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.