Centrifuge Modeling of Permanent Ground Deformation
Effects on Buried HDPE Pipelines
Da Ha1; Tarek H. Abdoun2; Michael J. O’Rourke3; Michael D. Symans4, Thomas D.
O’Rourke5; and Harry E. Stewart6
1Doctoral
Student, Dept. of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. E-mail:
had@rpi.edu
2Associate
Professor, Dept. of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. E-
mail: abdout@rpi.edu
3Professor,
Dept. of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. E-mail:
orourm@rpi.edu
4Associate
Professor, Dept. of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. E-
mail: symans@rpi.edu
5Professor,
Dept. of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853-3501. E-mail: tdo1@cornell.edu
6Associate
Professor, Dept. of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853-3501. E-mail:
hes1@cornell.edu
1
ABSTRACT
It is generally agreed that permanent ground deformation (PGD) is a severe hazard for continuous
buried lifelines. In this paper the results of four centrifuge tests are presented. The tests were
designed to investigate the influence of pipe-fault orientation on the pipe behavior under PGD. The
experimental setup and procedures are described and the test results are presented. Tests results
show that design against horizontal PGD using the ASCE guideline (1984) is conservative
especially at small displacements.
Introduction
Permanent ground deformation (PGD) is a significant hazard for many man-made structures including houses, highways, tunnels, bridges, as well as water, gas, oil and sewer pipelines. The principal
forms of PGD are surface faulting, landsliding, seismic settlement and lateral spreading due to soil
liquefaction. The water, gas and sewer pipelines are usually referred to as lifelines as they are necessary for the support of human life. PGD frequently involve differential ground movement wherein
two sides moving either horizontally or vertically, with respect to each other (Fig. 1), across a slip or
fault plane. Whether the differential ground movement results in a pipe primarily in tension or compression depends on the relative orientation of the fault and the pipe (Fig. 2) as well as the direction
of faulting. In most cases, both axial strain and bending strain will be induced in the pipeline whenever PGD occurs. Even though most fault displacement is confined to a narrow zone, the potential
for pipeline damage is high since the offset imposes large strain on the pipe (Eidinger et al. 2002).
The design of buried pipeline for the permanent ground deformation hazard is usually based on
Finite Element simulation following the ASCE guideline (1984). There is a pressing need to systematically verify and calibrate this design procedure. Unfortunately, field case histories which could be
used to verify current design procedure are limited. Similarly full-scale laboratory tests of buried
pipeline response to fault offsets are not commonly available.
2
To address this difficulty, a centrifuge based method was first investigated by O’Rourke et al.
(2003) using the Rensselaer Geotechnical Centrifuge and a split container which was designed to
simulate horizontal fault offsets. Aluminum pipes with two different diameters were tested with dry
sand in the simulation. The sand used has a friction angle  = 35o and unit weight of 18.9kN/m3. All
of their tests were conducted at 50g with pipe and fault oriented 90o to each other and a pipe burial
depth (depth of soil above pipe centerline) of 1.2m. The tests were successful in the sense that the
experimental equipment functioned well and the recorded strains were generally in good agreement
with those predicted by Finite Element models.
Fig. 1. Types of surface faulting (After Meyersohn, 1991).
3
Fig. 2. Different ground rupture patterns.
In the current centrifuge tests reported in this paper, the offset was simulated using a split-box
container. The container is capable of simulating both vertical and horizontal offset in flight, although only horizontal offsets were considered herein. Additional information on the split container
is presented in a separate paper (Ha et al. 2006).
Centrifuge Modeling of HDPE Pipe Response to PGD
Table 1 and Fig. 3 summarize the four centrifuge experiments which were designed to evaluate
the behavior of buried pipelines subjected to horizontal offset. Specifically, the tests are designed to
determine the influence of the pipe-fault angle. Fig.3 presents sketches of the RPI split container
(CMC SB3) and the HDPE pipe before and after the offset. In Fig. 3(a) the initial pipe-fault angle is
85o, which corresponds to model 1 and 2. As one might expect, the 85o (close to perpendicular) ini4
tial pipe-fault angle induces primarily flexural strain in the pipe. Fig. 3(b) applies to models 3 and 4,
which have an initial pipe-fault angle of 63.5o. As one might expect the non-perpendicular initial
orientation and the direction of the offset results in significant axial as well as flexural strain.
