = 32º
111
Figure 4.28 shows the influence of two layers of geogrid reinforcement provided along the springline with 50 mm of loose sand packing in-between the layers on the diametric strain and compared it with the diametric strains of pipe without geogrid reinforcement. The diametric strain along the horizontal direction (i.e. springline) of pipe varies linearly with applied pressure for the entire range of pressure as shown in the Figure 4.28. For the Type IV condition of geogrid reinforcement, the diametric strain in the pipe is reduced when compared to pipe without geogrid reinforcement as seen in Type III reinforcement. The response of vertical diametric strain due to Type IV reinforcement is different from horizontal diametric strain. There is practically no reduction in vertical diametric strain due to type IV reinforcement at the springline. Infact the diametric strain along the vertical direction (crown and invert line) is increased for the initial pressures. The springline deflection is reduced considerably, which is around 40% but the Type IV reinforcement does not show any change on the crown deflection of the pipe at the particularly mid section of the pipe. The provision of reinforcement Type IV along the springline is effective in reducing lateral deflection of the pipe alone in loose sand.
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)
Near edge w ithout Geogrid
Near edge w ith Geogrid(Type IV)
Horizontal
Vertical
Figure 4.29 Diametric strain vs. Applied surface pressure near edge of the pipe with Type IV reinforcement
H/D = 2, ø = 32º
112
Figure 4.29 compares the deformation of the pipe both at the crown
and springline for the pipe section near the edge of the pipe with and without
geogrid reinforcement (Type IV). Reinforcing the backfill material at the
springline of the pipe reduced the diametric strain both in the horizontal and
vertical directions. However for the initial pressures (i.e. less than 40 kN/m2),
almost no difference in diametric strains due to the inclusion of Type IV
geogrid reinforcement at the springline. Average reduction of 30% and 32%
was observed at the crown and the springline respectively. At the edge of the
pipe the magnitude of vertical and horizontal diametric stains are almost
equal, which is due to springline reinforcement and it confirms perfect
elliptical deformation at the edge.
The influence of Type IV reinforcement for a pipe embedded at
H/D = 3 condition in loose and dense sand backfills is presented in Table
4.10. A reduction ranging from 26% to 42% over the surface pressures of 50
kN/m2 to 150 kN/m2 is observed at the mid section and near the edge of the
pipe. A similar trend is noticeable in dense sand backfill also. However the
percentage reduction in horizontal strain is not appreciable when compared
with the Type III reinforcement.
Table 4.10 Horizontal diametric strains (%) at mid section and near
edge of the pipe in loose and dense sand with Type IV reinforcement
Surface pressure (kN/m2)
Loose sand (ø = 32º) Dense Sand (ø = 42º) H/D=3 H/D=3
Without geogrid Withgeogrid Without
geogrid With geogrid
At mid section
Near edge
At mid section
Near edge
At mid section
Near edge
At mid section
Near edge
50 0.050 0.050 0.036 0.046 0.034 0.030 0.018 0.021 100 0.085 0.095 0.050 0.064 0.065 0.070 0.036 0.045 150 0.120 0.140 0.070 0.092 0.10 0.110 0.058 0.063
113
4.3.3.3 Two layers of geogrid with 50 mm Dense sand packing (Type V
reinforcement)
The Figure 4.30 given below shows the Type V reinforcement (two
layers of geogrid reinforcement at the springline of the pipe with 50 mm of
dense sand packing in-between the layers). The effect of Type V
reinforcement is studied on the deformation response of the pipe and is
presented.
