Article

Physical Modeling of the Seismic Response of Gas Pipelines in Laterally Inhomogeneous Soil

Abstract and Figures

This paper reports on results from a series of 1-g, reduced-scale shake table tests of a 216-m-long portion of an onshore steel gas transmission pipeline embedded in horizontally layered soil. A set of first-order dynamic similitude laws was employed to scale system parameters appropriately. Two sands of different mean grain diameter and bulk density were used to assemble a compound symmetrical test soil consisting of three uniform blocks in a dense-loose-dense configuration. The sand-pipe interface friction coefficients were measured as 0.23 and 0.27. Modulated harmonics and recorded ground motions were applied as table excitation. To monitor the detailed longitudinal strain profiles in the model pipe, bare Fiber Bragg Grating (FBG) cables were deployed. In most cases, the pipe response was predominantly axial while bending became significant at stronger excitations. Strain distributions displayed clear peaks at or near the block interfaces, in accord with numerical predictions, with magnitudes increasing at resonant frequencies and with excitation level. By extension to full scale, peak axial strain amounted to 10−3, a demand half the yield strain, but not negligible given the low in situ soil stiffness contrast and soil-pipe friction.
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Physical modelling of the seismic response of gas
pipelines in laterally inhomogeneous soil
N. Psyrras1; A. Sextos2, M. ASCE; A. Crewe3; M. Dietz4; G. Mylonakis5, M. ASCE
Abstract: This paper reports on results from a series of 1-g, reduced-scale shake table tests of a 216m-
long portion of an onshore steel gas transmission pipeline embedded in horizontally layered soil. A set
of first-order dynamic similitude laws was employed to scale system parameters appropriately. Two
sands of different mean grain diameter and bulk density were used to assemble a compound symmetrical
test soil consisting of three uniform blocks in a dense-loose-dense configuration. The sand-pipe
interface friction coefficients were measured 0.23 and 0.27. Modulated harmonics and recorded ground
motions were applied as table excitation. To monitor the detailed longitudinal strain profiles in the
model pipe, bare Fiber Bragg Grating cables were deployed. In most cases, the pipe response was
predominantly axial while bending became significant at stronger excitations. Strain distributions
displayed clear peaks at or near the block interfaces, in accord with numerical predictions, with
magnitudes increasing at resonant frequencies and with excitation level. By extension to full-scale, peak
axial strain amounted to 10-3, a demand half the yield strain, but not negligible given the low in-situ soil
stiffness contrast and soil-pipe friction.
Author Keywords: gas pipelines, seismic excitation, inhomogeneous soil, shake table experiment
1 Ph.D. Candidate, Dept. of Civil Engineering, University of Bristol
2 Professor, Dept. of Civil Engineering, University of Bristol; M. ASCE
3 Reader, Dept. of Civil Engineering, University of Bristol
4 Research Fellow, Dept. of Civil Engineering, University of Bristol
5 Professor, Dept. of Civil Engineering, University of Bristol; M. ASCE
Introduction 1
The vulnerability of long-span structures to differential earthquake-induced ground motion is a 2
perennial topic of concern in engineering practice. Notably, attention is increasingly shifting towards 3
seismic protection of future-proof energy infrastructure assets like underground gas pipelines, reflecting 4
the global transition to cleaner energy sources. 5
Gas transmission pipelines cross terrain of variable morphology to move natural gas from wells to 6
storage facilities, power plants and urban distribution networks. Typology data on this class of pipes 7
can be sourced from Psyrras et al. (2019). Experience from past earthquakes suggests that damage 8
inflicted to transmission networks of this type can cause long service disruption and severe (often 9
difficult-to-predict) socioeconomic losses. While the majority of pipeline damage reported to date is 10
rightly attributed to permanent ground deformation (Chen et al. 2002; O’Rourke and Palmer 1996), 11
there is sufficient field evidence to suggest that seismic wave propagation is also a source of damage 12
(EQE Summary Report 1995; O’Rourke 2009; Sakurai and Takanashi 1969). Local buckling failures 13
in steel pipelines have been observed (Housner and Jennings 1972; O’Rourke and Liu 1999), in which 14
cases localized curvatures and strains can become large and lead to non-linear collapse of the section, 15
or even rupture and content leakage in the long run. 16
Pioneering works on soil-pipe interaction include those of Shinozuka and Koike (1979), Trautmann and 17
O’Rourke (1985) and O’Rourke and Hmadi (1988). In a seminal effort, Hindy and Novak (1979) 18
developed a matrix-based formulation of the dynamic equilibrium of a soil-pipe system to study the 19
elastic response of pipelines to seismic excitation both in homogeneous sites and in sites consisting of 20
laterally variable media. It was found that for body waves propagating along the pipeline, peak axial 21
and bending stresses occur near the boundary of the two media and are larger than those in homogeneous 22
sites. Predictions also revealed that bending stresses due to S-waves are much smaller than the axial 23
stresses due to P-waves. Nishio et al. (1980) and Nishio et al. (1983) conducted laboratory tests of 24
buried pipelines in valley and cut-and-fill settings subject to horizontal base excitation. Analytical 25
methods were used to study the strain response of buried pipelines laid through dipping soil layers 26
(Akiyoshi and Fuchida 1988; Liu and O’Rourke 1997), cut-and-fill embankments (Ando et al. 1992), 27
and multiple soil media (Liang 1995). Psyrras and Sextos (2017) present a comprehensive review on 28
multiple aspects of seismic safety of pipelines, including some recent advances in analysis and design 29
methods. More recently, a series of studies reported on the buckling potential of gas pipelines buried in 30
media with sharp stiffness transitions during seismic shaking (Psyrras et al. 2018, 2019a; Tsinidis et al. 31
2018); in these, non-linear finite element models were developed to analyze the factors that contribute 32
to the development of localized deformation in the pipe walls leading to plastic buckling, and to describe 33
the type of the resulting buckling response. Along the same vein, Yu et al. (2018) proposed elastic 34
analytical solutions for the dynamic bending response of tunnel liners running through dissimilar soils 35
due to harmonic shear waves and confirmed that demand in terms of internal forces increases with 36
increasing stiffness contrast across different soil layers. 37
However, experimental verification of pipeline strain concentrations in zones of changing soil 38
properties and the associated consequences for pipeline structural integrity, as predicted in the above 39
references, is quite limited. This is understood in light of the spatially extended character of the problem 40
and the difficulty in scaling down the prototype systems into manageable dimensions to test in the 41
laboratory with acceptable fidelity. This study is a contribution towards the lab-scale physical modelling 42
of dynamic axial soil-pipeline interaction in the case of a gas transmission pipeline running through 43
laterally non-homogeneous cohesionless soil, subjected to vertically propagating shear waves. The test 44
platform combined the 3m-by-3m shake table and the 5-m-long Equivalent Shear Beam soil chamber 45
(referred to as ESB hereafter) of the Earthquake and Large Structures (EQUALS) Laboratory at the 46
University of Bristol. The specific objectives of the test campaign were to 47
physically model the actual dynamic soil-pipe interaction (SPI) effects in the presence of lateral 48
gradients in soil properties; 49
measure the magnitude and distribution of the induced axial and bending strains along the pipe; 50
compare the experimental results with theoretical predictions; 51
infer the possibility of plastic buckling failure at prototype scale; 52
explore the role of the interface Coefficient of Friction (COF) as a mitigating factor. 53
This work aims at developing through new experimental data know-how on the mechanisms of axial 54
SPI in laterally inhomogeneous soil and its effects on high-pressure gas pipelines in seismically active 55
areas. The experimental setup used is briefly discussed in Psyrras et al. (2019b) and is elaborated here. 56
Experimental setup 57
Laboratory equipment 58
This study used the earthquake simulator at the EQUALS Laboratory at University of Bristol (Fig. 1a). 59
The shake table comprises a 3m×3m cast aluminum platform powered by 8 hydraulic actuators and is 60
able to excite all 6 DOFs simultaneously. Each actuator has a dynamic capacity of 70 kN and a 61
maximum stroke of 300 mm. The platform has a maximum payload of 15 Mg and is laid inside an 62
isolated reinforced concrete block weighing 300 Mg. The table can attain maximum horizontal 63
accelerations of 1.6g at 10 t payload, with operational frequencies in the range 0-100 Hz, depending on 64
the dead load. 65
To hold the test soil in place, the ESB developed by Crewe et al. (1995) was used. This apparatus is one 66
of a series of similar devices built in the 90s at the University of Bristol to enable physical modelling 67
of geotechnical systems under seismic shaking (Fig. 1b and c). The ESB is made of eleven RHS 68
aluminum rings, stacked alternately with soft rubber blocks to create a flexible hollow box measuring 69
4.81.2m×1.0m (L×H×W). Its relatively large size makes it an ideal candidate for pipeline testing in 70
an earthquake lab. Its floor is roughened with a thin sand layer to maximize shear wave transmission; 71
the internal end walls (in the short direction) are similarly treated, while the internal side-walls (in the 72
long direction) are lubricated to better approximate plane strain conditions. Rigid steel-restraining 73
frames support the side walls on a system of bearings to prevent undesirable motion in the transverse 74
direction. Designed to provide minimum resistance to shearing, the ESB allows the test soil to drive the 75
horizontal motion, while it offers minimum inertia thanks to its low weight, and sufficient soil 76
confinement for geostatic conditions to develop. When empty, its natural frequency has been measured 77
at 3.5 Hz. 78
Soil profiles and properties 79
To adequately reproduce the free field boundary conditions at the ESB ends, the same geomaterial 80
should be used in the vicinity of both end-walls to ensure the best possible coupling between the 81
compound soil mass and the ESB rings. To this end, the geological structure of the test soil had to utilize 82
reflection symmetry with respect to the mid-transverse vertical plane of the ESB. Common geological 83
formations in nature exhibiting lateral inhomogeneities are often sediment-filled valleys of various 84
shapes and aspect ratios; other possibilities include fault sites and cut-and-fill embankments. To 85
simplify the test configuration while retaining the essential components of the problem, a profile 86
consisting of three uniform equivoluminal blocks of sand in the long ESB direction was assembled, 87