Table 1. Summary of Test Models (all dimensions in prototype scale)
Model
Number
Initial PipeFault Angle
(degree)
Instrumentation
Pipe
Diameter
(m)
Pipe Wall
Thickness
(m)
Burial
Depth
(m)
Offset Rate
1
-85
2
Peak
Offset
Strain Gage
0.408
0.024
1.124
0.318
(m)
1.06
-85
Tactile Sensor
0.408
0.024
1.124
0.318
1.06
3
-63.5
Strain Gage
0.408
0.024
1.124
0.318
1.06
4
-63.5
Tactile Sensor
0.408
0.024
1.124
0.318
1.06
(m/min)
Split Container
0.04m
Fixed
Portion
0.04m
Test Pipe
0.57m
Movable
Portion
85o
4cm
0.04m
Before Offset
After Offset
a)
85o Test Setup
5
Split Container
0.04m
0.04m
Test Pipe
0.64m
Movable
Portion
Fixed
Portion
63.5o
0.04m
0.04m
Before Offset
After Offset
b) 63.5o Test Setup
Fig. 3. Sketch of the centrifuge model before and after offset (dimensions in model scale).
To capture the behavior of the pipe during the offset, two sets of instrumentation were used. In
model 1 and 3, the HDPE pipe was instrumented with strain gages which were attached along the
pipe spring-line and hence measured the strain distribution on both active and passive sides of the
pipe. The strain gages were wired as a Quarter Bridge so that both axial and bending strains were
captured. In model 2 and 4, the pipe was instrumented with tactile pressure sensor manufactured by
TEKSCAN Inc. The sensor sheet (Model 5250 by TELSCAN) was wrapped around the testing pipe
for a distance of 0.25m (model scale, 3m in prototype) on either side of the fault. The tactile sensor
sheet measures the normal pressure at the soil-pipe interface. Fig. 4 shows the pictures of the both
types of instrumentations in a partially prepared pipe model (Note: top soil backfill yet to be placed).
The model pipe on the left was instrumented with strain gages while the one on the right was instrumented with tactile pressure sensors.
6
(a) Strain gage instrumentation
(b) Tactile pressure sensor instrumentation
Fig. 4. Testing pipe in the split container, prior to backfilling.
All tests were conducted on high density polyethylene (HDPE) pipe which satisfies AWWA
standard C901 for water service. The pipe has an outside diameter (OD) = 33.4 mm and a wall
thickness t = 1.96 mm (SDR = 17). Since all the centrifuge tests were carried out at a g level of 12.2,
they simulate a prototype pipe with OD = 407.5 mm and t = 24.0 mm. Due to the direction of offset,
flexural strain and greater or lesser amounts of axial strain, were induced in the pipe.
Grain size effects on soil-structure interaction are an important issue in centrifuge modeling. In
this study the backfill material was processed so as to guarantee that no significant grain size effect
was expected. The soil used in the Rensselaer centrifuge tests were sieved from a glacio-fluvial, well
graded sand. The original sand was sieved to produce sand suitable for centrifuge testing, and soil
passing the #40 sieve (0.42 mm), but retained on the #200 sieve (0.075 mm) was kept. The sieving
process resulted in very uniform sub-angular or sub-rounded quartz grains with an average grain size
diameter of 0.29mm. Hence, a pipe outside diameter to average grain size ratio OD/D50 = 115 was
reached, which satisfied the criterion of OD/D50 ≥ 48 recommended by the International Technical
Committee TC2 (2005) based on the centrifuge test data from Ovesen (1981), and Dickin and Leung
(1983). Table 2 lists the properties of the sand used in this series of the centrifuge tests.