Figure 4.30 Two layers of geogrid reinforcement with 50 mm Dense
sand packing (Type V reinforcement)
Figures 4.31 and 4.32 show the response of pipe at two sections viz.
middle of the pipe and near the edge respectively due to Type V
reinforcement for the entire range of load applied on the backfill. In the
figures response of pipe without reinforcement condition is also presented for
comparison. The response of pipe cover depth of 400 mm in loose sand for
Cover Height
H
Trench Width
Two layers of Geogrid with 50mm dense sand packing
Backfill
Loading Plate
Bedding
D
D/4
114
the Type V reinforcement is unlike other two types of spring line
reinforcement (Type III and IV). In Type V reinforcement though the
variations of diametric strains both in the horizontal and vertical directions are
linear, the reduction in the strains at both the directions of the pipe is
considerable. Reduction in the diametric strains of the pipe due to Type V
reinforcement indicates over all increase in the pipe- soil stiffness. The layers
of geogrid reinforcement provided with dense sand supported the pipe by
offering additional passive resistance to the pipe. An average reduction of
24% and 71% at the crown and springline respectively was observed at the
mid section and 59% and 58% was observed at the edge of the pipe.
-1.5
-1
-0.5
0
0.5
1
0 50 100 150 200
Applied Surface pressure(kN/m 2)
Dia
met
ric S
trai
n (%
)
At mid section w ithoutGeogrid
At mid section w ithGeogrid (Type V)
Horizontal
Vertical
Figure 4.31 Diametric strain vs. Applied surface pressure at mid section
of the pipe with Type V reinforcement
H/D = 2, ø = 32º
115
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Applied Surface pressure(kN/m2)
Dia
met
ric S
trai
n (%
)Near edge w ithout Geogrid
Near edge w ith Geogrid(Type V)
Vertical
Figure 4.32 Diametric strain vs. Applied surface pressure near edge of
the pipe with Type V reinforcement
Table 4.11 presents the results obtained with Type V reinforcement
for a pipe embedded at H/D = 3 condition in loose and dense sand backfill.
An appreciable reduction in the horizontal diametric strain is noticeable both
in loose and dense sand backfills. For the range of surface pressures
considered there is a reduction of 72% in the case of dense sand backfill. This
is due to the lateral confinement and stiffness offered by the geogrid
reinforcement of Type V.
Table 4.11 Horizontal diametric strains (%) at mid section and near
edge of the pipe in loose and dense sand with Type V reinforcement
Surface pressure (kN/m2)
Loose sand (ø = 32º) Dense Sand (ø = 42º) H/D=3 H/D=3
Without geogrid Withgeogrid Without geogrid With geogrid At mid section
Near edge
At mid section Near edge At mid
section Near edge
At mid section
Near edge
50 0.050 0.050 0.014 0.021 0.034 0.030 0.007 0.009 100 0.085 0.095 0.024 0.040 0.065 0.070 0.017 0.029 150 0.120 0.140 0.030 0.056 0.10 0.110 0.025 0.038
H/D = 2, ø = 32º
Horizontal
Vertical
116
0.001.002.003.004.005.006.007.008.009.00
10.00
0 50 100 150 200
Applied surface pressure kN/m2
Def
lect
ion
ratio
without geogrid
with Type I reinforcementwith Type II reinforcement
with Type III reinforcementwith Type IV reinforcement
with Type V reinforcement
Figure 4.33 Comparison of Deflection ratio at mid section of the pipe
with and without geogrid reinforcement in loose sand
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 50 100 150 200
Applied surface pressure kN/m2
Def
lect
ion
ratio
without geogrid
with Type I reinforcement
with Type II reinforcement
with Type III reinforcement
withType IV reinforcement
with Type V reinforcement
Figure 4.34 Comparison of Deflection ratio at mid section of the pipe
with and without geogrid reinforcement in dense sand
H/D = 2, ø = 32º
H/D = 2, ø = 42º
117
Figures 4.33 and 4.34 show the ratio of vertical deflection (Δy) to
horizontal deflection (Δx) of pipe with and without geogrid reinforcement of
five types for pipes tested in loose and dense sand backfills respectively. The
results presented are for the cover depth ratio of 2. In loose backfill the
deflection ratio remains almost constant for a given condition of installation
and range of surcharge pressures applied on the backfill. This shows that the
deformation of pipe in the vertical and horizontal directions follow uniform
trend and this trend is not influenced by the intensity of pressure applied.