with a stiffness contrast between the central block and its neighbors. This configuration guaranteed a 88
degree of lateral stiffness gradation, symmetry and feasibility of construction. 89
Two dry sand grades were used to form the 3-block profile: Leighton Buzzard sand fraction B (LBB) 90
and Silica Sand (SS). The first is an uncemented medium-coarse sand with rounded grains and well-91
documented properties (Cavallaro et al. 1992; Stroud 1971) and was readily available in the laboratory. 92
The second consists of uniform fine particles and was procured for the purposes of the experiment. 93
Index data for these sands obtained by sieve analysis are reported in Table 1. SS was on delivery found 94
to contain 2.2% water by weight, but this was judged too low to affect the drainage conditions. The 95
target was to prepare a dense-loose-dense configuration by filling the side blocks with LBB and the 96
middle one with SS, as illustrated in Fig. 2. By manipulating soil density and in light of its stress-97
dependency, soil stiffness could be controlled indirectly. More details on sand deposition are provided 98
in the ‘Specimen preparation’ section. 99
Scaling laws 100
Following the line of reasoning developed in Wood et al. 2002, a set of first-order similarity laws were 101
adopted to establish a valid connection between prototype and model, where not all physical quantities 102
obey dimensional analysis principles simultaneously. Like in many 1-g geotechnical models, physical 103
quantities chosen as independent were acceleration (by definition), length, mass density and material 104
stiffness. Scaling was dictated, on one hand, by the reduction of the prototype dimensions, which had 105
to be reasonably large to accommodate lateral variations in soil properties in a realistic way. Given the 106
ESB length, the linear scale for length was decided to be 30 (amounting to a full-scale length not 107
smaller than 30×4.8 = 144 m) to ensure adequate representation of the spatial extent of the problem. 108
The final value chosen was =45. On the other hand, a constraint inevitably enforced by the 109
simultaneous reduction in the pipe dimensions was the market availability of very thin sections. For the 110
convenience of having the same geomaterial in prototype and model, the scale factor for density was 111
unity. Based on the observation that the small-strain shear modulus of sands, , is related to the mean 112
effective confining stress,
, through a power law, empirically expressed as (
). (Hardin and 113
Drnevich 1972; Seed and Idriss 1970), the scale factors for all relevant variables were derived in Table 114
2. The order of derivation follows the listing order: from stress to strain to displacement to velocity to 115
time (=displacement/velocity) and frequency. Derivation of the velocity scale factor was based on the 116
consideration that the ratio of potential to kinetic energy from model to prototype must be preserved. 117
A modified version of the Transitgas pipeline crossing Switzerland was selected as the prototype. Its 118
section was redesigned for a lower operating pressure according to a typical safety factor, keeping the 119
same diameter and steel grade, in order to obtain a higher / ratio. The resulting pipe characteristics 120
were =900 ; = 8.7 ;  
103; = 1.5 ;  
= 0.57;  = 1.75; =200 ;
121
=448  ( being the burial depth to crown;
= 2/ the yield pressure;  the safety 122
factor). 123
The authors’ original goal was to experimentally observe plastic buckling effects in the model pipe 124
under test conditions, as predicted numerically in Psyrras et al. (2019). To achieve this in a consistent 125
manner, the scaled pipe should simultaneously obey similitude laws for parameters governing the mode 126
of buckling and the under-pressure collapse axial load, namely / ratio, / ratio, internal pressure 127
and the plastic material properties, if one ignores the role of geometric imperfections (Yun and 128
Kyriakides 1990). 129
An additional critical requirement at model scale would be a minimum pipe anchorage length to allow 130
mobilization of the downscaled collapse load of the model pipe section from frictional stresses at the 131
soil-pipe interface. This length is straightforward to determine analytically given the Coulomb friction 132
force per unit length at the centerline and the target collapse load. An iterative design process was 133
undertaken to find a suitable pipe section in the market to satisfy all, or nearly all, the above conditions. 134
This approach proved troublesome though as it required extremely thin metal alloy tube sections (<135
0.2 mm) that no supplier could provide. As a result, it was decided to restrict the model pipe deformation 136
in the elastic range and use a section that approximately retains secant stiffness similarity to the 137
prototype. Fig. 3 illustrates this idea; the nominal axial stress-axial deformation paths computed from 138
FE shell analysis for the prototype pipe are plotted for various levels of soil confinement and 139
imperfection amplitudes, and the critical (limit) loads are identified. A secant elastic modulus 
() is 140
calculated corresponding to the point of collapse at full scale, and the model scale analogue 
() is 141
deduced according to the adopted scaling rule (Fig. 3). As long as the actual elastic modulus of the 142
model material approximates 
(), a reasonable similarity in material stiffness is preserved. As can be 143
observed, the estimated scaled secant modulus ,
() for =45 approaches the typical range of 144
values for plastics; thus, unplasticized Polyvinyl Chloride (uPVC) was selected as the model pipe 145
material having an experimentally determined elastic modulus of about 2.1 GPa. Model pipe properties 146
are presented in Table 3. 147
Care was further taken to preserve dimensionless ratios controlling the pipe response. Because the 148
expected deformation mode of the pipe is alternating compression-extension, the relative soil-pipe axial 149
stiffness is a critical factor. This can be quantified by considering the axial flexibilities of an arbitrarily 150
long straight pipe, clamped at one end, and of an equivalent solid soil bar of equal length and diameter, 151
under uniaxial strain conditions. Then, the soil-to-pipe axial flexibility ratio can be expressed as 152
Fa=4 t
D
E
p
Es
1ν
p
(1+ν
s
)(12ν
s
)
(
1
νs
)
1+νp

1
2νp
(1)
where , and , are the elastic moduli and Poisson’s ratios of the soil and the pipe material, 153
respectively. Another influencing parameter is the stiffness contrast between the different soil regimes, 154
which may be correlated to the achieved density contrast  
between the two sands; the latter
155
ratio is preserved from model to prototype at any rate. Note that / cannot be preserved, but it is 156
rendered irrelevant since the model pipe response was designed to be elastic, without elastic buckling 157
being a concern. The ratio / was handled by the length scaling factor, while a separate dimensionless 158
ratio for internal pressure need not be considered since the effect of pressure was already accounted for 159
in 
(). In evaluating grain size effects, the criterion / 50 (: median grain size) is tested for 160
the two sands (Fioravante 2002). Fine-grained SS passes the test by a margin ( 
=141), with
161
LBB failing closely ( 
=32).
162
Specimen preparation 163
164 The ESB was securely bolted on the shake table and shaken lengthways. Installation of falsework in the 165
ESB was necessary to partition the three soil blocks throughout the pouring process. In order to maintain 166
a level of density control on the sand blocks, an inversestaged construction solution was opted for to 167
facilitate independent compaction of the blocks. A small-scale earth retaining wall system consisting of 168
steel sheets and timber studs was designed and fabricated to temporarily retain the side LBB blocks and 169
permit their compaction before SS was poured in the middle (Fig. 4a). The construction sequence was 170
as follows: the retaining structure was first placed in the ESB and restrained by timber guides; 208-liter 171
drums filled with LBB were crane-lifted above the ESB top and LBB was poured in 10~15 cm layers 172
in the side blocks, up to a target pipe bed elevation of 1005 mm (Fig. 4b). After each layer pouring, 173
LBB was compacted by persistent low amplitude white noise table vibration, as well as by hand, using 174
custom tamping tools, and the average density of the whole block was calculated from the soil mass 175
poured and the volume occupied. For the 6 layers of LBB below backfill, the cumulative densities 176
measured were 1.61, 1.67, 1.68, 1.62, 1.64 and 1.63 Mg/m3, showing good uniformity. Deposition of 177
SS in the middle compartment followed again in layers, combined with gradual uplift of the retaining 178
structure until its complete removal; SS layers were only slightly compacted and leveled (Fig. 4c)the 179
average density of this block was calculated at the end of pouring, since it was intended to be loose. 180
The pipeline specimen was then laid, the sensing instruments were installed and finally the backfill soil 181
was poured, spread and gently leveled to avoid sensor damage or dislocation. 182
The final free surface elevation was 1085 mm, leaving an embedment depth to pipe crown of roughly 183
60 mm. This violated the prototype / ratio of 1.67 but was necessary to ensure a sufficient degree of 184
confinement since the uppermost sand layers were unavoidably very loose. For LBB, the achieved mass 185
density was calculated at 1.63 Mg/m3 for the bed layer and 1.49 Mg/m3 for the backfill, while for SS it 186
was 1.40 Mg/m3 for the bed and 1.37 Mg/m3 for the backfill. A reason why a higher density state for 187
LBB was not achieved as in other tests (e.g., Taylor and Crewe 1996) may be that some local 188
disturbances were induced in the soil while pulling up the retaining structure during preparation. On 189
pulling up the retaining structure, lateral-downward sliding of soil grains was observed locally at the 190
block interfaces to fill the narrow voids formed. These disturbances were brief in time and might have 191
caused development of active lateral earth pressures. However, on pouring the overlying layers, the 192
stress state gradually reverted to at-rest values and further densification occurred due to the surcharge. 193
It is to be noted that, partly on grounds of ease of installation, the pipe ends were left unrestrained. 194
Under uniform ground excitation, this set of boundary conditions represents the most favorable of two 195
extremes in terms of induced axial strain in the pipe, the other being clamping one or both pipe ends. 196
The real condition lies between these two extremes, as the spatial continuation of the pipeline implies 197
a finite axial stiffness (and force) at the ends of the truncated portion of the pipe. The theoretical 198
argument behind this choice of boundary conditions is that, away from any lateral ground 199
heterogeneities or man-made boundaries (e.g., compressor stations), a straight pipeline is expected to 200
displace effectively as a rigid body in tandem with the soil mass under uniform ground excitation 201
parallel to the pipe axis. This study did not investigate the effect of other pipe end restraints on the pipe 202
response. 203
Instrumentation 204
