Conference PaperPDF Available

Experimental Identification of Stiffness and Ultimate Resistance of Buried Soil-Pipe Systems


Abstract and Figures

In context of pipeline design, the soil’s stiffness and ultimate lateral resistance are critical values. Existing approximations for ultimate lateral resistance vary significantly and there are few expressions for the soil stiffness parameters. These parameters are implemented in soil constitutive models for pipeline design under different displacement induced conditions. This research focusses on the experimental investigation of the response of the soil-pipe system to enforced horizontal loading for application to natural gas pipelines. The study examines shallow burial depths (<5.5D), using a section of solid acrylic pipe in dry Leighton Buzzard grade B sand. Plane-strain conditions have been replicated and experiments run to evaluate quantities for soil stiffness, through lab experiments and validated finite element analyses (FEA). Monotonic loading was applied onto the pipe within varied conditions, changing both burial depth and soil density to establish the relationship with soil stiffness. The FEA results were used to ratify such behaviors, establishing an analysis for displacement response and corresponding stiffness parameters. Absolute and relative stiffness values from both analyses were then compared with existing literature and the results reflect the importance of relative soil properties and expected displacements. Results find that horizontal loading within shallow burial depths induce 2D displacements, which could be modelled as vectors rather than horizontal displacements.
Content may be subject to copyright.
, Anastasios SEXTOS
, Rebecca STUBBS
In context of pipeline design, the soil’s stiffness and ultimate lateral resistance are critical values.
Existing approximations for ultimate lateral resistance vary significantly and there are few expressions
for the soil stiffness parameters. These parameters are implemented in soil constitutive models for
pipeline design under different displacement induced conditions. This research focusses on the
experimental investigation of the response of the soil-pipe system to enforced horizontal loading for
application to natural gas pipelines. The study examines shallow burial depths (<5.5D), using a section
of solid acrylic pipe in dry Leighton Buzzard grade B sand. Plane-strain conditions have been replicated
and experiments run to evaluate quantities for soil stiffness, through lab experiments and validated finite
element analyses (FEA). Monotonic loading was applied onto the pipe within varied conditions,
changing both burial depth and soil density to establish the relationship with soil stiffness. The FEA
results were used to ratify such behaviors, establishing an analysis for displacement response and
corresponding stiffness parameters. Absolute and relative stiffness values from both analyses were then
compared with existing literature and the results reflect the importance of relative soil properties and
expected displacements. Results find that horizontal loading within shallow burial depths induce 2D
displacements, which could be modelled as vectors rather than horizontal displacements.
Keywords: Soil stiffness; pipelines; soil-pipe interaction, experimental investigation
Soil stiffness influence the response of a soil-pipe system under earthquake-induced faulting, landslides,
liquefaction, urban excavations and tunneling (O’Rourke, 1985). The exact failure displacement,
ultimate force and failure mechanism are a product of in-situ stresses and soil parameters, therefore
several expressions have been proposed in the literature and design documents. Relevant guidelines in
the US (American Lifelines Alliance (ALA), 2005), consider some of these effects by mean of horizontal
bearing capacity factors, Nqh, which are a function of peak friction angle, ϕ and burial depth, H.
Commonly used Winkler soil models represent the soil stiffness via a series of parallel springs attached
to the pipe. Each individual spring has stiffness constant value, K(x) based on hyperbolic functions for
the force-displacement curves, which are simplifications of the soils non-linear behaviour as shown in
eq. 1, where P is lateral force, and y is horizontal displacement.
Pipe-soil interaction is a complex phenomenon and modelling such interactions numerically is
challenging, particularly given the extended geometry of the pipe, the associated subsoil conditions and
the 2D or 3D site response under earthquake loading within the media crossed by the pipe. The resulting
failure mechanisms due to lateral displacements are also not well defined due to multiple material and
geometric nonlinearities near and on the soil-pipe interface, respectively. Previously numerical models
have been validated through experimental results, and these simple equations, such as within ALA
guidelines, have naturally stemmed from experimental literature. However, there are large discrepancies
Associate professor, Department of Civil Engineering, University of Bristol, Bristol, UK
Associate Professor, Department of Civil Engineering, University of Bristol, Bristol, UK & Aristotle University
of Thessaloniki, Greece
Structural Engineer, at Mott MacDonald, UK
Chair in Geotechnics and Soil-Structure Interaction, Department of Civil Engineering, University of Bristol,
Bristol, UK & University of Patras, Greece
in existing literature due to different limitations and assumptions made within all experimental and
analytical methodologies. For example, micro and macroscopic behaviour of soils is often not accounted
for within analytical models (Roy, Hawlader, Kenny, & Moore, 2015) and this behaviour can govern
failure mechanisms. The soil’s stiffness value is a function of the interface conditions with the pipe, the
soil’s elastic modulus, E, Poisson’s ratio, ν, and the relative burial depth to diameter ratio, H/D (eq. 2).