Deflection ratio is more than unity for the installation conditions analysed in
this study, which indicates that the deflection along the crown is higher than
springline for all the conditions studied in this research work. Among the
different installation conditions, the deflection ratio is the highest for the Type
V reinforcement and lowest for the pipe installed without reinforcement. Such
a high deflection ratio (>4) is attributed to lateral support offered by the
reinforcement to the walls of the pipe at its springline. Though the deflection
ratio is higher for all the reinforcement conditions the absolute diametric
deflection of pipe both in the vertical and horizontal direction is less than
unreinforced condition. From the results it is observed further that the
deflection ratio between the reinforced conditions of Type I and Type II is
almost same. This indicates that location of reinforcement above the pipe
crown within the distance equal to diameter of the pipe does not make much
difference in the pipe response. Similarly between Type III and Type IV
reinforcement, the difference in deflection ratio is almost zero indicating no
variation in the pipe response. Thus provision of single geogrid layer at the
springline of the pipe in loose backfill performed in equal level if not better
with two layers of geogrid. However reinforcement provided at the springline
reduced the lateral deformation effectively than the reinforcement placed
above the crown of the pipe. The trend is different in dense backfill.
In dense backfill, the deflection ratio is not uniform for the entire
range of applied surface pressure. At the pressure of 50 kN/m2 the deflection
118
ratio is maximum and it decreases thereafter with increase in pressure. This
trend is seen in all the reinforcement conditions adopted in dense backfill.
The vertical deflection (Δy) is generally assumed to be the same as the
horizontal deflection (Δx) but from the tests conducted it is clear that the
ratios ranged depending on the shape of the pipe deformation and is
influenced by the placement condition of the pipe. It is evident from the
study that the deformation is not perfectly elliptical on the application of
applied pressure. The deformation ratios indicate a rectilinear shape in the
case of stiff backfill.
4.4 STRAIN ON THE CROWN OF THE PIPE
The experimentally obseved strain data has been reduced in the
form of principal strain as given by Dally and Riley,1978 and shown in
Appendix 3. The major principal strains obtained at the crown of the pipe for
various levels of embedment of the pipe in loose and dense sand backfills are
presented. The influence of Type I and Type II reinforcement on the major
principal strain in two different densities of the backfill is presented and
discussed.
4.4.1 Effect of different levels of embedment of the pipe in two different densities of sand without geogrid reinforcement
From the Figures 4.35 and 4.36 the variation of ε1 with p/γD can be
seen to be linear at the crown of pipe for pipes tested in loose sand and dense
sand respectively. The above graphs were found to originate from near the
origin (but not exactly passing through the origin probably because of soil
confining pressure) and ε1 value was found to increase linearly for the pressures applied. The ε1 value was found to decrease as the H/D value
increases form 1 to 3.
119
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60
Dimensionless surface pressure
Maj
or p
rinci
pal s
trai
n
-Єx1
0-5H/D=1
H/D=2
H/D=3
CROWN
Figure 4.35 Variation of ε1 with p/γD at crown for 200 mm PVC pipe in
loose sand
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60Dimensionless surface pressure
Maj
or p
rinci
pal s
trai
n
- Єx1
0-5
H/D=1
H/D=2
H/D=3
CROWN
Figure 4.36 Variation of ε1 with p/γD for 200 mm PVC pipe in dense
sand
The strain values were found to be more for loose sand backfill
than those for dense sand backfill particularly for H/D = 2 and 3, because
ø = 32º
ø = 42º
120
modulus of soil in the former case was less than in the latter case. This in a
way shows the effect of relative modular ratio (Ep/Es).