Monitoring the deformation profile in the model pipe at multiple locations was an ideal application for 205
the use of state-of-the-art fiber optic sensors. Two identical Draw Tower Grating (DTG®) chains were 206
custom-ordered; these are spliceless, high-strength FBG cables of ultra-small diameter (125μm) 207
produced by drawing the optical fiber concurrently with inscribing the gratings. As shown in Fig. 5b, 208
cables C1 and C3 were attached to the crown and invert of the pipe, respectively, to monitor the total 209
longitudinal strains. Each one came with 25 strain sensors in a symmetrical configuration having a 210
biased distribution towards the soil block borders. Bonding of the cables on uPVC was achieved using 211
strong instant adhesive. The DTG cables were connected to a Micron Optics interrogator to acquire and 212
process the data. A second identical pipe specimen equipped with two horizontal arrays of resistance 213
strain gauges was also buried in a distance from the basic specimen to evaluate the accuracy of the FBG 214
measurements. A comparison is presented in Psyrras et al. (2019b), showing generally a very good 215
match between the measured strains. 216
Linear, high output acceleration transducers were also deployed to record accelerations in the shaking 217
direction at free-field, table and ESB top. A total of 13 free-field accelerometers were encapsulated in 218
miniature plastic boxes with artificially roughened external faces (via sand adhesion) to maximize 219
friction; 11 of them were aligned parallel to the pipe centerline and two of them were embedded deeper 220
to help extract estimates of the induced shear strains, as shown in Fig. 5a. One of the instruments was 221
secured to the shake table to measure the table motion and another at the third-from-the-top ring to help 222
evaluate the soil-ESB coupling. All deployed transducers are summarized in Table 4. 223
Testing protocol 224
Gaussian white noise with RMS amplitude of 0.02g was imposed as horizontal table excitation 225
strategically throughout the core testing sequence in an attempt to identify the modal characteristics of 226
the system. The seismic platform was first shaken with modulated harmonics (“sine dwells”) at 227
frequencies in the range 8.7-85.0 Hz, equivalent to a range of 0.5-5.0 Hz at full scale, and acceleration 228
amplitudes increasing from 0.01g to 0.1g. At each intensity level, motions were applied from the highest 229
to the lowest frequency to delay unavoidable dilation and contraction effects (Crewe et al. 1998). The 230
time histories of a typical white noise signal and a sine dwell are depicted in Fig. 6. 231
The second phase of the shaking protocol comprised a set of broadband signals in the form of time-232
compressed versions of recorded strong ground motions, with peak accelerations from 0.06g to 0.49g. 233
Since time was to be compressed by a factor of 0.06, a significant portion of the frequency content of 234
these motions was unavoidably shifted substantially higher (>50 Hz). However, this had implications 235
on the ability of the loaded table to reproduce these high-frequency motions, given that (i) it is a complex 236
hydraulic-mechanical system whose response to input is determined by a nonlinear transfer function 237
and (ii) it exhibits a cut-off frequency that drops significantly with increasing payload. Normally, an 238
iterative approach is taken to match the realized table motion to the target one; due to the risk of sample 239
disturbance and stiffness deterioration under strong excitations, this was not done here, but rather a suite 240
of pre-matched, deconvoluted motions from a previous testing program SERENA (Fiorentino et al. 241
2019) were used along with some unmatched target motions, whose frequency spectrum was scaled up 242
by a factor of 8.7 instead of the target 17.4. Table 5 lists the properties of these ground motions. 243
Test results 244
Data processing 245
The first operation performed on all raw signals acquired was removal of the mean; where a residual 246
response was observable, only the initial ordinate offset of the signal was subtracted. To convert voltage 247
fluctuations to time-histories of the desired physical parameters, the calibration factors listed in Table 248
4 were used ( stands for light wavelength). For soil acceleration histories except the random noise 249
response, de-noising was achieved using a wavelet transform scheme by soft-thresholding (Donoho 250
1995); the ‘db8’ (8th order) wavelet belonging to the Daubechies wavelets family was adopted as basis. 251
This approach was found more effective in reducing noise in seismic signals than the standard band-252
pass filters requiring specification of cut-off frequencies (Chanerley and Alexander 2007), and was 253
particularly suitable herein because displacement histories were to be derived by time-integration. Raw 254
Fourier Amplitude Spectra (FAS) of acceleration histories were smoothed by passing them three times 255
through a moving average filter with a 49-sample smoothing width; this ensured “smooth ratios” of less 256
than 0.2, sufficient to minimize distortion of the peak heights and bandwidths (O’Haver 2018). 257
Modal identification 258
Frequency-Response Functions (FRF) were constructed by computing the FAS of free-field 259
acceleration response histories to random noise input, and then dividing by the FAS of the table input 260
(station A1). FRFs at recording stations A4 (LBB) and A11 (SS) are plotted in Fig. 7 for three cases: 261
before the testing sequence begins, after shaking at 0.1g and in the end of the sequence. It is seen that 262
the responses at both A4 and A11 are predominantly amplified at the same frequency (about 37 Hz for 263
case 1); this confirms the coupled behavior of the sand blocks. FRFs at A11 give a second higher peak 264
amplification at about 56 Hz, which suggests a stiffer middle deposit despite its looser state; this may 265
be explained by the sub-angular shape of SS grains. The resonant frequency of the system drops 266
moderatelywith excitation level to 34.3 Hz, as does maximum amplification. The half-power 267
bandwidth method was used to extract soil internal damping estimates from the FRF low-end peaks. 268
Fig. 8a plots these estimates as a function of the maximum table PGA recorded in the sequence history; 269
evidently, there is a general but inconsistent upward trend across all recordings, from a minimum of 270
3.1% up to a maximum of 5.7%, with SS exhibiting higher dissipative action. However, it is 271
acknowledged that the derived values might not be reliable due to the strongly spiked shape of the 272
spectra and the associated dependence of the method on the employed smoothing operation. In contrast, 273
Pitilakis et al. (2008) and Chidichimo et al. (2014) measured damping ratios for LBB in excess of 10%. 274
It is not straightforward to obtain estimates of the shear wave velocities
 and
 of the two sands 275
using the expression
= 4 ×
× for horizontally layered deposits. Instead, an attempt was made to 276
approximate these parameters in an average sense from the arrival times of the first incident wave in 277
the recorded signals at surface, providing also statistical variance of the observations in terms of the 278
standard error of the sample mean. These results are presented in Fig. 8b, where one can identify an 279
initial densification phase for both sands up to 0.05g, and a subsequent non-linear softening phase at 280
higher table accelerations, which is more pronounced for the initially denser LBB. The reduction in 281
mean
from the low-strain to the final state is 24% and 10% for LBB and SS, respectively, and the 282
mean stiffness contrast


achieved at final state is 1.3. Note that, for low table PGAs (<0.05g), 283
no clear peaks were detectable in the acceleration signals, hence the large variability in derived
. 284
Harmonic excitations 285
286 Results for the first phase of single-frequency excitations are reported in this section. Primary outputs 287
obtained are the soil accelerations and pipeline bending strains; derived output includes displacements, 288
axial strains, shear strains and stresses of the soil, and axial strains of the pipeline. Where peak 289
magnitudes are more of interest, unfiltered results are presented to retain the original character of the 290
measurements. 291
Fig. 9 plots filtered soil acceleration histories as recorded by sensors A1 (table), A4 and A11 for 292
different harmonic testsa description of each test is supplied in Table 6. At a loading frequency close 293
to the resonant frequency of ~36 Hz (Test H06), horizontal surface motion is amplified by both sands, 294
more strongly by LBB, as shear waves propagate upwards through the soil mass. The degree of 295
amplification depends on the ratio ,
, where is the forcing frequency and , is a resonant 296
frequency of a soil block determined by the FRFs of Fig. 7, with zero or negative amplification being 297
possible as experienced in Tests H08 and H11, respectively. It is noted that erratic behavior is observed 298
in SS in some cases in the form of double peaks (e.g., Test H10), which is possibly related to slipping 299
of the instrument casing in the sand. 300
Instantaneous soil acceleration profiles along the recording array A15-A11 are illustrated in Fig. 10. 301
The profiles are extrapolated by reflection beyond the mid-point to cover for the lack of accelerometers 302
in the right half of the setup. For verification, output from sensor A12 is overlaid, showing a good match 303
with the reflected value at the same location. Profiles are plotted for two time instants when a peak and 304
a trough occur. In Test H06, the varying amplification levels in the two soils generate two fairly flat 305
responses across each soil domain, in reasonable agreement with analytical soil amplification studies 306
(Gelagoti et al. 2010; Psyrras et al. 2019). This behavior results in a relative horizontal motion at the 307
block interfaces, which produces axial normal strain in the soil as shown in the following. On the other 308
hand, surface accelerations are uniform across all blocks in Test H08, in consistency with Fig. 9. Note 309
that sensor A2 was found to be dysfunctional while A11 had undergone unwanted tilting after 310
embedment and for this reason its output was discarded. 311
Fig. 11a displays the total longitudinal pipeline strains as tracked by the crown and invert optic fibers. 312
As anticipated, the shapes of the profiles are antisymmetric with respect to the mid-point, exhibiting 313
alternating compression-extension at the soil interfaces, depending on the motion direction. Trends also 314
agree very well with analytical studies (e.g. Psyrras et al. 2019). The strain distributions of the crown 315
and invert are very similar, suggesting that bending in the pipe is generally negligible. To get the axial 316
strain profiles, the arithmetic mean of the total strains at the extreme fibers of the tube section 317
(+)/2 suffices, as long as the pipe remains elastic and the neutral axis coincides with the
318
centerline. The axial strains in this first loading phase show mild deviation (<20%) from the total strains, 319
indicating fairly small in-plane bending effects. 320
Moreover, to provide a picture of the axial strain transmissibility from soil to pipe, a crude calculation 321