Stiffness can also can be evaluated differently, depending on the soil’s strain level, based on the non-
linear nature of the soil behavior (Figure 1).
! " #
" )*
Figure 1: Lateral stiffness of the soil-pipe system (O’Rourke & Liu, 1999)
Table 1: Summary of the sand properties within existing experimental literature
Density, KN/m3
(Ovesen, 1964)
Friction angle, °
(Ovesen, 1964)
Density KN/m3
Cornell Sand
(Trautmann, 1985)
Friction angle, °
Very Dense
ALA defines the maximum lateral soil force per unit length, Pu, for sand as per equation 3, which
incorporates a bearing capacity factor Nqh (Trautmann & O’Rourke, 1985). The equation for maximum
horizontal elastic displacement, yu, varies with density as shown by equation 4; yielding a range of
values depending on burial depth, pipe diameter, D and coefficient A within equation 4. Interpretation
of these equations is subjective as the density of such material tends to be relative based on the individual
material properties, as seen within Table 1; however, no guidance is given to define the bounds. The
values for upper and lower bounds (O’Rourke, 1999) are used in this study. Implementing these design
charts as part of pipeline design therefore requires laboratory testing to find peak friction values for the
material as well as accurate quantification of in-situ density.
!2" )345678)
(sand) (3)
$4 : -
where A =
for loose sand,
for medium sand, and
for dense
conditions. Recent works (Kouretzis, Sheng, & Sloan, 2013) looked to create design charts for shallow
burial (<5.5D) backfilled trenches based on burial depth and relative density only, which would avoid
this challenge within large scale applications where the backfill material may vary significantly over the
length of a gas-pipeline. O’Rourke & Liu (1999) identify stiffness values depending on the
corresponding strain level within the material, or so-called relative displacements. These stiffness
expressions can be seen in Figure 1 and are based on the literature (Audibert & Nyman, 1977)
considering initial tangential stiffness KL1, secant stiffness at 70% of the ultimate lateral force, KL2, and
secant stiffness at ultimate lateral force, KL3. Their values are shown below in equation 5. O’Rourke &
Liu (1999) presented a bi-linearisation of the soil’s behaviour with an expression for equivalent elastic
soil spring constant as 2Pu/yu, which was adopted by ALA; in Figure 1 this corresponds to KL2 but
depending on the shape of the force-displacement curve this is not always the case.
where α =6.67 for KL1, α =2.7 for KL2 and α =1 for KL3. To quantify and study the forces and
displacements reported within the existing literature, values are herein normalised to the dimensionless
force P/γHD, where L is the length of the pipe and γ is the shear strain of the soil. Other important
literature considered in this paper relates to experimental and analytical findings and the role played by
plane-strain conditions, soil-pipe interaction, Mohr-Coulomb (MC) and Modified Mohr-Coulomb
(MMC) modelling, and large scale testing. The influence of shear modulus, G and the elastic modulus
E on soil behaviour has also been discussed. Overall, focus has been made on simulating behavioural
trends with different burial depths and soil densities, within expected failure behaviours expressed
qualitatively (Chaloulos, Bouckovalas, & Karamitros, 2017). Static stiffness values for axial springs
have been proposed as a function of G (El Hmadi & O’Rourke, 1988), within the range 1.0G<K<3.0G,
and updated within the range 1.57G<K<1.7G to account for small ground movement.
Other experimental studies have been conducted in the past to understand lateral pipeline–soil
interaction in sand (Audibert & Nyman, 1977; Daiyan, Kenny, Phillips, & Popescu, 2011). Based on
these experiments design curves for the bearing capacity factors have been concluded, predominantly
from the work of (Trautmann & O’Rourke, 1983). Large scale experiments were also presented of
dimensions 1.2m width x 2.3m length x 1.2m deep with the aim to measure the variation of maximum
lateral soil force and the force-displacement as a function of pipe burial depth and soil density.
Audibert’s research looked at four diameters between 25.4mm and 254mm, O’Rourke with two pipe
diameters, 102mm and 324mm. They looked at burial depths ranging from 1.5D to 11D and density
from 14.8KN/m3 to 17.7KN/m3. Tests reported to be working under plane strain conditions; their
findings as well as others are summarized in Table 2 along with the results reported herein that will be
discussed in the following section.
