Factors Influencing the Behavior of Buried Pipelines Subjected to Earthquake Faulting
by
Tarek H. Abdoun, Da Ha, Michael J. O’Rourke, Michael D. Symans, Thomas D. O’Rourke;
Michael C. Palmer, and Harry E. Stewart
Affiliation:
Tarek H. Abdoun, Associate Professor, E-mail: abdout@rpi.edu
Da Ha, Doctoral Student, E-mail: had@rpi.edu
Michael J. O’Rourke, Professor, E-mail: orourm@rpi.edu
Michael D. Symans, Associate Professor, E-mail: symans@rpi.edu
Department of Civil and Environmental Engineering
Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Thomas D. O’Rourke, Professor, E-mail: tdo1@cornell.edu
Michael C. Palmer, Research Associate, E-mail: mcp5@cornell.edu
Harry E. Stewart, Associate Professor, E-mail: hes1@cornell.edu
School of Civil and Environmental Engineering
Cornell University, Ithaca, NY 14853-3501, USA
Corresponding Author:
Da Ha
JEC4049
Department of Civil and Environmental Engineering,
Rensselaer Polytechnic Institute
110 8th Street
Troy, NY 12180-3590, USA
Phone: 518 276 2064
Fax: 518 276 4833
Email: had@rpi.edu
ABSTRACT
Seismic ground faulting is a severe hazard for continuous buried pipelines. Over the years, researchers have attempted to understand pipe behavior, most frequently via numerical modeling
1
and simulation.
However, there has been little, if any, physical modeling and tests to verify the
numerical modeling approaches and assumptions.
This paper presents results of five pairs of
centrifuge tests designed to investigate the influence of various factors on the behavior of buried
HDPE pipelines subject to strike-slip faulting. Parameters considered are the soil moisture content, fault offset rate, relative burial depth (H/D), and pipe diameter. The centrifuge tests results
show that pipe behavior, specifically pipe strain is nominally not affected by the soil moisture
content and fault offset rate when the pipe is subject to strike-slip faulting. On the other hand,
the burial depth ratio (H/D) and pipe diameter both influence both peak pipe strain, and in some
cases, the ground soil failure pattern.
Introduction
Over the past 30 years, researchers have tried to understand the complex behavior of buried
pipelines subject to ground ruptures most often via numerical simulation. Unfortunately, there
was a lack of laboratory tests, either full scale or small scale centrifuge tests, which are needed to
validate and confirm numerical simulation assumption and results. Fortunately, a recent NEESRSG grant (Grant Number: CMS-0421142) provided an opportunity for Rensselaer Polytechnic Institute and Cornell University to conduct a comprehensive laboratory investigation on the behavior of buried pipeline subject to ground faulting. The tests utilized state of the art testing equipment and cutting-edge sensing technologies. Both full-scale and centrifuge tests were conducted
to simulate the situation of buried pipelines subject to ground faulting. Because of cost and other
considerations, more centrifuge tests were conducted than full scale tests. Some centrifuge tests
were used to directly compare with the full scale testing while others were used to study the influence of various parameters.
2
The response of continuous buried pipe to fault offset is a function of a number of parameters. Among the most important are the types of fault (e.g. normal faults, strike-slip faults) and
for strike-slip faults, the orientation of the pipe with respect to the fault trace. In previous papers,
researchers at Rensselaer Polytechnic Institute and Cornell University have addressed the influence of fault type (Abdoun, et al. 2008), the influence of angle between the pipe and fault for
strike-slip faults inducing net axial tension in the pipe (Ha, et al. 2007a), and the differences in
the pipe behavior for strike-slip faulting which induces net axial compression in the pipe (Ha, et
al. 2007b).
Herein, the influence of four potentially significant variables on the response of HDPE pipe
subject to strike-slip faulting is studied. The variables are fault offset rate, soil moisture content,
burial depth ratio, and pipe diameter.
Centrifuge Modeling of HDPE Pipe Response to PGD
The centrifuge tests reported herein were designed to evaluate the influence of various parameters on the behavior of buried HDPE pipelines subjected to strike-slip faulting. Table 1 is a
summary of the parameters for each of the five pairs of centrifuge tests, including the soil moisture content, the offset rate, burial depth (ground surface to pipe springline) and pipe diameter.
Table 1 also indicates the type of instrumentation used for each test. The parameters for each pair
of tests were identical except for the type of instrumentation.
For one of the two tests in each pair, the HDPE pipe was instrumented with strain gages along
the pipe springlines. They were used to measure the total longitudinal strain distribution on both
the active and passive sides of the pipe. The longitudinal strains are due to a combination of axial
and bending (flexural) strains. Axial strains were calculated as the average of the strain at opposite springlines. Bending strains were calculated as one-half the difference between the longitu-
3
dinal strains at opposite springlines. For the other test in each pair, the pipe was instrumented
with tactile pressure sensor sheets manufactured by TEKSCAN Inc. The sensor sheets were
wrapped around the test pipes for a longitudinal distance of 0.25 m at model scale (3.0 m in prototype) on either side of the fault. The pressure sensor sheet measures the pressure at the soil-pipe
interface, which is used to calculate the strength and stiffness of equivalent soil springs.
The
details about the tactile pressure sensor instrumentation and data interpretation can be found in a
separate paper (Ha et al., 2007a).