7
Table 2. Material Properties for Sand Backfill
Soil Properties
Quantities
Unit Weight) (kN/m3)
14.7
c, (Cohesion) (kPa)
0
, Friction Angle (deg)
40
D50, (average particle size) (mm)
0.29
Cu, (coefficient of uniformity)
1.55
Cc, (coefficient of curvature)
1.0
The sieved sand was moistened to get a water content of about 4～5%, which represents a common condition in the field. The moisture content of the soil is considered particularly important
since full scale tests by Turner (2004) show that moist sand has almost twice the lateral resistance of
dry sand.
The moist sand was compacted to reach a dry unit weight of 14.7 kN/m3 (friction angle = 40o)
and filled up to 1.12 m (in prototype) above the center line of the pipe (H/D = 2.8). Both the filling
and compacting was done by layers. During the test the movable portion of the container was offset
horizontally about 1 m in prototype.
As noted above, the pipe is made of high density polyethylene for which the stress-strain behavior is strain rate dependent (Merry and Bray, 1997). Prior to the centrifuge tests with soil backfill,
pure tension test were carried out on the pipe using the split container without soil. Strain gages
were mounted at the middle of the pipe to measure induced strains during the offset. Fig. 5 shows
the stress-strain relations for the HDPE material at different strain rates from the Rensselaer tests as
well as corresponding values from the literature (Merry and Bray, 1997). As shown in the figure the
stress-strain relationship of the material is very strain-rate dependent with stiffness or secant modulus increasing with strain rate. The stress-strain information is presented in a different format in Fig.
6. The HDPE secant modulus evaluated at three particular strain levels, are superimposed on a se8
cant modulus versus strain rate plot from Merry and Bray (1997). The secant modulus measured in
the slow tension test (0.1%/min) is about half of the value measured in the fast tension test
(300%/min).
The offset rate used in the centrifuge tests is 0.318m/min, which corresponds to a strain rate
around 1%/min in the pure tension (no soil) tests. An upper bound for the expected prototype offset
rate is around 1m/sec (60m/min), which corresponds to a pure tension test strain rate around
190%/min. Hence, the offset rate used in this series of centrifuge tests was much smaller than the
expected prototype offset rate by a factor of almost 200. This offset rate for the centrifuge tests was
chosen to allow comparison with full scale tests on the same HDPE pipe material being conducted at
Cornell University. That is, there are physical limitations for the offset rate achievable in the full
scale tests at Cornell. Since the HDPE material is very strain rate dependent, comparison between
centrifuge pipe strain and full scale pipe strains require the same offset rate. Further research will be
conducted to investigate the effect of fault offset rate on the HDPE pipe response to PGD. Note that
although the pipe material is strain rate dependent, the soil-structure interaction forces apparently are
not. For example, Turner (2004) investigated the influence of loading rate on the soil-pipe interaction with three loading rates of 0.03mm/sec, 0.3mm/sec and 25mm/sec and found that the influence
of loading rate is almost neglectable.
9
25
Hypobolic Fit (Merry & Bray, 1997)
RPI Uniaxial Tension Test
300%/min
20
Axial Stress (MPa)
130%/min
300%/min
100%/min
15
10%/min
1%/min
1%/min
0.1%/min
10
0.16%/min
5
0
0
1
2
3
4
Axial Strain (%)
Fig. 5. Stress-strain relation of HDPE at different strain rate.
20
secant moduli are evaluated
at strains denoted in legend
Secant Modulus (MPa/%)
10
9
8
7
6
5
4
3
Merry and Bray 0.5%
Merry and Bray 1.0%
Merry and Bray 2.0%
RPI 0.5%
RPI 1.0%
RPI 2.0%
2
1
1000
100
10
1
0.1
0.01
0.001
0.0001
Strain Rate (% per minute)
Fig. 6. Secant modulus of HDPE at different strain rate.
10
The pipe was pinned to the split container end wall. As such, the centrifuge tests simulate the
case where a thrust or anchor block is located at the end wall. The tension force at the end of the
pipe was measured by a load cell during the offset.