4.4.2 Comparison of strain at the crown of the pipe with and without
geogrid reinforcement in two different densities of sand
In Figures 4.37 and 4.38, the variations of the major principal strain
with the dimensionlless surface pressure are presented and compared with the
values obtained for the unreinforced condition, the Type I and Type II
reinforcements respectively. It is observed that the geogrid reinforcement at
100mm (i.e. D/2) above the pipe crown reduced the principal strain on the
crown of the pipe by 55 % and by 28 % when the geogrid reinforcement was
provided at 1D above the pipe crown. Its effect was found to increase with the
increase in the surface pressure.
0
2
4
6
8
10
12
14
16
18
20
0 10 20 30 40 50 60
Dimensionless surface pressure
Maj
or p
rinci
pal s
trai
n
-Єx1
0-5
Without geogrid
With Type I reinforcement
Figure 4.37 Variation of ε1 with p/γD with Type I reinforcement
CROWN
H/D = 2, ø = 32º
121
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60
Dimensionless surface pressure
Maj
or p
rinci
pal s
trai
n
-Єx1
0-5
Without geogrid
With Type II reinforcement
Figure 4.38 Variation of ε1 with p/γD with Type II reinforcement
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60
Dimensionless surface pressure
Maj
or p
rinci
pal s
trai
n
-Єx1
0-5
Without geogrid
With Type II reinforcement
Figure 4.39 Variation of ε1 with p/γD with Type II reinforcement in
dense Sand
It is clearly evident from the Figure 4.39 that the provision of
geogrid reinforcement at 200 mm (1D) above the pipe crown has reduced the
H/D = 2, ø = 32º
H/D = 3, ø = 42º
CROWN
CROWN
122
maximum principal strain by about 90% in dense sand with pipe buried at a
depth of 600 mm from the surface of the backfill.
4.5 STRAIN ON THE SPRINGLINE OF THE PIPE
The major principal strain at the springline of the pipe without the
provision of geogrid reinforcement at different levels of embedment of pipe is
studied and presented. The effect of providing Type III, Type IV and Type V
reinforcements on the maximum principal strain is observed. Typical results
are presented for the midsection of the pipe.
4.5.1 Effect of depth of embedment of the pipe without geogrid reinforcement
The Figure 4.40 shows the variation of the major principal strain at
the springline of the pipe with p/γD for the pipe buried in loose sand at three
different levels of embedment.
0102030
405060708090
100110120
0 10 20 30 40 50 60
Dimensionless surface pressure
Maj
or p
rinci
pal s
trai
n
-Єx1
0-5
H/D=1
H/D=2
H/D=3
SPRINGLINE
Figure 4.40 Variation of ε1 with p/γD at springline for 200 mm P.V.C
pipe in loose sand
ø = 32º
123
It is evident from the figure that the major principal strain reduced
considerably with the increase in the depth of burial of the pipe. This
observation is in agreement with the conclusions reported by Kataria and
Kameswara Rao (1982). It is observed that strains are higher for the
embedment ratio of 1(i.e. 200 mm from the surface of the backfill) but
reduces considerably for embedment ratios of 2 and 3 (i.e. 400 mm and 600
mm from the surface of the backfill). This is due to the lateral confinement of
the soil along the sides of the pipe, which is higher for higher depth of
embedment. Further the stress on the pipe due to surcharge pressure is also
lesser for deeper embedment.
4.5.2 Comparison of strain at springline of the pipe with and without
geogrid reinforcement along the springline
It is evident from the Figure 4.41 that the principal strain reduced
by 25% with the provision of single layer of geogrid reinforcement at the
springline of the pipe. The reduction in the principal strain with the provision
of Type III reinforcement is found to be constant with the increase in the
surface pressure.
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50 60
Dimensionless surface pressure
Maj
or p
rinci
pal s
trai
n
-Є x
10- 5
Without geogrid
Type III reinforcement
Type IV reinforcement
Type V reinforcement
Fgure 4.41 Variation of ε1 with P/γD at springline with and without
geogrid reinforcement
H/D = 2, ø = 32º
124
The provision of two layers of geogrid with 50 mm loose sand
packing in-between the layers along the springline of the pipe does not show
considerable reduction in the major principal strain initially, but with the
increase in surface pressure a reasonable reduction is observed. The effect is
more pronounced in the case of geogrid reinforcement with dense sand
packing and is found to reduce the major principal strain by 24 %.