In all the tests, the fault offset was simulated using a recently upgraded hydraulic servocontrolled split-box container (inside dimension: 1.14 m x 0.76 m x 0.45 m) shown in Error!
Reference source not found.. The container is capable of simulating both vertical and horizontal
offset in flight, although only horizontal (strike-slip) offset were simulated in this series of test.
Additional information about the split container was presented by Ha et al. (2006).
Error! Reference source not found. also shows the high density polyethylene (HDPE) experimental pipeline before and after fault offset. In all tests, the initial angle between the pipe and
fault trace was 63.5o, and the right lateral offset results in net tension in the pipe. As shown in
Error! Reference source not found., during the test the movable portion of the container was
offset horizontally a total of 0.088 m in model scale and since all tests were conducted at a centrifugal gravity level of 12.2 g, this corresponding to a prototype offset of 1.06 m.
4
Table 1 Summary of Centrifuge Test Parameters (all dimensions in prototype scale)
Model
Number
Instrumentation
T_3
T_4
T_9
T_10
T_11
T_12
T_13
T_14
T_15
T_16
Wc, %
Gage
Tactile
Gage
Tactile
Gage
Tactile
Gage
Tactile
Gage
Tactile
4.0 ~ 4.5
4.0 ~ 4.5
4.0 ~ 4.5
4.0 ~ 4.5
0
0
3.5 ~ 4.0
3.5 ~ 4.0
3.5 ~ 4.0
3.5 ~ 4.0
Offset
Rate
(m/min)
0.318
0.318
41.3
41.3
0.318
0.318
0.318
0.318
0.318
0.318
H
(m)
1.12
1.12
1.12
1.12
1.12
1.12
2.4
2.4
1.12
1.12
D
(m)
H/D
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.19
0.19
2.8
2.8
2.8
2.8
2.8
2.8
6.0
6.0
5.9
5.9
Split Container
0.044m
0.044m
Fixed Portion
Test Pipe
0.64m
Deformed Pipe
Movable
Portion
63.5o
Movable
Portion
Fixed Portion
0.044m
0.044m
a) Before Offset
b) After Offset
Figure 1 Plan view of the centrifuge model before and after offset (dimensions in model scale).
The pipeline was pin-connected to the split container end walls. 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 strain gage instrumented connecter. Using the material
(aluminum alloy) properties, cross-sectional area and the measured strain, the pipe force at the
end wall can be readily calculated.
5
The larger diameter tests (T_3 through T_14) were conducted on HDPE pipe that complies
with AWWA Standard C901 (AWWA, 2003) for water service. The pipe has an outer diameter,
D = 33.4 mm and a wall thickness t = 1.96 mm (model scale), and hence a SDR (Standard Dimension Ratio) = D/t = 17. The small diameter tests (T_15 and T_16) were conduced on HDPE
pipe that complies with United States Food and Drug Administration (FDA) Specification CFR
21 177.1520. The pipe has an outer diameter, D = 15.9 mm and a wall thickness t = 1.59 mm
(model scale), and hence a SDR (Standard Dimension Ratio) = D/t = 10. Given a gravity level of
12.2 g, the large diameter pipe tests simulate a prototype pipe with D = 407.5 mm and t = 24.0
mm, while the small diameter pipe tests simulate a prototype pipe with D = 194.0 mm and t =
19.4 mm.
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 glaciofluvial, well graded sand to produce sand suitable for centrifuge testing. Soil passing the #40
sieve (0.42 mm), but retained on the #200 sieve (0.075 mm) was used in the testing. The sieving
process resulted in very uniform sub-angular or sub-rounded quartz grains with an average grain
size diameter of D50 = 0.29 mm. Hence, a pipe outer diameter to average grain size ratio D/D50 =
115 for the large diameter pipe, and D/D50 = 55 for the small diameter pipe were obtained. Hence
both pipes satisfied the criterion of D/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 centrifuge tests.
6
Table 2 Material Properties for Sand Backfill
Soil Properties
Value
′Dry Unit Weight) (kN/m3)
, Friction Angle (deg)
D50, (average particle size) (mm)
Cu, (coefficient of uniformity)
Cc, (coefficient of curvature)
14.7
40
0.29
1.55
1.0
The sieved sand was placed at water content (wc) of about 4.0%. This replicates the expected
burial conditional in the field. The moist sand was placed and compacted in layers to a dry unit
weight of 14.7 kN/m3 (internal peak friction angle = 40o, determined from direct shear test) and
to a prototype depth Hc of 1.12 m in all tests except T_13 and T_14. The sand was compacted using an aluminum compacter (weight = 18.7 N, width = 0.157 m, length = 0.310 m). The thickness of each compacted lift is about 2.5 cm (1 inch). The compacting is equivalent to raising the
compacter to a height of 10 cm and dropping it 10 times. Hence the input energy is about 384.2
J/m2.
Offset Rate Effect
High Density Polyethylene (HDPE) pipe is becoming more widely used for buried pipelines due to its excellent ductility. However, the HDPE material is strain rate dependent (i.e.
stiffener at higher strain rates) and centrifuge tests were undertaken to determine the influence of
this parameter with respect to fault crossing behavior.