Pipe Axial and Bending Strains
Fig. 7 shows the measured axial and bending strains in pipe models 1 and 3. At small offsets,
where the pipe material can be treated as elastic, there is a linear decrease in axial strain with distance from the fault. This is consistent with a constant longitudinal friction force per unit length at
the soil-pipe interface. At large offsets, where the pipe material is inelastic, the axial strain vs. distance plot is more convex. For inelastic material this is also consistent with a constant friction force
per unit length at soil-pipe interface. For a given offset, the bending strain are consistent with double
curvature bending, as sketched in Fig. 3, concave on one side of the fault and convex on the other.
The fault offset was discomposed into two components: one is parallel to the original pipe longitudinal axis, and the other perpendicular to the initial pipeline orientation (Fig. 8). The peak axial
and bending strains were plotted versus the longitudinal and transverse offsets, respectively, in Fig.
9. Note the peak axial strain vs. longitudinal offset plots for both model 1( = -85o) and model 3 (
= -63.5o) are essentially the same curve. Similarly, the peak bending strain vs. transverse offset plots
for model 1 and 3 are essentially the same curve. Note that the axial strain measured in test model
1( = -85o) is much smaller than the axial strain measured in model 3 ( = -63.5o). All the axial
strains measured from model 1 ( = -85o) are less than 1% and are more or less proportional to the
offset. In model 3 ( = -63.5o) there is a slight deviation from linear behavior (slight hardening) for
the level of longitudinal offset larger than 0.3 m. The peak bending stains measured from model 1 is
only slightly larger than the peak bending strains measured in model 3 and both have a peak final
bending strain at a distance of about 1.2m from the fault. In relation to the peak bending strains, we
11
get slight deviation from linear behavior (slight softening) at lower levels of fault offset and no increase in peak flexural strain (plateau) for transverse offset greater than 0.7 m.
6
Axial Strain (%)
 = -85o
 = -63.5o
0.122m
0.244m
0.488m
0.732m
1.06m
4
2
0
2
Bending Strain (%)
 = -85o
 = -63.5o
1
0
-1
-2
-6
-4
-2
0
2
4
6
Distance from Fault (m)
-6
-4
-2
0
2
4
6
Distance from Fault (m)
Fig. 7. Axial and bending strain of testing pipe in model 1 and 3.
12
Fault
l = f*cos

t = f*sin
f
Pipeline
Fault

t = f*sin
Pipeline
Fig. 8. Decomposing of fault offset in to two components.
3
6
= -63.5
= -63.5o
o
Peak Bending Strain (%)
Peak Axial Strain (%)
= -85o
4
2
= -85o
2
1
0
0
0
0.2
0.4
Longitudinal Offset (m)
0.6
0
0.4
0.8
1.2
Transverse Offset (m)
Fig. 9. Peak axial and bending strains versus longitudinal and transverse offsets, respectively.
Fig. 10 shows the axial force measured at the end of the testing pipe for both model 1 and 3. The
axial force measured in model 1 ( = 85o) is much less than that measured in model 3 ( = 63.5o).
At the final offset, the peak axial force measured is about 140 kN in model 1 and 330 kN in Model
3.
13
400
 = -63.5o
End Force (kN)
300
200
 = -85o
100
0
0
0.4
0.8
1.2
Offset (m)
Fig. 10. Force at the end of the testing pipe in model 1 and 3.
The final end force values in Fig. 10 may look incorrect at the first glance. That is, the end force
should equal the axial strain in the pipe near the split container end wall times the axial rigidity, EA,
of the pipe (i.e. F = EA). According to Fig. 7 the final axial strains near the end of pipe are: a=
3.3% in model 1 and a= 0.7% in model 3 (a factor of 4.7). However, according to the Fig. 10, the
end forces differ only by about a factor of 2.3 at the final offset of 1.06m. The difference is explained by the fact that the material is inelastic (i.e. E is not a constant). As shown in Fig. 6 the corresponding secant modulus for a= 3.3% and a= 0.7% differ by a factor of around 0.5, which explains the difference in the end forces (i.e. 4.7 * 0.5 ≈ 2.3). Finally, the shapes of the curves in Fig.