of soil axial strains at the recording stations was performed using a 2nd-order finite-difference 322
approximation given by Equation 2: 323
(2)
324
where is the soil horizontal displacement at station , computed by double integration of measured 325
acceleration, and is the horizontal coordinate of station . Fig. 11b shows the near-surface axial strain 326
profiles for Test H06, taken at the same time instants as in Fig. 11a. The distributions resemble the ones 327
measured in the pipe, with magnitudes at the spike being significantly larger; about 50% of the soil 328
strain is seen to be ‘transferred’ to the pipe in this case, an indication that some interface sliding has 329
occurred. 330
To gain further insight into the hysteretic response of soil, shear stress-strain loops were developed 331
according to the procedure outlined in Brennan et al. (2005), using the recordings from the two vertical 332
arrays A4-A13 and A11-A14. According to Fig. 12, LBB undergoes much larger shear strains (up to 333
0.06% in Test H10) than SS for the same excitation level. The loops are fairly stable, but nonlinearity 334
is hardly discernible; the slopes through the origin equating to secant shear moduli confirm that SS is a 335
stiffer sand than LBB. Also, the deeper the station, the stiffer the sand as one would expect. 336
Broadband excitations 337
Along similar lines, select results obtained for broadband table input are presented here. In the top row 338
of Fig. 13, representative acceleration responses for the two sands as recorded by the mid-block 339
instruments A4 and A11 are plotted for cases SM06 and SM08. Again, variable surface motion 340
amplification is understood to impose increased relative axial displacements on the pipeline. The bottom 341
row of Fig. 13 shows the axial pipe strains calculated at stations falling on the block interfaces, for the 342
same loading cases. By close inspection, it is seen that the peak strains are nearly in phase with the soil 343
acceleration peaks. Axial strain histories at stations 6 and 20 are rough reflections of each other about 344
the -axis, which again confirms the alternating compressive-extensional deformation mode in the pipe 345
close to the block interfaces. Moreover, in the cases shown, residual stresses and (elastic) strains are 346
observed post-shaking due to residual ground deformations that alter the configuration of the pipe. 347
Critical tensile and compressive strain profiles for the same test cases are presented in Fig. 14. The 348
profiles in solid line refer to axial strain; dashed lines show actual recorded total strain at the extreme 349
fibers. It is evident that absolute peaks are substantially increased compared to the harmonic tests, up 350
to 66 με for axial strain and 140 με for total strain. Interestingly, bending strains are becoming significant 351
as revealed by the disparity between total and axial strains; their proportion of total strains amounts to 352
51%, as can be seen in Fig. 15. The reason for this is that higher dilatational modes are more strongly 353
excited in the ground; these modes involve vertical components of motion, manifesting close to the 354
block interfaces, that bend the pipeline. Table 6 summarizes all directly measured and derived peak 355
response parameters: soil acceleration, soil horizontal normal (axial) strain, soil shear strain, pipe total 356
longitudinal strain, pipe axial tensile and compressive strain. 357
Numerical validation of test results 358
ABAQUS (Dassault Systèmes 2014) and Opensees (McKenna et al. 2010) were employed to simulate 359
these experimental tests with the finite element method. Given the irregularity in geometry and 360
inhomogeneity in material properties of the geotechnical specimen, 2-D continuum elements were used 361
in the first place to verify the experimentally observed free-field response at the surface. Salient details 362
of the experimental assembly were included in the model, such as the lateral boundaries of the ESB and 363
their contact response with the soil mass. 364
Eigenvalue extraction 365
The modal and material characteristics of the system as of Test WN4 were considered as reference to 366
compare against. Only the soil and components of the ESB were included in the eigenvalue analysis. A 367
structured mesh with plane-strain finite elements was created to discretize six distinct subdomains in 368
the test soil (Fig. 16), accounting for the difference in measured densities between pipe bed layer () 369
and backfill () for both sands. Shear moduli were determined as =
and a constant Poisson’s 370
ratio = 1/3 was assumed across all subdomains. To couple the motion between the two ESB ends, 371
tie constraints were enforced at all ring levels. The interaction of test soil and ESB at their interface was 372
modelled using a finite-sliding, surface-to-surface contact discretization, assuming an interface COF 373
equal to the as-measured internal COF of LBB, tan(32.)= 0.64, in view of the sand-roughened 374
internal ESB surfaces. Using mean observed
values from Fig. 8b, the numerical model was found to 375
be more flexible in its first mode, with the corresponding natural frequency underestimating the 376
experimentally observed frequency of 35.8 Hz by ~10%. Fig. 17 shows the first four eigenmodes; the 377
lowest eigenfrequency is associated with a coupled shear-dilatational mode of vibration, as a result of 378
the non-uniform shear stiffness of the soil. Higher modes involve more dominant flexural and vertical 379
modes, both symmetric and antisymmetric ones. By comparison with Fig. 7, it is seen that the numerical 380
model captures well the second and fourth eigenfrequency as well. 381
Transient response 382
To reproduce numerically the time-varying response of the soil and pipe to base excitation for Test H10, 383
the two-step approach adopted in Papadopoulos et al. (2017) was employed. In the first step, the 2-D 384
soil-ESB model in Fig. 16 was solved for the realized table motion and the horizontal and vertical 385
acceleration response histories were extracted at soil nodal points along the pipe centerline. The soil 386
behavior was assumed as damped linearly elastic and an effective stiffness was determined from the 387
mean observed
for the two sands. Viscous damping of the Rayleigh type was introduced using target 388
damping ratios as identified for the respective excitation level in Fig. 8a. 389
Ignoring kinematic and inertial interaction effects, a separate, bi-directional, multi-support-excitation 390
model of the pipeline idealized as an assembly of 2-D Euler-Bernoulli beams was developed in 391
Opensees in the second step, where the frictional and transverse vertical SPI was represented by non-392
linear spring elements. A fine element mesh was created to match the spatial resolution of the strain 393
sensors. Spring parameters were evaluated according to standard expressions proposed by the ALA 394
(American Society of Civil Engineers 2001), with the axial mobilizing relative displacement computed 395
from separate FE pipe pull-out analysis as 2 × 10 m and 3 × 10 m for LB and SS, respectively. 396
The ground spring nodes were subjected to the previously obtained horizontal and vertical free-field 397
displacements at pipe bed level. 398
As illustrated in Fig. 18, the steady-state response of LBB sand compares favorably with the recorded 399
response at A4, less a minor time lag. The average peak-to-peak discrepancy in the constant-amplitude 400
window is ~5% and ~17% in the positive and negative direction, respectively, the difference being due 401
to the lack of -symmetry in the experimental response. Similarly, the match for SS is better in the 402
negative than in the positive direction. Here, the effect of the double peaks, briefly discussed earlier, 403
becomes obvious as it leads to a markedly larger discrepancy in the positive direction. 404
Shown in Fig. 19 are the axial strain histories at stations 6 and 20 as computed from analysis and as 405
measured from test. For station 20, the results show differences in the strain magnitudes, though this is 406
exaggerated by the fact that the experimental response is drifting away from the baseline. Ignoring the 407
drift, the model underpredicts the pipe strains by an average 55%. The overall shapes are in good 408
agreement. For station 6, the match appears better, if one again ignores the drift. To trace the source of 409
these discrepancies, an attempt was made to back-calculate the time-varying frictional force profile 410
generated along the pipe specimen and compare against the frictional resistance used for the axial 411
springs. The general equation of motion of a continuous Euler-Bernoulli beam on dynamic non-linear 412
Winkler foundation for axial excitation was used, given by 413
 
= (3) 414
where =(,) is the absolute axial pipe displacement and =(,) is the friction force per 415
unit length. Using the recorded pipe strain profiles and safely assuming that the inertial term is 416
negligible (if the recorded soil acceleration is used in place of pipe acceleration, this term is two orders 417
of magnitude smaller than the axial restoring force), the envelopes of were calculated at each strain 418
monitoring point for four different test outputs. Fig. 20 plots these envelopes normalized with respect 419
to the Coulomb frictional resistance , =(
). Where the envelopes do not cross the 420
dotted horizontal line (=ALA), it means that , captures reliably the friction response. It can be seen 421
that, for the low-intensity test HM06, the envelopes lie below the ALA line almost everywhere. In stark 422
contrast, the friction envelopes for test HM10 exceed the ALA resistance by a factor of 9.5 within the 423
ground stiffness transition zones. This indicates that the soil conditions developing in these zones offer 424
additional to the pipe, allowing increased axial strains to develop, as measured. In particular, as 425
shown in the foregoing, the soil in these zones undergoes compression-extension cycles; during 426
compression, the confining stress in the soil increases near the soil-pipe interface, leading to an increase 427
in the contact stress, hence an increase in locally. This increase in is evident in the other two tests 428
too, although not as sharp. The main reason why is so much larger in HM10 is that the test soil in 429
this case experiences near-resonance effects, which entails stronger amplification of the lateral 430
displacements, thus more excessive compression. 431
Overall, the comparison for the soil response is judged acceptable, permitting to say that the computer 432
model developed lends credence to the test results. For the response of a pipe buried in a laterally 433
inhomogeneous soil, more refined SPI models are essential to capture the cyclic variation in frictional 434
resistance with the changing confining conditions at inhomogeneity features, as the ALA springs were 435
developed for pipelines in laterally uniform soil. 436
Discussion 437
When the peak pipe response obtained from the experiment is extrapolated to full-scale using the 438
similitude laws outlined above, the peak total strain is on the order of 0.1% (by division by the scale 439
factor for strain of 0.149), which is nearly half the yield strain of the prototype steel and nearly 1/6 of 440
the limit strain corresponding to the plastic buckling load, shown in Fig. 3. This result reveals a 441