The offset rate used in most of the centrifuge tests was 0.32 m/min, which corresponds to a
strain rate around 1%/min in the pure tension (no soil) tests. This offset rate for the centrifuge
tests was chosen so that comparisons could be made with full-scale test measurements at Cornell
University on the same HDPE pipe material in similar, partially saturated sand. However, an up-
7
per bound for the expected prototype (actual earthquake) offset rate is around 1 m/sec (60
m/min), which corresponds to a pure tension test strain rate around 190%/min. Hence, the offset
rate used in the Cornell tests and a majority of the centrifuge tests was much smaller than the expected prototype offset rate by a factor of 190.
In this series of centrifuge tests, two test pairs were conducted at different strain rates (one
pair at around 1%/min and another pair at around 190%/min) 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 moist sand backfill at
three loading rates of 0.03 mm/sec, 0.3 mm/sec and 25 mm/sec and found that the influence of
loading rate is almost negligible.
Measured pipe strains from both the fast and slow offset tests are presented in Figure 2. At
small offsets (offset less than about 0.25 m), where the pipe material is nearly linearly elastic,
and there is an approximately linear decrease in axial strain with distance from the fault. For an
elastic pipe, this is consistent with a constant longitudinal friction force per unit length at the
soil-pipe interface. At large offsets, the pipe material becomes highly nonlinear. Here the same
constant longitudinal friction per unit length results in a more convex axial strain versus distance
plot, with strain increasing at a more rapid rate near the fault trace. As shown in Figure 2, for a
given offset, the bending strain distribution is consistent with double curvature bending, concave
on one side of the fault and convex on the other. As one could expect, the locations of the peak
axial strains for both fast and slow test are at the fault location. The peak bending strains are located at about ±1.2 m from the fault.
The influence of fault offset on axial and bending strains can be studied in detail by decom-
8
posing the fault offset, f, into two components: one parallel (longitudinal offset) and one perpendicular (transverse offset) to the initial pipeline orientation (as shown in Figure 4). The peak
axial and bending strains are plotted versus the longitudinal offset, l, and transverse offset, t,
respectively, in Figure 4. Note that for both fast and slow offsets, the peak axial strain versus
longitudinal offset is the same straight line until the longitudinal offset exceeds 0.3 m (axial
strain of about 3%). However, the bending strain recorded in the fast offset rate test is almost always larger than the bending strain recorded in the slow offset rate test. At the maximum offset,
the peak bending strain in the fast offset test is about 30% more than the value in the slow offset
test. Hence the overall behavior of larger strains at faster offsets is consistent with HDPE material properties. However, it seems that the influence is stronger for flexural strains (peak flexural
strains in the 1.5 to 2.0% range) than for the axial strains (peak axial strain in the 4.5 to 5.0 %
range). This suggests that, in contrast to Turner’s findings, there may be a mild offset rate effect
in relation to the transverse strength and stiffness of the moist sand backfill.
9
10
 = -63.5o
Vo= 41.3m/min
Axial Strain (%)
8
 = -63.5o
Vo= 0.318m/min
0.122m
0.244m
0.488m
0.732m
1.06m
6
4
2
0
3
 = -63.5o
Vo= 41.3m/min
Bending Strain (%)
2
 = -63.5o
Vo= 0.318m/min
1
0
-1
-2
-3
-6
-4
-2
0
2
Distance from Fault (m)
4
6
-6
-4
-2
0
2
4
6
Distance from Fault (m)
Figure 2 Pipe axial and bending strains for two offset rates, plotted as functions of distance from the fault trace (tests
T_3 and T_9)
10
l = f*cos
t = f*sin
Fault

f
Pipeline Before Offset
Fault

t = f*sin
Pipeline After Offset
l = f*cos
Figure 3 Decomposition of fault offset into longitudinal parallel and transverse perpendicular components.
3
8
= -63.5 Fast
= -63.5o Fast
= -63.5o Slow
= -63.5o Slow
Peak Bending Strain (%)
Peak Axial Strain (%)
o
6
4
2
2
1
0
0
0
0.2
0.4
0.6
0
0.2
0.4
0.6
0.8
Longitudinal Offset (m)
Transverse Offset (m)
(a)
(b)
1
Figure 4 Peak pipe axial and bending strains for two offset rates, plotted as functions of the longitudinal and transverse offsets (tests T_3 and T_9)
Figure 5 shows the effect of fault offset rate upon the transverse soil-pipe interaction pressure.
An increase in the fault offset rate by a factor of around 130 results in only about 10% increase in
the peak soil-pipe interaction pressure. However, well away from the fault (i.e. points more than
1.5 m away from the fault) the soil-pipe interaction pressure for the fast offset rate test is higher
than that for the slow offset rate test. This is generally consistent with Figure 4(b), which shows
11
an increase in pipe bending strain with increased offset rate. Note that the pressure sensors record
normal pressure only. As described in more details by Ha et al. (2007) one needs to assume a
friction coefficient in order to calculate the total lateral force or pressure acting on the pipe. In
Figure 5 and later figures showing the pressure sensor data, results for an assumed friction coefficient of  = 0.4 are presented.
For design purposes, the ASCE Guidelines (1984) provide a bi-linear relationship for the
transverse pipe-soil interaction force, based in part on the results from full scale two-dimensional
tests on dry sand by Trautmann and O’Rourke (1985). The peak lateral force per unit length on
the pipe, Pu:
Pu  N qhH c D
(1)
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 the pipe; and D is the pipe outer diameter.