Table 2: Expected displacements for ultimate lateral resistance of pipes in sand
Audibert and Nymann
Das & Seeley
Neely et
Al. (1973)
0.060H (D=25.4mm)
0.041H (D=61mm)
0.030H (D=114.3mm)
0.025H (D=254mm)
0.036H (D=25.4mm)
0.026H (D=61mm)
0.022H (D=114.3mm)
0.019H (D=254mm)
Existing literature has limited experimental work that isolates parameters and their implications within
the problem; due to the parametric nature of soil, specific graphs/equations can be difficult to maintain,
and comparisons between works can be difficult, because density is not even a parameter that can
directly be compared. Specifically looking at application to natural gas pipelines, where pipes are laid
within very shallow, backfilled trenches (typically less than 2D burial depth) Chaloulos, 2017 found
that critical parameters tend to govern the soil’s response due to dilation and low stress conditions.
However, ALA design codes begin their quantification of
from a burial depth of 1.5D depending
on the peak friction angle of the soil. This means that the design codes are quite inaccessible to
researchers and designers, due to their reliance on density and peak friction angles. Making
quantification of seismic risk to such pipelines challenging. Along these lines, this work aims to (a)
design and execute experiments which isolate plane-strain behaviour whilst minimising boundary
condition effects, (b) quantify experimental displacement responses for monotonic loading of a pipe-
soil system, within a burial depth range of 1-5.25D and (c) study the failure mechanisms involved and
their relationship with changing burial depth and density.
3.1 Scope of experiment
Given that the emphasis of this study is on natural gas pipelines, which typically sit within backfilled
shallow trenches, burial depth is limited to 5.25D (Chaloulos, 2017); most previous literature for
pipeline behaviour extends beyond this range, however, this would have significantly increased scale of
experiment with minimal benefit. An experimental procedure was developed and tested that created a
repeatable set of test conditions where both the burial depth and sand density could be varied to acquire
lateral force-displacement curves. Experimental dimensions were chosen so that ultimate lateral force
could be reached within the range of the apparatus for all burial conditions specified enabling a full
range of stiffness values; KL1, KL2, and KL3 to be evaluated. Scale effects of the experiment are likely,
due to the reduction of geo-static stresses, therefore ideally the material should be a looser density than
experienced in real terms to represent this, and better mimic the critical state behaviour.
3.2 Experiment scale and dimensions
To decide on scale and dimensions of the experiment, existing literature was reviewed to establish the
expected influence of boundary conditions, and these findings informed experimental dimensions. The
width of the box is dictated by three factors: the influence of friction between the sand and the near tank
surfaces, achieving plane strain conditions, and the achievable practical width for experimental
preparation. The length and depth of the tank is dictated by the influence of distant lateral boundaries,
as well as burial depths required. According to the literature (Matsii & Derevenets, 2005) for piles being
tested for lateral displacements, the minimum spacing to avoid interaction was 2D-4D, where D is pile
diameter. In other studies (Yimsiri, Soga, Yoshizaki, Dasari, & O’Rourke, 2004) a minimum distance
to the boundary was estimated as 6D. Similarly, (Drescher, Vardoulakis, & Han, 1990) used soil samples
of 40mm width to acquire data for bi-axial testing of soils under plane-strain conditions; the influence
of friction with the lateral boundary plates on plane strain testing caused artificial increased soil strength,
and therefore width was increased to 2/3D to reduce the stiffening effects on the results. Practitioners
found that the optimum results for analytical testing were for width < D/10; this yielded the best failure
mechanisms within a 2D plane; on the contrary, thickness’ greater than this found that failure
mechanisms tended to angle into 3D planes within the body.
In conclusion, the tank had to be wide enough that a consistent soil sample can be prepared, secured and
tested appropriately; a very thin tank would cause potential inaccuracies due to friction with boundary
conditions and a wide one would yield far higher results for ultimate failure load due to volume of
resisting material, causing more sophisticated equipment to be needed. Based on the above
consideration, the tank dimensions have been specified as 0.1m wide x 1.6m long x 1.1m deep, with a
pipe diameter of 100mm giving the tank thickness of 1D (Figure 2). Isolation of plane-strain conditions
and preparation of the sand is practically possible to achieve within this width whilst reducing effects
of friction, arching of the sand and minimising 3D failure mechanisms. The length of the tank is
apparently a compromise, based on creating asymmetry that allows multi-functionality of the tank with
multiple orientations. The pipe location is 5.5D from the surrounding edges, giving a minimum distance
of 4.55D when at maximum displacement; within this research, monotonic loading, from left to right,
into the larger volume of sand was be undertaken with the aim to keep stiffness influence from lateral
boundaries to the minimum.
Figure 2: Tank elevation dimensions, all references to the tank dimensions and displacements are in respect to
this orientation.