significant margin of safety for the prototype pipeline; however, it shows a non-negligible reduction of 442
the safety factor against buckling. Accordingly, it would be unwise to assume that axial strain 443
concentrations generated at soil boundaries would never result in shell buckling. If a more unfavorable 444
combination of parameters were in place, such as a higher interface COFas normally is the case for 445
the steel-sand interfaceand a larger soil stiffness contrast, the axial and bending strains developing 446
in the pipe inside the transition zone may become substantially larger. Note that the ratio


in 447
this study varied from an initial 1.1, to 1.3 post-shaking, that is fairly low ratios. 448
From another standpoint, this series of tests demonstrates the benefit of a low interface COF as a means 449
of reducing the dynamic axial loads transferred from ground to pipe during ground shaking. For 450
comparison, using the simple SPI model presented above, the peak total strain in the pipe for the seismic 451
input of Test HM10 and a uniform COF = 0.8 across both sands is computed at 58 με, nearly three 452
times larger than for = 0.23. Given that the pipe is constructed along an engineered trench, this 453
mitigating effect could be achieved in a number of ways, such as by using smooth, low-friction pipe 454
coatings, or installing layers of geosynthetic wrapping around the pipe to trigger axial slip at these 455
interfaces (Honegger et al. 2002). 456
It is also worth noting that the testing sequence was performed in an uninterrupted fashion, assuming 457
independent seismic events. However, the initially ‘perfect’ soil state and soil-pipe contact state was 458
disturbed after the first strong table motions. This may have led to a gradual reduction in the in-situ 459
COF, hence placing a cap on the stress transfer to the pipe in subsequent tests. Unfortunately, there was 460
no capability to measure the level of contact pressure at the pipe walls in this study. The implication is 461
that, in the scenario of a single strong earthquake event where no loss of interface contact has previously 462
occurred, the frictional stresses will likely induce larger axial strains in the pipeline than measured here. 463
Further experimental work could shed more light on these aspects by deploying additional sensors, such 464
as tactile pressure transducers and displacement transducers to measure settlements. 465
Concluding remarks 466
New data from 1-g shake table tests of a 1:45 model of an onshore transmission gas pipeline embedded 467
in a laterally non-homogeneous site were presented and discussed. The experiment physically modelled 468
the coupled dynamic response of the site and the pipeline under a set of uniaxial harmonic excitations 469
and modified earthquake records applied in the pipeline direction. Three blocks made up from two types 470
of dry sand were cast in a special 4.8-m-long, 1.2-m-tall, 1.0-m-wide soil container to form a symmetric 471
test site with three zones of different soil stiffness, i.e. soft-stiff-soft, and the pipeline specimen was laid 472
in and covered. Pipeline strain measurements were obtained from two chains of fiber optic sensors 473
bonded on the pipeline specimen. The test data were validated against finite element models. The main 474
findings are summarized below: 475
The state of deformation in the system is similar to the one reported in other studies dealing with 476
ground stiffness transitions, the difference being that in this study the stiffness pattern in the soil 477
was reversed. It was confirmed that alternating compression-extension zones develop in the 478
pipeline very close to the soil block boundaries, following the ground deformation pattern, while 479
non-shear ground deformation remains negligible far from those interfaces. This anti-symmetric 480
strain pattern is a result of the varying horizontal free-field motion amplification and vertical 481
ground vibrations associated primarily with higher modes, which mobilize increased frictional 482
stresses on the pipe walls. 483
From the harmonic motion sequence, it was found that for a given inhomogeneous site, pipeline 484
strain magnitudes are governed by resonance effects on the site response. Peak strains were 485
monitored for ,
1 for two different table excitation levels, 0.05g and 0.1g. Tests for
486
stronger input motions showed that the induced strains increased notably also with surface PGA, 487
reaching values as high as 140 με for PGA = 0.57 g. 488
Bending strains in the pipeline became considerable at stronger excitations, amounting up to 50% 489
of the total strains. This is an indication of vertical-flexural ground modes becoming active at 490
higher exciting frequencies, forcing the pipe to bend near the stiffness transition zones. 491
A relatively simple plane-strain finite element model was successful in reproducing the recorded 492
site surface response; however, using a beam-on-springs model with ALA spring parameters 493
proved inadequate to predict satisfactorily the pipe strain response, especially close to the 494
stiffness transitions zones. This is attributed mainly to the inability of the axial springs to capture 495
the large increment in frictional resistance offered by the increased confinement in these zones, 496
which allows transfer of additional axial stresses to the pipe. 497
Results show that the prototype would accommodate the scaled-up strains of 0.1% without 498
yielding. Nevertheless, subtle variations in configuration, such as a higher soil stiffness ratio and 499
a higher interface COF, may potentially incur a more critical response in the pipeline. 500
The above conclusions refer to buried steel pipelines crossing soils of abruptly changing 501
properties and are subject to specific assumptions made in the employed test setup and general 502
limitations associated with 1-g testing. Most prominently, the test model is adequate to first order 503
and the extrapolation of the pipe response was performed with respect to the limit point of the 504
full-scale pipe. The model pipe ends were left unrestrained; this set of boundary conditions 505
generally leads to reduced axial distress due to friction forces compared to a pipe model with 506
clamped ends. Lastly, the test protocol was carried out as an earthquake sequence and the test-507
to-test change of the soil-pipe contact conditions was not possible to monitor. 508
Data Availability Statement 509
Some or all data, models, or code generated or used during the study are available from the 510
corresponding author by request. Items included are the raw experimental data, the signal processing 511
scripts, and the finite-element models used for reproduction of the tests. 512
Acknowledgements 513
This work was funded by the Horizon 2020 Program of the European Commission through grant 514
MSCA-RISE-2015-691213-EXCHANGE-Risk. The first author also expresses his gratitude to the 515
Engineering and Physical Sciences Research Council for financially supporting his doctoral studies 516
(grant no.: EP/M507994/1). The invaluable assistance of all technical staff involved in the project is 517
acknowledged, with special thanks to L. de Leeuw for carrying out the direct shear tests. Finally, the 518
authors thank Dr G. Tsinidis, Dr D. Karamitros, Dr T. Horseman and Dr N. Alexander for their 519
contribution through critical discussions of this work.520
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Tables and Figure Captions
Table 1. Index properties for the sands used in the test
Grade
Void ratio
Grain size
(mm)
Uniformity
coefficient
Grain shape
Source
Min
Max
d
10
d
50
d
60
C
u
Leighton
Buzzard B
0.49 0.78 0.450 0.620 0.70 1.56 Rounded
Lings and Dietz
(2004)
Silica Sand 0.67 0.93 0.094 0.141 0.156 1.66 Sub-angular
Supplier; in-house
testing
Table 2. 1-g scale factors employed in this study; variables in italics taken as independent
Variable
Scale factor
(prototype-to-model)
Value for
n = 45
Length
1/
0.022
Density
1
1
Stiffness
1/.
0.149
Acceleration
1
1
Stress/Pressure
1/
0.022
Strain
1/.
0.149
Displacement
1/.
0.003
Velocity
1/.
0.058
Time
1/.
0.058
Frequency
.
17.37
Wave propagation
velocity
1/.
0.386
Force
1/
0.000011
Table 3. Model pipe properties
Parameter
Unit
Value
Elastic modulus,
MPa
2100
Poisson ratio,
-
0.4
Mass density,
Mg/m3
1.36
External diameter,
mm
20
Wall thickness,
mm
1.5
Axial rigidity,
kN
261.5
Interface COF against LBB
*
-
0.23
Interface COF against SS
-
0.27
*, Measured at a normal pressure of 10 kPa
Table 4. Details of transducers deployed in the test
Type
Number
Measured parameter
Characteristics
Calibration
Accelerometer
SETRA 141A
14
Horizontal free-field
and base acceleration
High output linear sensor
Operating frequency: 0-3000 Hz
Low transverse sensitivity
0.012g/g
1 g/V
Draw Tower
Gratings (DTG®)
by FBGS
Technologies
3×25
Pipeline bending and
axial strain
Bare FBG strain sensors in low
bend loss fiber; reflectivity >15%
Interrogator: Micron Optics si255
(
 = 1000 Hz)
1.2 (/)
Table 5. Target ground motions used in this study
ID
Location and year
Station
Magnitude
Mw
PGA
(g)
Mean period at 1:1
(s)
Time scale factor
1
Italy 2017
AMT
5.4
0.09
0.40
0.2
2
Italy 2016
CSC
5.4
0.06
0.48
0.2
3
Italy 1998
SELE
5.0
0.09
0.36
0.2
4
Italy 2016
AMT
6.2
0.34
0.62
0.2
5
Italy 2016
AMT
6.5
0.44
0.48
0.2
6
Kocaeli 1999
Yarimca
7.6
0.35
1.34
0.1
7
Lefkada 2003
No. 1
6.2
0.42
0.48
0.1
Table 6. Recorded and derived peak values of response parameters of interest for all test cases
Test
ID
Description
Target
table PGA
(g)
Peak
soil
(g)
Peak
pipe

(με)
Max
pipe
(με)
Min
pipe
(με)
Peak
soil
(με)
Peak
soil

(%)
WN1
White noise
0.02
H01
SD
*
0.01g 85Hz
0.01
0.064
10
7
-8
11
0.003
H02
SD 0.01g 34Hz
0.01
0.069
9.7
8
-8
20.6
0.01
H03
SD 0.01g 17Hz
0.01
0.02
8
6
-6
10
0.01
H04
SD 0.01g 8.7Hz
0.01
0.028
8
7
-6
27
0.05
WN2
White noise
0.02
H05
SD 0.05g 85Hz
0.05
0.23
48
25
-10
22
0.01
H06
SD 0.05g 34Hz
0.05
0.23
26
23
-22
88
0.05
H07
SD 0.05g 17Hz
0.05
0.05
8
8
-7
21
0.04
H08
SD 0.05g 8.7Hz
0.05
0.07
9
8
-8
28
0.3
WN3
White noise
0.02
H09
SD 0.1g 85Hz
0.1
0.29
13
12
-10
40
0.02
H10
SD 0.1g 34Hz
0.1
0.36
54
32
-25
155
0.08
H11
SD 0.1g 17Hz
0.1
0.11
12
10
-9
45
0.08
H12
SD 0.1g 8.7Hz
0.1
0.14
23
12
-14
80
0.8
WN4
White noise
0.02
SM01
GM 1
0.068
0.14
13
11
-11
35
0.23
SM02
GM 2
0.063
0.19
19
16
-17
58
0.41
SM03
GM 3
0.0925
0.09
27
14
-7
31
0.24
WN5
White noise
0.02
SM05
GM 4
0.34
0.42
62
37
-46
332
3
WN7
White noise
0.02
SM06
GM 5
0.42
0.64
96
78
-72
930
2.3
WN8
White noise
0.02
SM07
GM 6
0.35
0.44
68
39
-46
248
3.9
SM08
GM 7
0.49
0.57
140
73
-87
821
4.2
WN9
White noise
0.02
H13
SD 0.3g 34Hz
0.3
0.58
89
54
-46
407
0.16
* SD = sine dwell; GM = ground motion
... In such cases, a realistic earthquake will not trigger the same amount of high axial compression or bending moment that are commonly employed in a monotonic or cyclic elbow specimen test [3]. Concerning this matter, the seismic behaviour of pipelines affected by external geometrical nonlinearity has been placed under scrutiny, where an elevated seismic demand for above-ground piping systems [4] [5] and buried pipelines [6][7] subjected to differential end movements have been observed both numerically and experimentally. In the present work, a critical scenario of a natural gas (NG) pipeline coupling two industrial structures that are typically found in an NG processing plant is studied. ...