The parameter Nqh is a function of both the soil internal friction angle  and the dimensionless
pipe depth (H/D). For the tests shown in Figure 5, the soil internal friction angle  = 40o, and
H/D = 2.8 (Hc = 1.12 m and D = 0.408 m), for which the corresponding Nqh = 8.5 in the ASCE
Guidelines for dry sand. Hence for an effective unit weight of the soil backfill  = 15.3 kN/m3,
the peak transverse force as per the ASCE guideline (Nqh = 8.5) is 58.3 kN/m.
As shown in Figure 5 ( = 0.4 assumed), the peak lateral force per unit length from the
ASCE Guidelines (1984) (dash line without symbols) compares well with measured peak lateral
force on the HDPE pipe at locations close to the fault.
12
Pipe Lateral Force_=0.4 (kN/m)
80
= -63.5o
Fast Offset
Pu = HNqhD = 59.0 kN/m
60
= -63.5o
Slow Offset
1.06 m
0.49 m
0.73 m
0.24 m
0.12 m
40
20
0
0
1
2
3
Distance from Fault (m)
4
0
1
2
3
4
Distance from Fault (m)
Figure 5 Lateral force distribution along the pipe for two offset rates (tests T_4 and T_10)
Finally, photographs of the ground surface were taken after centrifuge spin-down. For the tests
with different offset rate there is no obvious difference in the ground failure mode. Therefore, the
details of the ground failure mode in these tests are presented later with the comparisons with
tests using dry sand as backfill material.
Soil Moisture Content Effect
As noted above, most of the available relations for equivalent soil spring, such as those in the
ASCE Guidelines (1984), were based upon laboratory tests in dry sand. However, the typical insitu pipe burial condition corresponds to moist soil backfill. A pair of centrifuge test was performed to evaluate the influence, if any, of soil moisture content upon buried pipe response to
fault offsets.
13
Observations were made of the ground surface after centrifuge spin-down in both the moist
sand (test T_3) and the dry sand (test T_11) test. As shown in Figure 6, different ground surface
deformation patterns were observed. For both moist and dry sand tests there was soil disturbance
within a narrow band at the fault. Similarly, for both moist and dry sand tests at H/D = 2.8, there
were large cracks nominally parallel to the pipe on the passive side (indicated in Figure 6 as dotted lines). These cracks appear to be the surface expressions of passive soil wedges, mobilized as
the pipe displaces through the soil at a moderate H/D ratio. However, for the moist sand test, additional cracks also appear between the outermost surface expression of the passive soil blocks
and the trace of pipeline, likely due to soil heaving during the soil wedge formation process.
These additional cracks were not observed in the dry sand tests presumably due to the absence of
capillary effects in the dry soil.
(a) Moist Sand Backfill
(b) Dry Sand Backifll
Figure 6 Post-test surface condition for moist and dry sand tests (tests T_3 and T_11)
The effect of soil moisture content on the pipe strains can be clearly observed from the
comparisons in Figure 7 and Figure 8. Using dry sand as the backfill material does not appreciably change either the axial or bending strains on the HDPE pipe, in comparison with moist sand
14
backfill. As indicated by Figure 8, the peak axial strain on the pipe using dry sand backfill is only
about 5% higher than the peak axial strain obtained in the moist sand test. At small offsets, the
bending strain recorded in the dry sand test is slightly smaller than the bending strain recorded in
the moist sand test. However, the peak bending strain recorded in the dry sand test is about 13%
higher than that recorded in the moist sand test. The locations of the peak strains for both dry
sand test and moist sand test are nominally the same.
15
10
Axial Strain (%)
8
 = -63.5o
Moist Sand
0.122m
0.244m
0.488m
0.732m
1.06m
 = -63.5o
Dry Sand
6
4
2
0
3
 = -63.5o
Dry Sand
Bending Strain (%)
2
 = -63.5o
Moist Sand
1
0
-1
-2
-3
-6
-4
-2
0
2
Distance from Fault (m)
4
6
-6
-4
-2
0
2
4
6
Distance from Fault (m)
Figure 7 Pipe axial and bending strains for moist and dry sand tests, plotted as functions of distance from the fault
trace (tests T_3 and T_11)
16
3
8
Peak Bending Strain (%)
Peak Axial Strain (%)
Dry Sand
Moist Sand
6
4
2
Dry Sand
Moist Sand
2
1
0
0
0
0.2
0.4
Longitudinal Offset (m)
0.6
0
0.2
0.4
0.6
0.8
1
Transverse Offset (m)
Figure 8 Peak pipe axial and bending strains for moist and dry sand tests, plotted as functions of the longitudinal and
transverse offsets (tests T_3 and T_11)
Figure 9 shows the influence of soil moisture content on the transverse soil-pipe interaction pressure. The behavior is somewhat complex. At low offsets (less than 0.25 m) the transverse pressure at the fault in the moist soil test is some what larger than in the dry soil test. However, for prototype offset of 0.49 m and larger the reverse is true. This is generally consistent
with Figure 8(b) wherein at low offsets the flexural strains for moist sand test were larger, but not
at large offsets. In the dry sand test, the peak soil-pipe interaction pressure for the entire pipe occurs when the fault offset reaches about 0.73 m. When the fault offset reaches 1.06 m the soilpipe interaction pressure drops a little bit (less than 5%). In contrast, in the moist sand test, the
soil-pipe interaction pressure keeps increasing until the fault offset reaches its maximum value of
1.06 m. Although the influence of moisture content is complicated, the overall effect in terms of
changes in pipe strains is small.