10 are very similar to the stress-strain relation for HDPE material. This is because the axial strain at
the end of pipe is more or less proportional to the fault offset (Fig. 7), and the axial stress at the end
of the pipe is proportional to the end force.
Soil-Pipe Interaction Pressure
As noted above, tactile pressure sensors were used in models 2 and 4 to measure the normal pressure at the soil pipe interface. Fig. 11 shows one snapshot of data (i.e. for a given offset) from the
14
tactile pressure sensor. Fig. 12 is a sketch showing where the data in Fig. 11 is located on the pipe.
Each column in the data snapshot represents the pressure at one cross section of the pipe. Hence,
the pressure matrix on the screen shows the normal pressure distribution around the circumference
and along the length of the covered portion of the test pipe for one fixed value of the offset. The far
right in the sensor window represents the fault plane location, while the far left represents a location about 3.0m away from the fault. The tactile sensor continuously records during the test; hence
the development of soil pressure both around the circumference and along the pipe as a function of
the offset can be tracked.
Fig. 11 One snapshot of data from the tactile pressure sensor.
Bottom of sensor
display window
Top of Pipe
Top of sensor
display window
Passive
Zone
Active
Zone
Bottom of Pipe
Fig. 12 Sketch of different pressure zones on the pipe.
15
Fig. 13 shows the recorded data at one cross section of the pipe (i.e. along a vertical line in the
pressure matrix) in model 4 ( = 63.5o) at offset = 1.06m. Pressure is measured at 19 locations (each
about 19o apart) around the pipe circumference. The pressure is a maximum at the springline on the
passive side, being about 10 times the at-rest pressure of  = h = 14.7*1.12 = 16.5 kPa.
(kPa) 1
Top
19 200
18
2
3
160
120
17
Passive
Zone
4
Active
Zone
80
16
5
40
Passive
Springline 15
Active
6 Springline
0
14
7
13
8
12
9
11
10
Bottom
Fig. 13 Pressure distribution at the cross section 0.3m from the fault (model 4, = -63.5o, Offset = 1.06m).
Fig. 14 shows a group of figures like Fig. 13 with different locations and offsets. The development of normal pressure around and along the pipe can be seen. The first row of figures represent
the moment before offset. Hence, the normal pressure measured around the pipe should be more or
less the soil pressure at rest, 16.5 kPa. This is difficult to confirm exactly since the maximum scale
of the plot as in Fig. 13 is 200kPa. As expected, at a fixed location (i.e. fixed distance from the fault
location) the normal pressure tends to increase with offset. Correspondingly, for a fixed offset the
normal pressure tends to decrease with distance from the fault plane. For example, as shown in Fig.
16
14, at 0.31 m from the fault the maximum normal pressure of about 155 kPa is reached at an offset
of 0.488 m and remains more or less constant for larger offsets. While at 0.93 m from the faults, the
peak pressure occurs at an offset of 1.06 m.
Fig. 14 Pressure distribution at different cross sections of the pipe (model 4,= -63.5o).
The pressure distribution at each cross section can be integrated to obtain the lateral force distribution along the pipe. Fig. 15 shows the model in which there is a normal pressure p(), which can
be measured by the tactile pressure sensor, acting on a small arc length R*d. In general, one also
expects a friction pressure to be acting on the same differential length. However, since the tactile
pressure sensor does not measure tangential pressure, a coefficient of friction needs to be assumed.
Taking the horizontal component of each, and integrating around the circumference, the lateral force
per unit length of pipe, Ph is determined as given in Eq. 1
17
p
p (normal pressure)
f (tangential friction
pressure)
A
R
A

d
O
Ph

O
Assuming Coulomb friction: f = p
Fig. 15 Sketch of the assumptions and equations used in integrating the normal pressure.