4.6 STRESS VARIATION ON THE PIPE DUE TO SURFACE
LOADS
The hoop stress developed in the pipe for different levels of
embedment in loose and dense sand backfills are computed and presented.
Typical results obtained with the provision of geogrid reinforcement are
presented.
4.6.1 Effect of three different levels of embedment of the pipe in loose
and dense conditions of sand backfill without geogrid
reinforcement
Figures 4.42 and 4.43 show the hoop stresses developed at the mid
section of the pipe embedded at three different levels in two densities of the
sand backfill. From the figures it is clear that the hoop stresses are
predominant at a shallow burial and get considerably minimized with the
increase in the depth of embedment both in the case of loose and dense sand
backfills. It is observed that the behaviour is almost identical both at the
crown and along the springline of the pipe.
125
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 50 100 150 200
Applied Surface pressure (kN/m2)
Hoo
p s
tres
s (k
N/m
2 )H/D = 1H/D = 2H/D = 3
Crow n
Springline
Figure 4.42 Hoop stress vs. Applied surface pressure for three different
levels of embedment in loose sand
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 50 100 150 200
Applied Surface pressure (kN/m2)
Hoo
p s
tres
s (k
N/m
2 )
H/D = 1
H/D = 2
H/D = 3
Crow n
Springline
Figure 4.43 Hoop stress vs. Applied surface pressure for three different
levels of embedment in dense sand
ø = 32º
ø = 42º
126
4.6.2 Comparison of stress at the crown and springline of the pipe
with and without geogrid reinforcement
Figure 4.44 shows the influence of geogrid reinforcement on the
hoop stresses developed at the crown in the mid section of the pipe with cover
depth of 400 mm (H/D = 2) from the surface. It is clear that the geogrid
provided at a height of D (= 200 mm ) above the pipe crown significantly
reduces the stress on the average by 66%. The geogrid provided at D/2 above
the pipe crown and along the springline of the pipe considerably reduced the
hoop stresses by about 57 % and 33% respectively on an average. The effect
of reinforcement tends to be insignificant at the beginning of loading but
significant reduction in the stresses is observed beyond the surface pressure of
50 kPa.
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
00 50 100 150 200
Applied surface pressure (kN/m2)
Hoo
p s
tres
s (k
N/m
2 )
Without geogrid
With Type Ireinforcement
With Type IIreinforcement
w ith Type IIIreinforcement
Figure 4.44 Hoop stress vs. Applied surface pressure at mid section of
the pipe with geogrid reinforcement at different levels
Figure 4.45 shows the influence of geogrid reinforcement on the
hoop stresses developed near the edge of the pipe embedded at the depth of
H/D = 2, ø = 32º
Crown
127
400 mm form the surface. It is evident from the figure that the geogrid
reinforcement provided along the springline significantly reduces the hoop
stresses on the average by 47% whereas geogrids provided at 100 mm (D/2)
and 200 mm (D) above the pipe crown show an average reduction of 34% on
the hoop stresses developed at the crown of the pipe. As seen in the case of
deflection ratio the reinforcement location is immaterial for reducing the hoop
stress also. However the reduction in hoop stress is more for type III
reinforcement at the edge of pipe line, whearas type III is effective for mid
section among the three types of reinforcement compared.