17
80
Moist Sand
Pipe Lateral Force (kN/m)
Dry Sand
Pu = HNqhD = 59.0 kN/m
60
1.06 m
0.73 m
0.49 m
0.24 m
0.12 m
40
20
0
0
1
2
3
Distance from Fault (m)
4
0
1
2
3
4
Distance from Fault (m)
Figure 9 Lateral force distribution along the pipe for moist and dry sand tests (tests T_4 and T_12)
Effect of H/D Ratio
Intuitively, one would expect that the pipe burial depth would influence pipe behavior – the
deeper the burial depth, the stiffer and stronger the equivalent soil springs and the larger pipe
strains for a given fault offset. The influence of burial depth and specifically the burial depth to
pipe diameter ratio H/D was investigated by comparing the results from the pair of high H/D tests
(tests T_13 and T_14) with those from the moderate H/D tests (tests T_3 and T_4). Figure 10
shows that the ground surface after each test is quite different. For the higher H/D case, there is
no soil failure observed except at the fault trace itself. There are two possible explanations for
these observations. One explanation is that the soil “failed”, but the failure mode did not result in
observable wedge-type deformation at the ground surface. In other words, such deep burial failure mode corresponds to the pipe plowing through the soil at depth without any surface deformations. Another possible explanation is that the soil did not reach the limit state for either type
of failure (wedge or plow-through). Additional results which will be presented shortly suggest
18
the latter. On the other hand, the moderate H/D tests show the familiar ground cracks, presumably at the toe of the soil failure wedge.
H/D = 6.0
H/D = 2.8
Figure 10 Post-test surface condition, for different H/D values (tests T_3 and T_13)
The measured pipe strains are plotted versus distance from the fault in Figure 11, and
plotted versus the longitudinal and transverse offsets in Figure 12. As before, the axial strains are
larger than the flexural strains, at least in part due to the pin connector at the split container end
wall. Note that the end wall pin connections efficiently decrease the pipe length over which the
longitudinal offset is accommodated. At low offsets, the axial strains for deep burial depth are
not greatly different from those for moderate burial depth, although at the largest offset of 1.06
m, the difference is about 45% (6.8% axial strain for H/D = 6.0, 4.7% for H/D = 2.8). At moderate to larger offsets, the pipe forces and strains at the end wall for deep burial depth is somewhat
less than those for moderate burial depth, the reverse holds true near the fault. Note that the integral of axial pipe strain between the end walls by necessity equals the longitudinal offset for either deep or moderate burial depths.
19
For all but the lowest level offset, the pipe bending strains for deep burial are larger than
those for moderate burial depth, being about twice as large for the largest offset of 1.06 m. At
moderate burial depth, the pipe bending strain reaches its peak value at an offset of 0.73 m and
remains unchanged for larger offsets. In contrast, for the range of offsets in this series of tests, the
pipe bending strain for deep burial depth continue to increase with increasing offset.
The peak bending strains for deep burial (H/D = 6.0) is located at about ±0.6 m from the
fault, while for moderate burial (H/D = 2.8) the peak bending strains are located at about ±1.5 m
from the fault. That is, as the burial depth increases and the equivalent soil springs become
stronger, the pipe flexural deformation is concentrated closer to the fault.
Figure 13 shows the lateral force distribution along the pipe for both H/D = 6.0 and H/D
= 2.8. The measured peak values for both tests are similar. This, however, is not consistent with
Figure 11 and 12 which show bending strains for deep burial being substantially larger than those
for moderate burial. Note in this regard that the pipe lateral pressures for H/D = 6.0 were concentrated at locations very close to the fault trace, where the two tactile pressure sensor sheets abut.
Due to sensor interference, it is possible that the tactile pressure sensor readings from these near
fault locations may be incorrect.
The maximum lateral force per unit length suggested by the ASCE Guidelines (1984)
values is plotted in Figure 13 as dash lines. For moderate burial depth (H/D = 2.8), the lateral
force near the fault (less than 0.7 m from the fault trace) is nominally the ASCE Guidelines value. For offsets at or above 0.73 m, soil failure (wedge formation) occurs, the soil forces remain
nominally constant and the pipe bending strain remain nominally constant. Note in this regard
that for H/D = 2.8 the ground cracks in Figure 10 (presumably indicating the location of the toe
of the soil failure wedge) extend roughly 3.0 ~ 4.0 m (prototype scale) along the pipe. However,
20
the lateral pressure in Figure 13, again for H/D = 2.8, is less than a third of its peak value at about
2.0 m or more from the fault. Hence it appears that wedge formation is not a series of narrow 2-D
wedges which form at various separate locations away from the fault when the lateral soil pressure at that location reaches its maximum value. Rather, it appears that a single 3-D wedge, with
significant horizontal extent along the pipeline, forms when the lateral soil pressure near the fault
reaches a maximum value.
The corresponding situation for deep burial is unknown. The pipe bending strain in Figure 11 and 12 for H/D = 6.0 show increasing flexural strains up to the maximum offset of 1.06
m. This increasing flexural strain suggests that the lateral pressures on the pipe were increasing,
and that soil failure which would presumably limit the soil lateral force had yet to occur. That is,
tests with larger offsets would be needed to establish the soil failure mode for deep burial and the
corresponding triggering soil pressure.