... Psyrras et al. [23] found that the pipe response was predominantly axial while bending became significant at stronger excitations using the shaking table model test. Strain distributions displayed clear peaks at or near the block interfaces, with magnitudes increasing at resonant frequencies and with excitation levels. ...
Article
Full-text available
The deformation and residual strength of the buried pipeline caused by the earthquake in nonuniform sites has an important influence on the safety of the pipeline. Most of the previous research focuses on the permanent ground deformation (PGD) caused by fault or transient ground deformation (TGD) due to seismic wave propagation independently. The mechanical character of buried pipelines crossing nonuniform sites during seismic sequence after ground settlement has not been studied. This article carried out a dynamic centrifuge experiment to simulate the seismic response of buried pipelines of polyvinyl chloride (PVC) and aluminum alloy (AL) horizontally crossing the loose and dense site and study the residual strength of pipelines after an earthquake. Two simulated seismic waves with 0.6 g and 0.3 g of input peak ground accelerations (PGAs) were inputted in sequence to simulate the strong and weak earthquakes. The deformations of ground and pipelines were obtained during and after seismic. The numerical model consistent with the experiment was established and compared with test, and it was found that the strain of pipeline caused by TGD was different between numerical and experimental results, especially in the loose site. The mechanical model of the pipeline by earthquake indicated that the total strain of the pipeline was composed of bending deformation by PGD and axial deformation by TGD. PGD caused by a strong earthquake had great effects on the deformation and residual strength of the pipeline. The strain of pipeline by TGD was compressive-extensional alternating mode between the loose and dense site and the strain amplitude reached peaks near the block interface in the loose site. The residual strain of pipeline in the dense site was a compressive strain, while in the loose site, it was compressive-extensional alternating mode and varied with the stiffness of the pipeline.
... Έχει αποδειχθεί (Mohammadi 1985) οτι οι βλάβες στα δίκτυα ενδέχεται να προκληθούν από την διάρρηξη του ρήγματος, καθώς και από καταπόνηση οφειλόμενη στην διαφορετική απόκριση τμημάτων του δικτύου. Αυτή η διαφορετική απόκριση αποδίδεται στην μεταβαλλόμενη στον χώρο εδαφική διέγερση, καθώς και σε γεωτεχνικές ή γεωλογικές ασυνέχειες (Psyrras and Sextos 2018;Psyrras et al. 2019). Δεδομένου οτι οι βλάβες ενός δικτύου εξαρτώνται και από τα χαρακτηριστικά της σεισμικής δράσης και από εκείνα του δικτύου, κατά τα τελευταία έτη καταβάλλεται προσπάθεια να προσδοθεί χαμηλή τρωτότητα έναντι σεισμού στα δίκτυα που κατασκευάζονται σε σεισμογενείς περιοχές, μέσω ειδικών μελετών που γίνονται για τον σκοπό αυτό (Menoni et al. 2002). ...
Technical Report
Full-text available
Technical report with multiple authors (please refer to pdf), edited by Anastasios Sextos, Basil Margaris and Nikolaos Klimis. Coordinated by the Hellenic Association of Earthquake Engineering, the Institute of Engineering Seismology and Earthquake Engineering (ITSAK-EPPO) and Democritus University of Thrace with the collaboration of Aristotle University of Thessaloniki, Geodynamic Institute - National Observatory of Athens, National Technical University of Athens, the University of Attica, the University of Thessaly and the University of Patras. Please cite as: Hellenic Association of Earthquake Engineering (ETAM), the Institute of Engineering Seismology and Earthquake Engineering (ITSAK-EPPO) and Democritus University of Thrace (2022) "the Thessaly Earthquake sequence of March 2021", Technical Report, Margaris, B., Klimis, N., Sextos, A.G. (editors), DOI 10.13140/RG.2.2.33758.51527 (in Greek)
... Lifeline infrastructures have been damaged severely in recent earthquakes, and buried pipelines are no exception (Psyrras et al. 2020;Hall et al. 1994;Tsinidis et al. 2019). Buried pipelines construction is rapidly increasing to meet societal demands, and more pipelines are laid in parallel due to the limitations of complex terrain (e.g., Central Asia gas pipeline, Sino-Russian oil and gas pipeline, China West-East gas pipeline). ...
... In the offshore sector, the increasingly important renewables sector also has significant supporting infrastructure such as cables where appropriate soil-surface interface strength is a key parameter. Furthermore, in seismic settings where ground motions impose displacement and loads on a buried pipe, the interface friction determines the amount of force that is imposed on the pipe (Psyrras et al., 2019;Psyrras et al., 2020). ...
Thesis
Pipelines are an integral part of offshore infrastructure supporting the oil and gas industry and the consequences of their failure have severe economic and environmental ramifications. Changes in pipe internal pressures and temperatures from the as-laid condition to their operational state cause large thermal expansions. When axial strain from thermal expansion is resisted by the pipe-soil friction, the effective axial force in an unburied pipeline is relieved by lateral friction-sliding-buckling. The phenomenon of pipeline buckling is a significant challenge in managing the global stability of high pressure-high temperature offshore on-bottom pipelines. Pipelines are commonly given a protecting coating to aid in protection from damage and to provide thermal insulation. The use of polypropylene in this application is prevalent but relatively recent so correct quantification of the interface shear strength between marine sand soils and polypropylene is key to robust global stability design. Herein, an extensive campaign of soil and interface shearbox testing has been undertaken to determine and evaluate the shear response of polypropylene surfaces. Parameters such as soil grading, density, surface texture, stress level, and cyclic behaviour have been investigated. The results show that the efficiency of the interface is strongly dependant on the soil grading and the surface texture at the interface. The shear response of soils at the interface with smooth surfaces is bilinear, characterised by an initially linearly elastic response at very small horizontal displacements, that transitions rapidly to a near constant shear stress plateau. Surfaces with greater roughness provoke a dilatant soil shear response more typical of a soil-only behaviour. Greater magnitude of surface texture engenders greater dilation leading to greater peak shear strengths. A relationship has been developed which can aid designers in predicting interface friction for polypropylene surfaces and sandy soils given surface texture, soil grain size, and stress level input parameters. The application of the experimental results to real-world problems was investigated through numerical modelling in Abaqus of an approximately 5 km long pipe on a rigid seafloor using friction penalty and non-linear springs to model pipe-soil interaction and force-displacement response. The impact on global stability and buckling parameters of changes in pipe-soil friction and of applying a differential friction regime along the pipe was investigated. Numerical analysis results showed that such techniques are able to significantly change the distribution and magnitude of buckles.
... In the seismic code, the strain can more intuitively reflect the force state and deformation characteristics of the pipeline under seismic excitation [14]. Under bidirectional seismic excitation, the pipe strain response is inconsistent along the pipe axial direction, and the El-Centro wave is used as an example to plot the variation of pipe bending strain and axial strain peak curves along the distance of the measurement point from the left boundary of the pipe under different loading levels, as shown in Figures 8 and 9. ...