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
00 50 100 150 200
Applied surface pressure (kN/m2)
Hoo
p s
tres
s (k
N/m
2 )
Without geogrid
With Type Ireinforcement
With Type IIreinforcement
With Type IIIreinforcement
Figure 4.45 Hoop stress vs. Applied surface pressure near edge with
geogrid reinforcement at different levels and locations
Table 4.12 Hoop stresses (kN/m2) at mid section and near edge of the
pipe with Type IV and Type V reinforcement in loose sand
Surface pressure (kN/m2)
Mid section of the pipe Near edge of the pipe
Without geogrid
With Type IV reinforcement
With Type V reinforcement
Without geogrid
With Type IV reinforcement
With Type V reinforcement
50 -0.169 -0.151 -0.149 -0.087 -0.077 -0.076
100 -0.334 -0.292 -0.285 -0.202 -0.164 -0.171
150 -0.476 -0.391 -0.382 -0.293 -0.237 -0.237
H/D = 2, ø = 32º
Crown
128
Table 4.12 shows the effect of Type IV and Type V reinforcement
on the hoop stresses developed on the crown of the pipe at its mid section and
near the edge of the pipe embedded at 400 mm from the surface of the loose
sand backfill due to applied surface pressures. It is observed that in both the
cases the reduction in the stress increases gradually with increase in the
applied surface pressure and reaches a maximum of 19% for the surface
pressure of 150 kN/m2. Similar observation is noticeable at the section near to
the edge of the pipe also.
Table 4.13 Hoop stresses (kN/m2) at the springline of the pipe with and
without geogrid reinforcement
Surface pressure (kN/m2)
Without geogrid
reinforcement
With Geogrid reinforcement
Type I Type II Type III
Type IV
Type V
50 0.126 0.112 0.116 0.125 0.128 0.096
100 0.304 0.220 0.192 0.251 0.308 0.169
150 0.440 0.310 0.392 0.370 0.399 0.238
Hoop stresses developed at the springline of the pipe embedded at a
depth of 400 mm from the surface of the loose sand backfill with and without
geogrid reinforcement is presented in Table 4.13. It can be clearly seen that
the provision of Type V reinforcement has reduced the stresses considerably
when compared to the reinforcement provided above the crown of the pipe.
The percentage reduction tends to increase with the increase in surface
pressure and the maximum reduction observed is 25% at an applied surface
pressure of 150 kN/m2. The results observed with Type III and Type IV
reinforcement are not appreciable but the percentage reduction obtained with
Type III reinforcement is higher than Type IV.
129
-0.25
-0.2
-0.15
-0.1
-0.05
00 50 100 150 200
Applied surface pressure (kN/m2)
Hoo
p st
ress
(kN
m2 )
Without geogrid
At 200mm above thecrow n
Figure 4.46 Hoop stress vs. Applied surface pressure at mid section with
Type II reinforcement
Figure 4.46 shows the typical result of the influence of geogrid
reinforcement on the pipe embedded at a depth of 600 mm from the surface in
dense sand backfill. It is evident that the geogrid provided at 200 mm above
the pipe crown has reduced the hoop stresses on the average by 83%. It is
observed that the effect of geogrid increases with the increase in the surface
pressure and is found to have a significant effect in the reduction of hoop
stresses at greater burial depths.
4.7 SUMMARY
The settlement of the loading plate, deflection responses at the mid
section and near edge of the pipe with and without geogrid reinforcements,
the influence of geogrid reinforcements on the strains and stresses at the
crown and springline of the pipe were studied on two different densities of
the sand backfill and three different embedment ratios.
The settlement of the loading plate was observed to be more in the
absence of the pipe. The provision of geogrid reinforcement at 200 mm
H/D = 3, ø = 42º
130
above the crown of the pipe (Type II reinforcement ) was much effective in
reducing the settlement of the plate. The provision of Type I and Type II
reinforcements considerably reduced the vertical diametric strains of the pipe
at the mid section and edge of the pipe. Eventhough the reduction in the
observed horizontal strains were comparable, the effect of reduction was more
pronounced in the case of vertical diametric strains. The provision of Type
III, Type IV and Type V reinforcements reduced the springline deformation
of the pipe considerably when compared to the vertical diametric strain at the
crown of the pipe. Similar observations were noticed with the provision of
geogrid reinforcement on the strains and stresses of the pipe.