3.3 Experiment apparatus
The experimental set up includes a narrow Perspex tank made of 5 sheets of 25mm transparent Perspex,
with the top side left open for compaction and ease of restraining tank. A large restraint frame clamped
to the floor and to the tank directly restrained any movement and isolated transfer of forces straight from
the pipe to the surrounding soil. Due to focus on system behaviour not pipe specifically, a solid acrylic
pipe was used rather than a hollow cylinder like traditional pipe, for simplicity; it was cut to 100mm
diameter and 99mm width with two O-rings that sat on its circumference to create an interface with the
Perspex sheets with minimal friction. Also, a series of instrumentation, including three celescos and a
load cell was integrated into the tank. Load application was via a hand actuator transferring forces to the
pipe via a simple mechanism to flat nylon ropes attached to a threaded bar into the pipe. The ropes were
very light in weight and critically has very low resistance to bending that did not add residual forces to
the system as seen in Figure 3. This setup was preferable to pushing the pipe into an active zone of soil,
due to long arms needed to transfer force between the actuator and the pipe, which would have been
prone to buckling. Restraining or supporting these arms would potentially impact the transferred forces,
the displacement direction or the corresponding failure mechanism.
As series of calibrations were made quantitatively and qualitatively within this set up, in order to
evaluate the residual forces present and the impact of adjustments to the system. Quantitative
calibrations of all celescos and load cell were undertaken, with repeat readings used, to gain calibration
factors that were applied to the experimental data. During these calibrations, it was found the horizontal
and vertical celescos added antisymmetric loading due to their resistances onto one side of the pipe,
causing it to no longer sit flush to the inside of the Perspex sheets. Therefore, to remove the influence
of these residual forces an additional celesco was added at an opposing angle to the resultant force of
the others (Figure 3).
Figure 3: Photographs of experimental setup, during filling of a preliminary loose experiment (left) the load
transfer mechanism with load cell (right).
To stiffen the tank steel bars were added horizontally below the pipe to prevent obstruction of failure
surfaces and to avoid interference with the load application. This was necessary due to deflections of
the Perspex sheets with self-weight of the sand; the Perspex appeared to be less stiff than initially
calculated and meant that the tight tolerances between the pipe, O-rings and the sheets were exceeded.
During loading and displacement of the pipe, this deflection allowed sand grains to move around the O-
rings and through the holes in the tank walls. In some cases, this loss was minimal but in other cases
was relatively significant. To accommodate this additional foam washers were added between the pipe
and the O-rings to give extra elasticity to the seal, and close the gap caused by such deflection of
approximately 1mm per sheet. Although these bars reduced the effects of deflection under self-weight,
under large load applications such as within the deeper burial depths, the sheets appeared to deflect
locally under large transverse forces, causing sand to again move into any gaps opening within the seal.
3.4 Limitations of the experimental methodology within this research
Within this experimental setup there are several aspects that were not considered, namely: (a) application
to partially saturated or saturated conditions, although it may be possible if the apparatus is adapted (b)
application to very deep burial depths of the pipe, (>5.25D); (c) materials with cohesion – the impact of
friction with the boundaries would be much more significant; (d) cyclic loading, although the actuator
system could be adapted in order to achieve this; (e) displacement of pipe beyond 0.54D, into the realm
of very large displacements and extensive residual forces; (f) different interface condition frictions; (g)
pipe deformations or strains induced in the pipe itself; (h) measurement of soil pressures on the pipe’s
surface; (i) impact of pipe’s self-weight in results; (j) direct impacts of scale effects due to reduction of
effective stresses around the soil, affecting the material’s elastic and shear modulus properties.
3.5 Test procedure
The main steps of the testing procedure are summarized in the following. A list of the experiments
undertaken is provided in Table 2.
1. Define burial depth required and set up horizontal marker on outside of tank for reference.
2. Fill tank in intervals of 50mm, pouring approximately 8kg of sand at a time uniformly across
the top, to create consistent density across the tank’s length.
3. Flatten and compact each layer if necessary (medium and dense tests) via the use of a timber
baton and a poker vibrator onto the soil’s surface, in increments along the tank’s length,
avoiding touching the Perspex sheets.
4. Before adding the pipe, fill and compact to a level 2.5cm below the bottom of the hole so that
the pipe sits at mid-depth within it; place pipe onto soil layer with bolt holes approximately
2mm from the left-hand side of the hole in the Perspex, so that the pipe’s displacement is
maximized. Support pipe whilst screwing threaded bar into both sides.
5. Fill tank carefully around the pipe’s lower half, ensuring full backfill under its lower side.
Compact sand at the pipe’s mid depth and repeat at 1cm above its surface. Continue filling the
tank evenly in 50mm layers until desired burial depth is obtained, ensure a level surface and
regular density throughout.