21
10
 = -63.5o
H/D = 6.0
Axial Strain (%)
8
 = -63.5o
H/D = 2.8
0.122m
0.244m
0.488m
0.732m
1.06m
6
4
2
0
3
 = -63.5o
H/D = 6.0
Bending Strain (%)
2
 = -63.5o
H/D = 2.8
1
0
-1
-2
-3
-6
-4
-2
0
2
Distance from Fault (m)
4
6
-6
-4
-2
0
2
4
6
Distance from Fault (m)
Figure 11 Pipe axial and bending strains for deep and moderate burial, plotted as functions of distance from fault
trace (tests T_3 and T_13)
22
4
H/D = 6.0
H/D = 2.8
8
Peak Bending Strain (%)
Peak Axial Strain (%)
10
6
4
2
H/D = 6.0
H/D = 2.8
3
2
1
0
0
0
0.2
0.4
0
0.6
0.2
0.4
0.6
0.8
1
Transverse Offset (m)
Longitudinal Offset (m)
Figure 12 Peak axial and bending strains for deep and moderate burial, plotted as functions of the longitudinal and
transverse offsets (tests T_3 and T_13)
200
Pipe Lateral Force (kN/m)
Pu = HNqhD = 184.0 kN/m
H/D = 2.8
H/D = 6.0
160
120
1.06 m
0.73 m
0.49 m
0.24 m
0.12 m
80
Pu = HNqhD = 59.0 kN/m
40
0
0
1
2
3
Distance from Fault (m)
4
0
1
2
3
4
Distance from Fault (m)
Figure 13 Lateral force distribution along the pipe for deep and moderate burial (tests T_4 and T_14)
Effect of Pipe Diameter
To further investigate the effects of pipe diameter, a pair of centrifuge tests (tests T_15 and T_16) were also conducted, using a smaller diameter pipe (D = 0.19 m) with a burial ratio of H/D = 5.9.
23
Figure 14 shows the surface condition of the two tests with different pipe diameters. Note that
in the small diameter test (H/D = 5.9) soil passive failure (presumably wedge formation) was observed on one side of the split-container but not on the other side. This indicates that H/D = 5.9 is
possibly the boundary or limiting value for this type of pipe which appears to have a passive soil
failure at 1.06 m of fault offset.
(a) H/D = 6.0，D = 0.41 m
(b) H/D = 5.9, D = 0.19 m
Figure 14 Post-offset surface condition for large and small pipe diameters (tests T_13 and T_15)
The measured axial and bending strains for both the large and small pipe diameter tests
are presented in Figure 15 as a function of distance from the fault and the peak strains are plotted
in Figure 16 as a function of the longitudinal and transverse offsets. Although the diameters differ substantially, the measured axial strains are almost identical. Recall that, due to the pin connection at the split container end wall, the integral of pipe axial strain over the length of pipe between the end wall pin connections must match the overall longitudinal offset.
The peak values of the measured bending strains from both pairs of tests are located at the
same points (about ±0.6 m from the fault). The magnitudes of the bending strains are similar for
24
fault offset up to around 0.49 m. However, the bending strains magnitudes for the small diameter
(D = 0.19 m) test did not increase much beyond those for the 0.73 m offset. This is consistent
with the measured lateral force data presented in Figure 17. Note that for the small diameter tests,
the lateral force remains nominally at the same magnitude for offset of 0.73 m and beyond. Again
this suggests soil failure (wedge formation in the small diameter test) at an offset of about 0.73
m. On the other hand, the bending strain for the large diameter test showed no such upper limit,
and hence presumably no soil failure.
In relation to the measured lateral forces, the ASCE Guidelines (1984) suggested maximum lateral force values are plotted in Figure 17 in dash lines. Note that the relatively low pipe
lateral forces for the small diameter (D = 0.19 m) is due to the smaller diameter itself. That is the
measured maximum pressures from the small and large diameters (tests T_14 and T_16) are very
similar. As noted above, wedge formation apparently occurred (fully developed passive soil pressure) in the small diameter tests. However, as shown in Figure 17(b), the peak lateral force was
only about 60% of the value from the ASCE Guidelines (1984). On the other hand, since the pipe
bending strain for the large diameter (D = 0.4 m) test was still increasing at the largest test offset
of 1.06 m, it is unclear at what lateral force level soil failure would occur. That is, although the
peak measured lateral forces in Figure 17(a) are well below the ASCE Guidelines (1984) values,
tests at larger offsets would be needed to confirm or reject the guideline values.