Article
Full-text available
This paper studies the seismic response of buried oil and gas pipelines under the bidirectional nonuniform excitation. Based on the bidirectional shaking table array test, the loading and testing scheme is designed and developed, analyzing the strain response of the buried oil and gas pipeline under the bidirectional uniform and nonuniform seismic excitation, as well as the acceleration response and displacement response characteristics of the pipeline and the surrounding soil body and their change rule by the test. The test proves to show that the developed bidirectional laminar shear continuum model soil box can meet the requirements of the bidirectional nonuniform seismic excitation and continuous laminar shear deformation of the soil. The peak strains of the pipeline in axial and bending caused by nonuniform excitation are larger than those of the pipeline under uniform excitation, the degree of unevenness in the distribution along the axial direction is greater, and the strain curves are large in the middle and small at both ends along the axial direction of the pipe. The acceleration responses of the pipeline and the soil body under the bidirectional nonuniform excitation are larger than those under the uniform excitation. The acceleration response of both the pipe and the soil under the nonuniform excitation is larger than that under the uniform excitation, and the differences are shown in the transverse and axial directions, the peak acceleration response of the soil body under the nonuniform excitation is about three times that of the transverse direction, and more peak points appear in the axial and transverse acceleration responses of the pipe under the nonuniform excitation as the loading level increases, the peak displacement response of the soil body increases gradually with the height, but the fluctuation range of the peak displacement of the soil body nearby the pipe is larger. The soil displacement curve starts to smooth out when the loading level reaches 1.0 g, and the axial displacement decreases, which indicates that the interaction between the pipe and soil is more intense and the relative motion between the pipe and soil is more obvious under the nonuniform excitation, and the soil is more likely to be damaged and enter the nonlinear stage. Therefore, it is necessary to analyze and design the seismic performance of buried pipes considering the nonuniform seismic excitation. 1. Introduction Buried oil and gas pipelines are called lifeline projects in oil and gas fields. A large number of earthquakes have shown that pipelines not only suffer direct damage during earthquakes but also may produce serious secondary disasters such as fires, explosions, and environmental pollution, so it is important to ensure their safety and reliability under the effects of earthquakes [1, 2]. Buried oil and gas pipelines are infinitely long structures and the propagation process of seismic waves has a traveling wave effect; i.e., due to factors such as experiencing different medium conditions, the ground vibration propagated to various points in space has a certain time difference, which makes the vibration caused by seismic waves at various points of the structure differ. Therefore, it is necessary to study the seismic safety of buried oil and gas pipelines under nonuniform seismic excitation [3]. Through the use of shaking table tests, understanding and verifying the pipe-soil dynamic model and analyzing the dynamic response characteristics and laws of buried pipelines under earthquake action have become an effective method of studying the seismic performance of buried pipelines [4, 5]. At present, many scholars have done a lot of research on this issue. Zerva et al. [6] analyzed the response of pipelines under random earthquakes, including differential motions between sections connected by joints, displacement and stress of continuous pipelines, and displacement and force variables of the idealized bridge segment, analyzing the incidence angle of seismic waves at different locations in the longitudinal and transverse directions of the pipeline, the arrival time of fluctuations, and the effects of different fluctuation characteristics, and other factors are analyzed. Research results show that the lateral and longitudinal responses of large-diameter pipelines are equivalent. When the span length exceeds the critical at length, the axial and bending stresses of the pipe reach a constant value. Yoshizaki and Sakanoue [7] investigated how EPS (expanded polystyrene) can reduce soil-pipe interactions through experiments. With EPS backfilling, as opposed to ordinary backfilling, the lateral firmness of the pipe can be greatly reduced during earthquakes as the foundation moves, which has a significant effect on improving the seismic performance of buried pipes with elbows under the action of permanent ground deformation (PGD) important influence. Rahimi et al. [8] conducted a series of shaking table tests on elbow buried pipes, and the results showed that under dynamic loads, small diameter buried pipes exhibited more suitable performance than large-diameter buried pipes, and buried pipes with high stiffness and low flexibility were subjected to higher stresses under dynamic loads. Comparing the strains of soil and pipes, two materials with different constitutive behaviors, it can be seen that the axial strain of the soil around the pipes is on average about 10 times greater than the axial strain of the pipe. Jafarzadeh et al. [9] carried out a shaking table test of pipe-soil interaction using a laminar shear box with PVC pipes, using a concrete base mounted at the bottom of the shear box to simulate the nonuniform of real foundations and investigated the effect of dynamic loading on soils and pipes of different materials and compared the axial strain. Larger axial load ratio leads to a larger load-carrying capacity and a weaker deformation capacity. Junyan Han et al. [10] developed a suspended continuum model box suitable for multiple arrays shaking table tests of long linear underground structures, carried out shaking table tests of buried pipelines with multipoint ground vibration inputs under different site conditions, conducted research on the selection of similar relationships in shaking table tests of long transmission buried pipelines and the study of test protocols, and analyzed the seismic response laws of pipelines and sites under consistent and noncoherent seismic effects. It can be seen that although scholars at home and abroad have conducted some researches on the seismic response law of underground pipelines, most of them take consistent seismic input when conducting researches; because oil and gas pipelines are infinite length structures, and there are differences in seismic waves at each place, consistent seismic input will make the research results have large errors. Therefore, considering the spatial and temporal characteristics of the ground-motion traveling wave effect and based on the actual operating environment of buried pipelines, the research on the seismic performance of pipelines still needs to be further developed. In this paper, we developed a bidirectional laminar shear continuum model soil box that can realize the laminar shear effect of soil and is suitable for noncoherent seismic excitation test, which can simulate the laminar shear performance of soil under real earthquake. Before the test, the pipeline is pressurized to simulate the actual operation of the pipeline, and the shaking table test is conducted under the bidirectional consistent and noncoherent seismic excitation to study the change process of seismic response of buried oil and gas pipeline under bidirectional noncoherent seismic excitation and reveal its seismic response characteristics and laws. 2. Experimental Overview 2.1. Test Soil Box and Similar Ratio Design The test was conducted on the horizontal bidirectional seismic simulation shaking table array system at the Key Laboratory of Structural Wind Resistance and Vibration Control in Hunan Province, which has a table size of 1000 mm × 1000 mm, a maximum load of 50 kN on a single table, and a distance of 2000 mm between two shaking tables, which can realize bidirectional loading in X and Y directions. The author developed a bidirectional laminated shear-type continuum model soil box for shaking table testing [11], which includes a laminated frame, a rolling slide device, a limiting device, and an articulated expansion device in conjunction with the test requirements. The Earth box is mainly composed of three parts, of which box No. 1 and box No. 3 are identical, and they are made of 9 layers of U-shaped frame stacked together. Each layer of the frame between the shelves has a bull’s-eye ball, in order to allow each layer to occur between the layers of misalignment. Each layer of the frame on both sides has bolts, nuts, and a limit plate to form a limit device. The limit plate through the limit of the slide allows each layer of the frame to occur in the slide range. A hinged telescopic device is equipped between each box and each layer of the frame of box No. 2 to make sure that the framework of box No. 2 can achieve the role of telescoping and rotation. Box No. 2 is made of 9 layers of rectangular rods, and there are 12 bull’s-eye balls with a diameter of 30.16 mm at the bottom of the box, which can bear the overall weight of box No. 2 and allow box No. 2 to slide freely when it vibrates without restricting the movement of boxes No. 1 and No. 3. The outer side of the middle section of the box is equipped with a flexible limit to pull rope, which is welded to the outer wall of the rectangular frame after a hole is made in the L-shaped plate and then the layers of the frame are connected together by the limit pull rope. The overall dimensions of the box are 4000 mm × 840 mm × 944 mm, and a rubber cloth with a thickness of 1 mm is attached to the inner wall of the box to prevent the soil in the box from seeping out when the shaking table vibrates. The designed and assembled soil box is shown in Figure 1. (a)
... Based on shaking table tests, Yan et al. (2018) highlighted the impact of spatial ground motions on the dynamic behavior by comparing the seismic responses of a buried pipeline under uniform and non-uniform excitations. Likewise, Psyrras et al. (2020) performed a reducedscaled shake table test to investigate the response mechanism of an onshore gas pipeline embedded in horizontally layered soil. However, it is noted that in the previous numerical studies regarding the seismic response analysis of buried pipelines, the influences of SPI were not properly considered with combination of the spatial seismic inputs, and the effect of multiple soil layers on the site amplification of ground motions was also commonly neglected. ...
Article
For underground structures with large spans, such as buried pipelines, the seismic motions may vary not only at distinct horizontal locations due to the wave passage, incoherence and local site effects; but also at different vertical soil depth owing to the site amplification effect. This paper numerically investigates the influences of underground spatially correlated earthquake motions (USCEMs) on the seismic behaviors of large-span buried pipelines. To accomplish this task, the widely used buried gas steel pipeline of API X65 is chosen as a case study and the corresponding three-dimensional finite element (3D FE) model is created using the ABAQUS software, which accounts for the soil-pipe interaction (SPI) by the beam on nonlinear Winkler foundation (BNWF) model. The three-dimensional USCEMs for the nonlinear time-history analyses of the buried pipeline are stochastically synthesized based on the computed underground transfer functions of local sites. A total of 11 analysis cases associated with different spatial variability parameters of USCEMs (i.e. seismic excitation type, incoherence loss, local site condition and seismic motions at different soil depths) are considered. Based on increment dynamic analysis (IDA), a parametric study is carried out to comprehensively examine and discuss the influences of different spatial variability parameters on the seismic responses and critical operable capacity of the exemplar buried pipeline by comparing the analysis results of different cases. Numerical results demonstrate that these influencing factors can impact the seismic behaviors of the exemplar buried pipeline in different degrees and cannot be neglected in the seismic analysis. This research can serve as a vital reference for the seismic performance assessment and design of large-span buried pipelines.
... Similarly, for buried NG pipelines, the impact of out-of-phase oscillation induced by differential earthquake inputs has been highlighted previously. Psyrras et al. (2019Psyrras et al. ( , 2020 numerically and experimentally investigated the seismic risk of buried NG pipelines when subjected to spatially varying transient ground deformations. Results showed that even for straight buried pipelines, the seismic vibrations at the vicinity of laterally inhomogeneous sites can produce differential movements on different locations of a long pipeline due to kinematic soil-pipe interaction. ...
Article
Full-text available
Though often overlooked, the impact of seismic transient ground deformation on natural gas (NG) pipes can be highly adverse. Particularly, pipe elbows may undergo excessive in-plane bending demand and buckling. In this paper, a critical scenario of a pipe coupling two industrial structures typically found in an NG processing plant is studied. High strain and cross-sectional ovalization on the elbows are probable during an earthquake due to the out-of-phase oscillation of the two structures imposing asynchronous displacement demands at the two pipe-ends. A parametric study was first performed to investigate various structure-pipe-structure configurations which increase seismic demands to pipe elbows. Simultaneous mobilisation of divergent oscillation between two supporting structures at the low-frequency range, a lower pipe-structure stiffness ratio, a shorter length of straight pipe segments in the linking pipe element and a higher pipe internal pressure have led to the onset of critical strain demands in pipe elbows.