6. Attach loading straps and instrumentation to the pipe, apply small amount force to the straps via
the hand actuator so that the catenary is taken up.
7. Start acquisition system and video recording, slowly apply force via the hand actuator until the
pipe reaches close to the hole’s edge on the right-hand side.
8. Unload and stop acquisition, reset for next experiment.
Table 3: List of experiments undertaken, firstly loose and then a series of denser experiments.
Test 1
Test 11
Test 2
Test 12
Test 3
Test 13
Test 4
Test 14
Test 5
Test 15
Test 6
Test 7
Test 8
NOTE: The densities achieved were ± 0.1KN/m3 for the medium-dense state and ± 0.3KN/m3 for the loose.
3.6 Compaction testing of sand
To densify the sand, various forms of vibration were considered and the impact on the density was
evaluated. Leighton Buzzard sand is relatively coarse and poorly graded, therefore was not very
sensitive to compaction methods; during preliminary compaction testing of the sand using very thin
layers made a small amount of difference within density observed, Table 3.
Table 4: Summary of compaction of sand tests, using approximately 9kg of sand
Layer depth
Density (KN/m3)
Layer depth
As can be seen, the density achieved in the experiments was less than expected, this appears to be due
to its grading and the pluviation that occurs when pouring the sand into the tank. Due to the volume of
material, small vertical and horizontal stresses and small disturbance within the tank it does not naturally
consolidate and retains this loosened state.
4.1 Force-vs displacement relationship with ranging burial depths
Presented within Figure 4 and Figure 5 are the displacement responses to applied lateral force,
normalised for comparative means. Loose sand showed no peak in the force-displacement curve; the
peak value was equal to the residual. For less than 3.5D burial depth maximum force was reached,
however, for the deeper burial depths there was no plateau within the data. The so-called medium-dense
responses showed peak behaviour, and therefore both peak and residual forces are expressed within
Table 4. There is some uncertainty within all the values summarised within Table 4 due to the difficulty
in defining the point of failure and therefore these ultimate values, cases where this is prevalent are
shown by the “+” indicator within Error! Reference source not found.. Where the maximum force
value was not reached, and the maximum value observed was taken as this, shown by the “*” indicator.
Figure 4: Force - displacement curve for loose sand
Force-horizontal displacement (left), vertical displacement-force (right).
Figure 5: Force-displacement responses for dense sand
Force-horizontal displacement (left), vertical displacement-force (right).
In all experiments an initial force was needed to begin displacement of the sand, above that of the
residual forces within the experiment. This initial force was not consistent but generally appeared to
increase with burial depth. If related to friction either within the material or in relation to boundary
conditions this would increase due to increased normal stresses to the surface near to the pipe. Inclusion
or exclusion of this value in the results makes a significant difference as this initial force varies between
8-32% of the maximum force observed, with the most influenced values being at low burial depths.
Observed forces are higher than expected due to potential impacts of trapped sand between the pipe and
the tank walls, friction with the tank walls, and friction within the load application. Analysis of the
residual forces within the experiment indicated that they appeared to be quite random, however with
increasing number of tests, and more robust and consistent techniques, 19.3N was found to be the
consistent value for step 6 of the experimental procedure. No adjustments were taken for friction with
the boundary conditions due to the unknown quantification of their interaction. During testing sand often
propagated and became trapped within the O-ring seals, and once this occurred forced open a larger gap
00.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Dimensionless horizontal displacement
Dimensionless force
Normalised Force - Displacement for Loose Sand
00.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Dimensionless horizontal displacement
Dimensionless force
Normalised Force-Displacement For Medium-Dense Sand
for more to move into; this meant that the pipe could become relatively stuck as its displacement was
extended, and allowed sand to escape. It is considered that these sand losses would have had negligible
effects on the forces exerted but the trapping of sand and consequentially increased friction would have
significantly affected results at higher values of displacement, explaining why a plateau of maximum
force was not seen in the results of several experiments.
The right chart of Figure 4 and Figure 5 shows how the vertical displacement varies with applied load,
plotted with opposite axis for ease. This shows the magnitude of such displacements between the
experiments and where within the load application they present; the majority of the movement is beyond
70% of the ultimate force. The magnitude of the displacement is largest within the shallow burial depths,
indicating stronger dilation effects. The downward direction seen within some of the deeper burial
conditions is considered to be due to the pipe’s initial positioning within the hole or consolidation under
the pipe with loading. Due to the fixed location of the actuator, vertical displacements relative to the
centreline of the apparatus mean that a small component of the applied force act against such
displacements, however within the range of the experiment the magnitude of this force is minimal.