2
2
0
0
Ph   Rp  cosd   Rp  sin d
(1)
As noted above, a friction coefficient needs to be assumed.A value of = 0was used here as a
lower bound with an expected value of  = 0.4 (= 22o) for HDPE-sand interface. Figs. 16 and 17
show the resulting pipe lateral force per unit length. As one might expect, the pipe lateral force generally decreases with increasing distance from fault, generally increases with offset and is larger for
 = 0.4 than for the lower bound of  = 0. Comparing Figs. 17 and 16, one can see that including
friction increases the soil-pipe interaction force by about 30%. For a given offset and distance from
the fault, the lateral force on the pipe is larger for = -85o than for = -63.5o. For example, at 1.25
m from the fault, the pipe lateral force for = 0 ranges from 10 kN/m to 41 kN/m for = -85o,
while for = -63.5o it ranges from 5 kN/m to 30 kN/m. Some of the difference is likely due to geometry. First of all, as noted in relation to Fig. 8, the transverse component of the offset for = -85o
is about 10% higher than for = -63.5o. Also, assuming that the net horizontal pipe force is parallel
to the fault trace direction as sketched in Fig. 18, the force is almost all transverse for = -85o,
while for = -63.5o the force has both a transverse and longitudinal components. The transverse
component is proportional to the sine of the angle, (sin 63.5o = 0.89). Hence, one expects about a
18
10% difference due to force decomposition, or about 20% difference due to combined displacement
offset and force decompositions.
For high offsets, the lateral pipe force reaches a plateau at locations close to the fault. As an example, for = 0.4 the plateau is about 70 kN/m for = -85o and 58 kN/m = -63.5o. This plateau
for the lateral pipe force is consistent with a maximum value for the normal pressure as noted in relation to Fig. 14. Some of the difference (about half of the 20% difference) in the plateau values for
different pipe-fault angles can be attributed to force decomposition as sketched in Fig. 18. Due to
the nature of the plateau, constant force for increasing offset, the displacement decomposition effect
sketched in Fig. 8 doesn’t contribute.
Pipe Lateral Force (kN/m)
80
1.06m
0.732m
0.488m
0.244m
0.122m
= -85o
=0
60
1.06m
0.732m
0.488m
0.244m
0.122m
= -63.5o
=0
40
20
0
0
1
2
3
Distance from Fault (m)
4
0
1
2
3
4
Distance from Fault (m)
Fig. 16. Lateral force distribution along the pipe - assuming no friction ( = 0).
19
Pipe Lateral Force (kN/m)
100
= -85o
 = 0.4
= -63.5o
 = 0.4
1.06m
0.732m
0.488m
0.244m
0.122m
80
1.06m
0.732m
0.488m
0.244m
0.122m
60
40
20
0
0
1
2
3
4
0
1
2
3
4
Distance from Fault (m)
Distance from Fault (m)
Fig. 17. Lateral force distribution along the pipe - considering pipe-soil friction ( = 0.4).
Direction of Faulting

fl
f
f
ft= f*sin
Total Soil resistance, f assumed to be parallel to
the fault trace direction
Fig. 18. Total soil resistance and its components.
From mechanics of materials, we have the following relation between bending strain and curvature:
b  c
d2y
dx 2
(2)
where, b = extreme fiber bending strain and c = distance to the extreme fiber (outside radius for our
circular pipe specimen). Hence, the deflection of the pipe perpendicular to the pipe longitudinal axis
is obtained by double integration of the bending strain:
20
y  
b
(3)
c
Figure 19 shows the resulting deflection of the pipe at both -85o and -63.5o tests. Note that because
of symmetry, only pipe deflections on one side of the fault are shown. As expected, for both models
1 and 3 the transverse deflection (perpendicular to longitudinal pipe axis) decreases from its maximum value at the fault to zero at the pin-end connection at the split container wall.