Article
Reliability analysis of buried pipelines subjected to spatiotemporal seismic involves modeling multiple uncertainties related to loads, soil, and mechanical mechanisms. The present study proposes a probabilistic modeling method that can couple random spatiotemporal seismic vibrations in the axial and transverse directions of the pipeline, enabling probabilistic incorporation of stochastic uncertainty (random variability) into the seismic response analysis of structures. Uncertainties of soil properties are probabilistically modeled to simulate the random pipe-soil interaction effect. Spatiotemporal dynamic response of the pipelines is discretized using extreme value distribution theory, thus making the seismic reliability analysis of the pipeline within a time-invariant framework. The applicability and accuracy of the proposed method are illustrated by numerical studies. The application of the probabilistic modeling method supports reliability- and risk-based inspection and maintenance planning for buried pipelines subjected to spatiotemporal earthquakes.
Chapter
Physical modeling is an established tool in geotechnical engineering for studying complex interaction problems involving soils. This chapter provides an overarching narrative of different aspects of such physical modeling include the challenging issue of designing meaningful (useful) tests and interpretation of the results for predicting prototype consequences. There are mainly two types of scaled physical modeling: (a) geotechnical centrifuge modeling under enhanced pseudo-gravity and (b) scaled modeling under 1-g, i.e., (Earth's gravity). Both approaches are briefly described together with the advantages and disadvantages. Furthermore, this chapter also discusses the two types of methods for designing and scaling model tests: (a) use of standard scaling laws available in textbooks which is “Black-box”-type modeling and (b) mechanics-based scaling. Few physical modeling examples (such as buckling instability of piles in liquefied soils, behavior of buried pipelines crossing faults and landslides, response of foundations for offshore wind turbines) are considered to show the mechanics-based scaling method. It has been shown that none of the techniques is perfect, and one needs the right tool for the right job. Black-box type modeling is suitable for simple interaction problems. However, for an unknown-unknown problem (typical of a multiple interaction problem), mechanics-based scaling method is appropriate. Do's and Don’ts in physical modeling are discussed.
Conference Paper
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Over the last decade, there was a renewed interest on Integral Abutment Bridges (IABs), characterized by the absence of bearing supports and expansion joints, leading to reduced construction and maintenance cost over ordinary bridges. Due to monolithic connections between abutments and deck, complex Soil-Structure Interaction (SSI) phenomena tend to develop between bridge and backfill in static and dynamic conditions, due to thermal expansion and earthquake action, respectively. An experimental campaign was conducted using the 3x3 m 6 DOF shaking table and the 5 m long shear stack of the University of Bristol, focusing on SSI effects between the IAB model and the backfill soil under earthquake loading. After a description of test setup and of protocol, preliminary results will be illustrated and discussed.
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Steel gas pipelines may be subjected to buckling failure under large compressive straining, caused by seismically induced ground deformations. This paper further elaborates on the buckling response of this type of networks, through the presentation of representative results from a series of axial compression static analyses that were conducted on segments of steel gas pipelines. Above ground and embedded segments of diverse radius to thickness ratios (R/t) were simulated by means of inelastic shell elements. The trench of embedded pipelines was modelled using solid elastic elements, while an advanced contact model was used to simulate the pipe-soil interface. Salient parameters that affect the axial response, including the internal pressure and the existence of imperfections on the segment, were considered in this study. In line with previous evidence, the results reveal a reduction of the axial response of the pipe segment with increasing levels of internal pressure. In parallel, internal pressure leads the limit stresses to occur at progressively higher axial deformations, while limit loads computed for embedded pipelines are higher compared to those predicted for equivalent above ground pipelines, as a result of the soil confinement.
Conference Paper
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The damaging potential of spatial variability in seismic ground motion on the integrity of buried pipelines is demonstrated in this paper. A numerical analysis methodology is developed first to determine the seismic demand of a typical straight steel natural gas pipeline running through a site composed of two different media with an impedance ratio of 2 and swept by vertically propagating SV-waves. The analysis follows a sub-structured, two-phase approach involving the computation of pipeline input excitation from 2D linear viscoelastic and linear-equivalent seismic site response models and the quasi-static application of the derived critical motion profiles on a near-surface 3D continuum soil model surrounding an extended inelastic shell model of the pipeline. The focus is then placed on identifying the ground and exciting conditions bearing adverse effects on the peak pipeline response. By comparing the pipeline demand in terms of stress and strain to capacity metrics prescribed in present seismic codes, the importance of the local site response is gauged. Results show that low-frequency ground vibrations produce the most unfavorable demand on the pipe for the set of cases examined. More importantly, even though pipeline axial strain demand-to-capacity ratios for elastic local site response under weak excitation imply a large safety margin, pipeline demand can exceed capacity near the site boundary under strong excitations and subsequent nonlinear soil response. Plastic local buckling may also develop in the pipeline under high-intensity input motions, thus highlighting the necessity to account for non-synchronous earthquake ground motion in case of horizontally nonhomogeneous sites.
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Evidence from past earthquakes suggests that damage inflicted to buried natural gas (NG) pipelines can cause long service disruptions, leading to unpredictably high socioeconomic losses in unprepared communities. In this review paper, we aim to critically revisit recent progress in the demanding field of seismic analysis, design and resilience assessment of buried steel NG pipelines. For this purpose, the existing literature and code provisions are surveyed and discussed while challenges and gaps are identified from a research, industrial and legislative perspective. It is underscored that, in contrast to common belief, transient ground deformations in non-uniform sites are not necessarily negligible and can induce undesirable deformations in the pipe, overlooked in the present standards of practice. It is further highlighted that the current seismic fragility framework is rich in empirical fragility relations but lacks analytical and experimental foundations that would permit the reliable assessment of the different parameters affecting the expected pipe damage rates. Pipeline network resilience is still in a developing stage, thus only few assessment methodologies are available whereas absent is a holistic approach to support informed decision-making towards the necessary mitigation measures. Nevertheless, there is ground for improvement by adapting existing knowledge from research on other types of lifeline networks, such as transportation networks. All above aspects are discussed and directions for future research are provided.
Conference Paper
Full-text available
In the past decades, a number of major earthquakes caused serious damage to natural gas pipeline networks. In most cases, the devastating effects were caused by permanent ground displacement. However, there exist at least two well documented cases (Mexico City and Northridge Earthquakes) where damage were due to seismic wave propagation. Response of buried pipelines is significantly different from that of above-ground structures. However, similarly to bridges or dams, pipelines are also prone to the effects of spatial variability of earthquake ground motion due to their length, which, in some cases, extends beyond national borders. This paper focuses on the effects of asynchronous excitation on the seismic response demand of natural gas pipelines belonging to transmission networks. Parameters examined include time delay due to finite wave propagation velocity and loss of coherency along the pipelines' length, a parameter known to contribute to seismic strains. Impact of local site effects on pipeline response is examined through the use of bedrock-soil surface slope that forms a basin, with impedance ratios varying with depth. Finite element analysis and lumped springs are used to model the interacting soil-pipeline system while excitation input motions are generated through 2D site response analyses. The paper summarizes the effects of various parameters on seismic demand to pipelines. The results indicate that ignoring the wave passage effect, the stress state in the pipeline is roughly symmetric, with the axial strains of the pipeline to be increased over the inclined sides of the basin and to be almost null in the middle. When the wave passage effect is incorporated in the analysis the stress state is no longer symmetric and the location of the maximum strains in the pipeline moves towards the central region of the basin but near to the inclined edge from which the seismic waves are coming. The comparison of the computed axial strains with the respective strains used in conventional design processes showed that in the case of irregular subsurface topographies the conventional may result in unconservative design.
Article
The damage potential of spatially variable seismic ground motion on buried pipelines has long been confirmed by field evidence, but it is still debatable whether transient seismic loads can be truly detrimental to the pipeline integrity. In the absence of systematic scrutiny of the effects of local site conditions on the seismic behaviour of such structures, this study presents a staged approach to numerically investigate the elastic-plastic buckling response of buried steel natural gas pipelines subject to transient differential ground motions arising from strong lateral site inhomogeneities. The first stage involves the study of 2D linear viscoelastic and equivalent-linear site response for the case of two sites and the resulting seismic demand in terms of longitudinal strains for input motions of various intensities and frequency content. The influence of key problem parameters is examined, and the most unfavourable relative ground deformation cases are identified. In the second stage of analysis, the critical in-plane ground displacement field is imposed monotonically on a near-field trench-like 3D continuum soil model encasing a long cylindrical shell model of the pipeline. Next, the performance of the buried pipeline is assessed under axial compression. The impedance contrast between the laterally inhomogeneous soil profiles is shown to govern the amplitude of induced elastic strains, which are maximized for low-frequency excitations. It is also demonstrated that peak axial strains along the pipeline considering equivalent-linear soil behaviour under strong earthquake motion can be as much as two orders of magnitude larger than their linear counterparts, as a result of the severe, spatially variable moduli degradation. It is finally shown that the seismic vibrations of certain inhomogeneous sites can produce appreciable axial stress concentration in the critically affected pipeline segment near the material discontinuity, enough to trigger coupled buckling modes in the plastic range. This behaviour is found to be controlled by pronounced axial force-bending moment interaction and is not accounted for in code-prescribed limit states.
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Observations of pipeline behavior during earthquakes have been conducted by using buried pipelines at three different sites. The records indicate that the idea of wave propagation along a pipeline has little significance in explaining the pipeline behavior, and that the model of upwardly incident earthquake motion to the bottom of surface soil layer will be effective.
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Shaking tables provide one means of obtaining data from physical models of geotechnical systems under simulated earthquake loading. While there may be challenges in ensuring exact scaling of all aspects of a geotechnical system between prototype and model, the large size of the shaking table models does give a good basis for validation of numerical modelling strategies. A shear stack provides a means of creating a mass of soil which can approximate the free field of the real world. Observations of the performance of the Bristol shear stack are presented and compared qualitatively with patterns of behaviour observed in laboratory simple shear tests. The results of some tests on model gravity retaining walls performed using the shear stack are used to show the relevance of simple models of geotechnical system performance and to illustrate the difficulty of correlating system performance with individual parameters of input time histories.