Table 5: Comparison of experimental results and theoretical values for ultimate and residual force with
corresponding displacement
γd = 14.6KN/m3
Burial Depth
yu lower
limit (mm)
γd = 15.4KN/m3
Burial Depth
yu lower
limit (mm)
yu upper
limit (mm)
NOTE:+Value taken where readings began to fluctuate. *Value taken as maximum observed within experiment
Figure 6: Dimensionless force factors for experimental data
Error! Reference source not found. demonstrates that the ultimate displacement for the low burial
depths fits well within the existing predictions, however the ultimate force has increased significantly,
generally by a factor of 2. Figure 4 and Figure 5 show that the ultimate force does not appear to have
been reached beyond 3.5D as the dimensionless force factor peaks at this value; within Figure
expected values are also plotted for comparison purposes from ALA guidelines using experimental
parameters. Figure 5 illustrates that within the medium-dense state, the maximum value of force reduces
relative to the residual value with depth; this reduction of peak behaviour could be contributed to by the
increasing frictional forces acting against the displacement and needs to be confirmed with more testing.
Error! Reference source not found. also illustrates that the ultimate displacements generally agree
with the findings of Trautmann, and O’Rourke (1985) and again indicate that the medium-dense
condition is so despite the low density.
Within the shallow burial depths an active wedge develops in front of the pipe with a shallow angle, and
a passive wedge with steeper angle behind, as shown in Figure 7, consistent with Rankine theory. The
sand’s surface illustrates such behaviour of large dilation in front of the pipe and a loss of material
behind. However, within deeper burial depths, smaller, more circular failure mechanisms are observed,
starting in front of the pipe leading to the back-top face, which mobilise less sand than the shallower
mechanism, resulting in less dilation of sand in front of the pipe, and less movement observed on the
surface. The secondary shear plane still develops behind the pipe, and connects to the surface, allowing
sand to flow down behind the pipe via passive behaviour to fill any voids created. A hole under the pipe
forms in most cases, where the sand cannot act to completely backfill the voids, especially where
movement is upward as well as horizontal as per shallow burial depths.
Figure 7: Comparison of failure mechanisms between different burial depths (a) loose (b) medium dense
Figure 8 also shows the differences between the failure surfaces and therefore the corresponding
mobilised soil wedges between the different burial depths and soil densities, the shaded areas move due
to either active (right-hand-side of pipe) or passive conditions (left-hand side), the arrows give a general
direction to this movement. Within the dense condition, the friction angles also increase and enables
steeper wedge angles comparatively, a larger area of soil behind the pipe within loose experiments
enables larger changes of height of the soil at the surface in this region, particularly at low burial depths.
With increasing burial depths the shape of the failure surface is modified due to higher confining
pressures and increased friction angles; increasingly becoming more curved, disconnecting from the soil
surface after burial of 3.5D. The size of this mobilised area of soil reduces significantly greater than
3.5D, which may contribute to why 3.5D appears to have higher than expected forces. The behaviour
seen here reinforces findings within Chaloulos et al. (2017), for general shear failure, type 1, and local
shear failure, type 3 and the intermediate shear failure, type 2.
Figure 8: Displacement trajectories for loose (left) and dense sand (right).
This paper describes an experimental study of soil-pipe interaction, particularly of the displacement
responses to laterally applied loading for the case of coarse grained sand under plane strain conditions.
Emphasis is placed on burial depths between 1-5.25D with the aim to investigate stiffness and ultimate
resistance implications for natural gas pipelines. A literature review shows the extent of current work in
experimental and numerical fields; however, few focus their efforts on quantifying soil stiffness
parameters in relation to implementation in modelling software.
Test results indicate that the experimental apparatus as a preliminary design are well founded, however
work needs to be done to quantify frictional interfaces as this appears to be significant within the results,
because of their relative magnitudes particularly at low burial depths. The displacement responses are
favorably comparable to other experimental results and the general trends of the data indicate that the
sand used does respond similarly to loose and then medium-dense conditions despite its density being
approximately 1KN/m3 less than anticipated, this highlights the subjective nature of interpreting the
design codes and the geotechnical understanding necessary of the design conditions.
As part of this research, maximum forces encountered in the experimental analysis were approximately
2x higher and this is thought to be due to sand grains jamming the seal between the pipe and tank sides.
This is very prominent within Leighton Buzzard sand due to its coarse nature, which would significantly
increase the friction between the pipe and the Perspex sheets. Repeating such tests with sands of different
geotechnical properties would help quantify such impacts on results.