0.6
Pipe Deflection (m)
= -85o
= -63.5o
0.122m
0.244m
0.488m
0.732m
1.06m
0.4
0.122m
0.244m
0.488m
0.732m
1.06m
0.2
0
0
2
4
6
Distance from Fault (m)
8
0
2
4
6
8
Distance from Fault (m)
Fig. 19. Pipe deflection at different offset level.
Combining the information in Figures 17 and 19, the transverse force-deformation or “p-y relation” for the pipe, can be determined. The p-y relations for the two different pipe–fault orientation
angles are shown in Fig. 20 for  = 0. The p-y data points are divided into two groups: one in the
high force, large relative displacement region within 1.5 m from the fault; and the other in the lower
force, smaller relative displacement region beyond 1.5 m from the fault. Note from Fig. 7 the point
of maximum curvature is about 1.5m from the fault. As shown in Fig. 20, the p-y relation is not
unique along the length of the pipe. A stiffer p-y is observed at points closer to the fault and much
softer p-y relation is observed at points farther away. Also note the peak pipe lateral force from  = 85o case is higher than that from  = -63.5o case by about 20%. As noted above, some of this differ21
ence is likely attributable to the orientation of the pipe with respect to the direction of relative displacement. Fig. 21 shows the same p-y relation for a pipe-soil friction coefficient  = 0.4.
80
0 ~ 1.5m
> 1.5m
Pipe Lateral Force (kN/m)
= -85o
0 ~ 1.5m
> 1.5m
= -63.5o
60
40
20
H/D= 2.8
= 0
H/D= 2.8
= 0
0
0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
Displacement (m)
Displacement (m)
Fig. 20. p-y relation of pipe-soil interaction assuming no friction (values in the legends are the distance from fault).
100
0 ~ 1.5m
> 1.5m
Pipe Lateral Force (kN/m)
= -85o
0 ~ 1.5m
> 1.5m
= -63.5o
80
60
40
20
H/D= 2.8
= 0.4
H/D= 2.8
= 0.4
0
0
0.1
0.2
0.3
Displacement (m)
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
Displacement (m)
Fig. 21. p-y relation of pipe-soil interaction_ = 0.4 (values in the legends are the distance from fault).
For design purpose, the ASCE guideline (1984) provides a bi-linear relation for the transverse
pipe-soil interaction force, based in part on the results from full scale test on dry sand by Trautmann
22
and O’Rourke (1985). As shown by the solid curves in the insert of Fig. 22, the elasto-plastic relation is characterized by peak force per unit length, Ph
Pu  N qhH c D
(4)
and a relative displacement yu
yu  (0.07 ~ 0.10)( H c 
D
)
2
(Loose Sand)
(5)-a
yu  (0.03 ~ 0.05)( H c 
D
)
2
(Medium Dense Sand)
(5)-b
yu  (0.02 ~ 0.03)( H c 
D
)
2
(Dense Sand)
(5)-c
where Nqh is the dimensionless maximum lateral force;  is the effective unit weight of soil; Hc is the
depth of soil from the surface to the center of pipe; and D is the pipe diameter.
Recently, Turner (2004) performed similar full scale test for moist sand. In both cases, the tests
simulated plane strain conditions. That is, at any particular instant during the test all locations along
the test pipe experienced the same relative displacement with respect to the soil. Hence, in both the
Trautmann and O’Rourke tests and the Turner’s tests the pipe-soil interaction is more or less in a 2D condition, which is not a true representation of the in-situ condition for a pipe under faulting offset.
The parameter Nqh is a function of both soil friction angle  and dimensionless pipe depth (Hc/D).
For  = 40o and Hc/D = 2.8, the corresponding Nqh = 8.5 in the ASCE guideline, while Turner tests
suggest Nqh = 16.5 as shown in Fig. 22.
For the centrifuge tests presented herein,  = 15.3 kN/m3, Hc = 1.12 m, D = 0.408 m. Hence the
peak transverse force as per the ASCE guideline is 58.3 kN/m (Nqh = 8.5), while using Turner’s suggestion value for moist sand Pu = 113.1 kN/m (Nqh = 16.5). Using either approach, yu, for our case of
dense sand is 0.033 m.