25
10
 = -63.5o
H/D = 6.0
D = 0.41 m
D/t = 17
Axial Strain (%)
8
 = -63.5o
H/D = 5.9
D = 0.19 m
D/t = 10
0.122m
0.244m
0.488m
0.732m
1.06m
6
4
2
0
3
2
Bending Strain (%)
 = -63.5o
H/D = 5.9
D = 0.19 m
D/t = 10
 = -63.5o
H/D = 6.0
D = 0.41 m
D/t = 17
1
0
-1
-2
-3
-6
-4
-2
0
2
Distance from Fault (m)
4
6
-6
-4
-2
0
2
4
6
Distance from Fault (m)
Figure 15 Pipe axial and bending strain for deep burial at two diameters, plotted as functions of the distance from the
fault trace (tests T_13 and T_15)
26
4
H/D = 6.0, D = 0.41 m
H/D = 5.9, D = 0.19 m
8
Peak Bending Strain (%)
Peak Axial Strain (%)
10
6
4
2
H/D = 6.0, D = 0.41 m
H/D = 5.9, D = 0.19 m
3
2
1
0
0
0
0.2
0.4
0
0.6
0.2
0.4
0.6
0.8
1
Transverse Offset (m)
Longitudinal Offset (m)
Figure 16 Peak pipe axial and bending strains for deep burial at two diameters, plotted as functions of the longitudinal and transverse offsets (tests T_13 and T_15)
200
Pipe Lateral Force (kN/m)
Pu = HNqhD = 184.0 kN/m
H/D = 6.0
D = 0.41 m
160
H/D = 5.9
D = 0.19 m
1.06 m
0.73 m
0.49 m
0.24 m
0.12 m
120
80
Pu = HNqhD = 39.0 kN/m
40
0
0
1
2
3
Distance from Fault (m)
(a)
4
0
1
2
3
4
Distance from Fault (m)
(b)
Figure 17 Lateral force distribution along the pipe for deep burial at two diameters (tests T_14 and T_16)
27
Summary of Test Results
The peak axial and bending strains versus offset data from Figures 4, 8, 12 and 16 were plotted
again in Figure 18. Test data from the three tests with H/D = 2.8 were plotted in blue, data from
the test with H/D = 6.0 and D = 0.41 m were plotted in black and data from the test with H/D =
5.9 and D = 0.19 m were plotted in red. Note in the series of centrifuge tests reported herein, the
tests with H/D = 2.8, D = 0.41 m and moist sand backfill were considered as “standard”. The legend of Figure 18 shows only the parameters different from the “standard” tests.
As shown in Figure 18 the fault offset rate and soil moisture content do not have significant
influence on the pipe strains. For tests with the same H/D = 2.8, different fault offset rates, and
different soil moisture contents, the peak axial strains varies from 4.7% to 5.0%, and the peak
bending strains varies from 1.6% to 2.0%.
The relative burial depth (H/D) on the other hand, has an important influence on pipe strains.
An increase in H/D from 2.8 to 6.0 results in an increase in peak axial strain from 4.7% to 6.8%
(i.e. 45% increases), and an increase in peak bending strain from 1.6% to 3.0 % (i.e. 88% increases).
The pipe diameter also has a significant influence on pipe flexural strains. The two tests with
H/D around 6.0 have almost the same peak axial strains. However, for bending strain, the large
diameter tests resulted in roughly 50% more peak flexural strain in comparison to the small diameter tests with the same H/D ratio. This could partly be due to the fact that the small diameter
pipe has a small D/t ratio (D/t = 10) in comparison with the large diameter pipe (D/t = 17).
28
4
H/D = 6.0
H/D = 5.9, D = 0.19 m
H/D = 2.8, Dry Sand
H/D = 2.8, Fast Offset
H/D = 2.8
8
Peak Bending Strain (%)
Peak Axial Strain (%)
10
6
4
2
3
2
1
0
0
0
0.2
0.4
0.6
Longitudinal Offset (m)
0
0.2
0.4
0.6
0.8
1
Transverse Offset (m)
Figure 18 Peak axial and bending strains versus offsets, all tests
The measured peak lateral forces from the tactile pressure sensor are plotted versus the fault
offset in Figure 19. Data from the three pairs of tests with H/D = 2.8 are plotted in solid blue
lines. Data from the two pairs of tests with H/D around 6.0 were not plotted since the pressure
sensor readings close to the fault are open to question. The data in Figure 19 is consistent with
Figure 18(b), as the three blue lines (H/D = 2.8) are more or less the same and the peak force
reaches more or less a constant value at about 0.6 m of fault offset. The peak soil forces (for H/D
= 2.8) are in very good agreement with the ASCE Guidelines (1984) suggested values (indicated
in red dash line).
29
120
H/D= 2.8
H/D = 2.8, Fast Offset
H/D = 2.8, Dry Sand
ASCE Guidelines
Peak Force (kN/m)
100
80
60
40
20
0
0
0.4
0.8
1.2
Fault Offset (m)
Figure 19 Peak pipe lateral forces versus fault offsets, tests with H/D = 2.8
The measured axial strain data can also be used to obtain the longitudinal resistance tu (in unit
of force per unit length) due to the friction at the soil-pipe interface. Assuming the longitudinal
resistance is uniform along the pipe, the following relation exists between the axial strain in an
elastic pipe and the longitudinal resistance:
 a
t
 u
L AE
(2)
where, a is the change in the axial strain over a length of L along the length of pipe. The
modulus of elasticity for HDPE was tested and presented in previous paper (Ha, et al. 2007a).
Hence the value of tu can be estimated once the slope of the axial strain versus distance plot was
obtained. To minimize the influence of the lateral resistance on the axial strain readings and to
insure “elastic” pipe behavior, only the axial strain data from the smallest fault offset (i.e. 0.12
m) was used in the calculation. The symmetric axial strain data from both sides of fault was plot-
30
ted on top of each other and fitted with a straight line. Figure 20 shows the data and the linear fits
for both the moderate and deep burial cases.