In particular, the dimensionless curves are dominated by the 3.5D burial depth in both loose and
medium-dense conditions. This is thought to be related to the relative size of the failure wedge being
mobilised, as the 3.5D wedge is the largest due to transitioning to more circular failure mechanism shape
at deeper depths. This force increase is amplified if friction with the Perspex tank sides is significant.
Due to these frictional effects, residual forces were not reached in some of the deeper burial conditions
contrary to expectations. The displacement measurements recorded within this research indicate 2D
movements of the pipe as a response to lateral forces, therefore conventional horizontal force-
displacement curves only capture one dimension of the resultant response. It is proposed that 2D coupled
springs are used to describe such soil-pipe system responses analytically, which capture the vector
displacements. The magnitude of vertical displacement increases significantly post 70% of the
maximum force, especially once residual forces have been reached; in combination to their low values
for ultimate displacement, this means that for very shallow pipelines subjected to large displacements,
shallow pipes are more vulnerable of moving to the surface. This directly impacts seismic vulnerability
and other causes of PGDs. Further research is currently undertaken that involves repetition of the tests
for different tank widths, refined numerical verification and explicit consideration of friction effects
between the soil and the tank surfaces.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Dimensionless horizontal displacement
Dimensionless vertical displacement
Vertical vs Horizontal Displacement
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Dimensionless horizontal displacement
Dimensionless vertical displacement
Vertical vs Horizontal Displacement
This work was supported by the Horizon 2020 MSCA-RISE-2015 project No. 691213 entitled
"Experimental Computational Hybrid Assessment of Natural Gas Pipelines Exposed to Seismic Risk
(EXCHANGE-RISK)". This support is gratefully acknowledged.
American Lifelines Alliance (ALA). (2005). Guidelines for the Design of Buried Steel Pipe (Vol. 2001).
Audibert, J. M. E., & Nyman, K. J. (1977). Soil restraint against horizontal motion of pipes. Journal of the
Geotechnical Engineering Division, ASCE, 103(GT10), 1119–1142.
Chaloulos, Y. K., Bouckovalas, G. D., & Karamitros, D. K. (2017). Trench effects on lateral p-y relations for
pipelines embedded in stiff soils and rocks. Computers and Geotechnics, 83, 52–63.
Daiyan, N., Kenny, S., Phillips, R., & Popescu, R. (2011). Investigating pipeline–soil interaction under axial–
lateral relative movements in sand. Canadian Geotechnical Journal, 48(11), 1683–1695.
Drescher, A., Vardoulakis, I., & Han, C. (1990). A biaxial apparatus for testing soils. Geotechnical Testing
Journal, 13(3), 226–234.
El Hmadi, K., & O’Rourke, M. J. (1988). Soil Springs for Buried Pipeline Axial Motion. Journal of
Geotechnical Engineering, 114(11), 1335–1339.
Kouretzis, G. P., Sheng, D., & Sloan, S. W. (2013). Sand-pipeline-trench lateral interaction effects for shallow
buried pipelines. Computers and Geotechnics, 54, 53–59.
Matsii, S. I., & Derevenets, F. N. (2005). Application of finite-element method to investigate interaction between
slide-prone soils and piles. Soil Mechanics and Foundation Engineering, 42(4), 120–126.
O’Rourke, M. J., & Liu, X. (1999). Response of Buried Pipelines Subject to Earthquake Effects, Monograph
Series #3. Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo.
Roy, K., Hawlader, B., Kenny, S., & Moore, I. (2015). Finite element modeling of lateral pipeline–soil
interactions in dense sand. Canadian Geotechnical Journal, 53(3), 490–504.
Trautmann, C. H., & O’Rourke, T. D. (1983). Behaviour of pipe in dry sand under lateral and uplift loading,
Geotechnical Engineering Report 83, School Civil and Environmental Engineering, Cornell University.
Trautmann, C. H., & O’Rourke, T. D. (1985). Lateral force-displacement of buried pipe response. Journal of
Geotechnical Engineering, 111(9), 1077–1092. 1077/$01.00
Yimsiri, S., Soga, K., Yoshizaki, K., Dasari, G. R., & O’Rourke, T. D. (2004). Lateral and upward soil-pipeline
interactions in sand for deep embedment conditions. Journal of Geotechnical and Geoenvironmental
Engineering, ASCE, 130(8), 830–842.
... In light of the geographically distributed hybrid test that is planned for year 3 of the project experimental framework has been initiated in the Universities of Bristol, Toronto and Patras. First, an experimental setup was constructed at the University of Bristol to study the in-plane stiffness of the soil-pipe system (Crewe et al., 2018) confirming good agreement with respect to numerical analyses and previous findings from the literature (Figures 2 and 3). A complementary setup has also been developed in Toronto to consider the cyclic nature of earthquake loading (Figure 4). ...