23
Pu  N qh  H c D
y u  ( 0 .02 ~ 0 .03 )(H c 
D
)
2
P
Pu
yu
yu
2
yu
2
yu
Y
Pu
Fig. 22. Design chart for both dry and moist sand (from O’Rourke and Turner, 2006) and ASCE (1984) design equations.
Since the ASCE guideline (1984) is still commonly used by both practitioners and researchers,
the p-y data from this study was compared with both the ASCE guideline (1984) formulas and the
updated curves by Turner (2004). The results are presented in Fig. 23. Note that both the lateral
force and displacement were normalized. For the data from this study, only the p-y data close to the
fault (less than 1.5m from the fault) is used. The friction between the testing pipe and soil is taken
into account by assuming a = 0.4 at the HDPE-soil interface. Note that the p-y relation thus obtained is much softer than the p-y relation suggested by the ASCE guideline although the peak values are compatible corresponding to Nqh of roughly 8.5. The recommended values of Nqh by Turner
(2004) are about double the observed peak value of resistance. This means that under a similar condition (soil and pipe material, water content, H/D ratio and etc.), a pipeline design against horizontal
PGD using the ASCE guideline would tend to be conservative, particularly for smaller offsets while
24
a design following Turner’s recommendations may well be overly conservative and possibly uneconomical.
24
H/D = 2.8
ASCE Guideline (Dry Sand)
Turner, 2004 (Moist Sand)
This Study,  = 85o, = 0.4
20
Dimensionless Force, Nqh
This Study,  = 63.5o, = 0.4
16
12
8
4
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Dimensionless Displacement, y/D
Fig. 23. Measured p-y relation compared with the ASCE guideline (1984) (locations within 1.5 m from fault).
Conclusion
Four centrifuge tests were carried out to investigate the behavior of buried pipelines systems subject
to permanent ground deformations. The material properties of HDPE were investigated and compared well with values previously reported in the literature. For both orientation angles, the pipe
model is pinned to the split container walls, simulating a prototype with a thrust block somewhere
near the fault. The axial and bending strains in the pipe as well as the axial force at the end of the
pipe are measured during simulated fault offset. For our test geometry and boundary condition, the
pipe axial strain is nominally a linear function of the longitudinal component of fault offset. The
flexure strain has nominally an elasto-plastic behavior with respect to the transverse component of
fault offset. The instrumentation for the models included, for the first time in a centrifuge investiga25
tion, tactile pressure sensor. Normal pressure distribution along and around the pipe was obtained
from this sensor. P-y relations were calculated based on data from both strain gage and tactile pressure sensor with assumed values for the coefficient of friction. It appears that the underlying p-y relation varies along the length of the pipe. That is, a stiffer p-y relation is observed at points closer to
the fault and much softer p-y relation is observed at points farther away. The stiffer p-y relation, appropriate for locations moderately close to the fault, was compared with the ASCE guideline (1984)
and Turner’s recommendation for moist sand. In both these existing p-y relations, the transverse
“soil resistance” is characterized as an elasto-plastic spring-slider. It was found that the force level
for plastic behavior in the centrifuge tests compared favorablely with that in the ASCE guideline
(1984). The “slider” force level from the centrifuge tests was about half that predicted by Turner’s
relation. In the centrifuge tests, the apparent stiffness of the “spring” was about a tenth of that in the
ASCE (1984) relation, and about a twentieth of that in Turner’s relation.
Acknowledgment
This work was supported primarily by the George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) Program of the National Science Foundation. It is part of a collaboration
project involving full scale buried pipe tests at Cornell University and companion centrifuge tests at
Rensselaer. Dr. Yun Wook Choo from KAIST provided assistance in the preparation of centrifuge
models and in the performance of the tests themselves. The authors also acknowledge lab technicians at the Rensselaer Geotechnical Centrifuge Center and at the Cornell University Lifeline Facility for their help in conducting tests presented in this paper.
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