0.8
0.8
0.6
Axial Strain (%)
0.6
Axial Strain (%)
H/D = 6.0, D = 0.4 m
H/D = 5.9, D = 0.19 m
H/D = 2.8, Slow Moist
H/D = 2.8, Fast Moist
H/D = 2.8, Slow Dry
0.4
0.4
0.2
0.2
0
0
0
2
4
6
0
2
4
6
Distance from Fault (m)
Distance from Fault (m)
Figure 20 Measured axial strains plotted as functions of distance from the fault trace
The ASCE Guidelines (1984) suggested the following equation for estimating the longitudinal
resistance:
tu 

2
DH (1  k o ) tan k
(3)
Where, D is the pipe diameter, H is the depth to the springline of the pipe, is the internal friction angle of sand backfill, ko is the coefficient of lateral soil pressure at rest, and k is the reduction factor depending on the outer-surface characteristics and hardness of the pipe. For normally
consolidated sand, the value of ko usually varies between 0.35 to 0.47. However, one expects the
value of ko to be larger due to the backfilling and compaction on the soil surrounding the pipe.
O’Rourke et al. (1985) recommended ko = 1.0 as a conservative estimate under most conditions
of pipeline burial. For concrete pipe, steel or cast iron pipe with concrete coating, k = 1.0, for cast
31
iron or rough steel, k ranges from 0.7 to 1.0, while for smooth steel or for a pipe with smooth,
relatively hard coating, k ranges from 0.5 to 0.7. By assuming ko = 1.0, the ASCE suggested values for the longitudinal resistance were calculated for two limiting values of k (i.e. k = 0.5 and k
= 0.7) for smooth pipe. Table 3 shows the calculated longitudinal resistance based on both centrifuge tests and the ASCE Guidelines. The experimental longitudinal resistance is generally consistent with the ASCE suggested values. Using k = 0.7 in numerical simulation generally results
in conservative (i.e. upper bound) estimate of pipe axial strain.
Table 3 Comparison of longitudinal resistance from centrifuge tests with ASCE suggested values
tu (kN/m)
Test
H/D
/L
A (m2)
E (MPa)
Centrifuge
Moist Slow
(T_3 & T-4)
Moist Fast
(T_9 & T_10)
Dry Slow
(T_11 & T_12)
Deep Large
(T_13 & T_14)
Deep Small
(T_15 & T_16)
ASCE
ASCE
(k = 0.5)
(k = 0.7)
2.8
0.0222
0.029
920
5.9
7.8
11.4
2.8
0.031
0.029
1280
11.5
7.8
11.4
2.8
0.0416
0.029
920
11.1
8.5
12.3
6.0
0.0503
0.029
920
13.4
16.8
24.5
5.9
0.0669
0.0107
920
6.6
3.7
5.4
Conclusion
Ten centrifuge tests were carried out to investigate the behavior of buried pipelines systems
subject to strike-slip faulting. Two tests with a slow fault offset rate, moist sand backfill and
moderate burial depth (H/D = 2.8) were used as a standard. Tests with a faster fault offset rate,
32
dry sand backfill and higher H/D values were used respectively to investigate the influence of
each individual parameter.
The test results show that fault offset rate and soil moisture content do not have significant influence on the amplitudes and locations of the peak strains, as well as the peak lateral forces on
the pipe. The relative burial depth (H/D) can significantly influence both the amplitudes and locations of the peak strains on the pipe. The pipeline diameter to thickness ratio (D/t) is also an
important influencing factor for the soil-pipe interaction.
The measured peak lateral force from the tactile pressure sensor compared well with values
suggested by the ASCE Guidelines (1984). The pipe axial strain data from strain gage measurements was used to estimate longitudinal resistance at the soil-pipe interface. The back calculated
longitudinal resistance is generally consistent with the ASCE Guidelines suggested values.
Acknowledgment
This work was supported primarily by the George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) Program of the National Science Foundation under Grant Nos. CMS0421142, CMS-0086555, and CMS-0217366. Any opinions, findings and conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the views
of the National Science Foundation.
This project is part of a collaborative project involving
full-scale buried pipe tests at Cornell University and companion centrifuge tests at Rensselaer.
Dr. Yun Wook Choo from Korea Advanced Institute of Science and Technology (KAIST) provided assistance in the preparation of centrifuge models and in conducting the tests. The authors
also acknowledge lab support personnel at the Rensselaer Geotechnical Centrifuge Center and at
the Cornell University Lifeline Facility for their help in conducting tests presented in this paper.
33
Notation
The following symbols are used in this paper:
Cc = coefficient of curvature
Cu = coefficient of uniformity
D
= pipe outer diameter
D50 = average particle size of sand backfill
H = depth of soil from the surface to the center of the pipe
Nqh = horizontal bearing capacity factor for sand
p
= soil resistance in horizontal transverse direction
Pu
= maximum soil resistance in the horizontal transverse direction
t
= pipe wall thickness
f
= maximum fault offset
l
= longitudinal component of fault offset
t
= transverse component of fault offset

= pipeline-fault orientation angle

effective unit weight of soil backfill
′
= dry unit weight of soil backfill
b bending strain in test pipe
  friction coefficient
  friction angle of sand backfill
34
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