... Experimental setup to study the soil-pipeline static stiffness(Crewe et al., 2018). ...
Conference Paper
Full-text available
Historically, a number of major catastrophic earthquakes have resulted in a real loss of life and property worldwide. During the last decades, in particular, the overall exposure to seismic risk has increased not only due to the higher population density but also due to the more challenging construction methods and the multilayered connection between the various urban socioeconomic activities. Within this complex built environment, the energy transportation systems, despite their structural simplicity, are seemingly one of the weakest links in terms of seismic safety. Currently, energy production, preservation and safe transportation is one of the top priorities. This demands the need to eliminate the probability of occurrence of a potential seismically induced failure (i.e., related to explosion, fire, leakage etc) that would not only have devastating environmental impact in the affected areas, but could also cause operation disruptions with equally significant socioeconomic consequences throughout Europe. EXCHANGE-Risk is an Intersectoral/International, Research and Innovation transfer scheme between academia and the industry in Europe and North America focusing on mitigating Seismic Risk of buried steel pipeline Networks subjected to ground-imposed permanent and co-seismic deformations. This paper discusses the challenges addressed by EXCHANGE-Risk and the recent advancements made in this topic. It also paves the road for further discussion on the methodologies, experiments and tools that need to be developed to mitigate seismic risk of natural gas pipelines at a European level and beyond.
... In 2017, Stubbs studied the SPI behavior of buried pipelines in shallow depths by implementing laboratory experiments, see Figure 4 (Stubbs 2017, Crewe, 2018. As it is shown in Figure 5, the SPI curves show a smooth transition from linear phase to the plastic one. ...
... Force-horizontal displacement curve for loose sand at different depths, where D denotes the diameter of the pipe(Stubbs 2017). ...
Conference Paper
Full-text available
The present work focuses on the response of pipelines traversing slopes under asynchronous acceleration time histories induced by earthquakes. To this end, nonlinear generalized mechanical models are developed and used in order to describe the soil-pipe interaction phenomena. More specifically, two basic types of models are used: the first one comprises two elastoplastic generalized spring elements connected in parallel with a trilinear elastic spring (labeled as sub-models 1 and 3), while the second model comprises three elastoplastic elements, all connected in parallel (labeled as sub-models 2 and 4). The purpose of the current study is twofold, firstly to introduce nonlinear mechanical models that enable a smooth transition between the elastic and plastic phases and at the same time control the damping in the soil-pipe interaction, and secondly to investigate the effect of the soil strength and soil damping on the axial force that develop in pipelines on slopes. Results are presented from a real pipeline subjected to asynchronous accelerations along a submarine slope.
Full-text available
This paper presents results from an experimental and numerical study on the axial-lateral interaction of pipes with dense sand. A series of centrifuge tests were conducted, with a rigid pipeline displaced in the horizontal plane in a cohesionless test bed. The relative pipe-soil interaction included axial, lateral, and oblique loading events. A three-dimensional continuum finite element model was developed using ABAQUS/Standard (Hibbitt et al. 2005) software. The numerical model was calibrated against experimental results. A parametric study was conducted, using the calibrated finite element model to extend the investigations. The ultimate axial and lateral soil loading was found to be dependent on the angle of attack for relative movement between the pipe and soil. Two different failure mechanisms were observed for axial-lateral pipeline-soil interaction. This study confirms and improves on a two-part failure criterion that accounts for axial-lateral coupling during oblique soil loading events on buried pipelines.
Full-text available
The soil-pipeline interactions in sand under lateral and upward movements are investigated with particular attention to the peak forces exerted on the pipe. The analytical solutions for estimating the peak forces are summarized and it is shown that, for deep embedment condition, there is large uncertainty in the true values since the bounds established by the analytical solutions are large. In order to find the solution for the peak force and to investigate its transition from shallow to deep failure mechanism, finite element analyses of lateral and upward pipe movements are performed for different embedment conditions. Two different soil models (Mohr-Coulomb and Nor-Sand models) are used for the simulations. The accuracy of the analysis is first examined by simulating experimental tank tests. The analysis is further extended to deeper embedment ratios of as large as 100. The obtained finite element results are used to construct a design chart for deep embedded pipelines.
Existing relationships for lateral backfill pressures on pipelines assume that the trench is adequately wide to contain the failure surface. This condition is commonly violated in design and construction practice, putting at risk the pipeline safety. In this context, size and shape effects for trenches excavated in stiff soils and rocks, are numerically investigated, through experimentally-calibrated parametric analyses. It is shown that, for narrow trenches, ultimate pressures and yield displacements may increase up to an order of magnitude compared to “infinite-trench” values, while excavation of inclined walls reduces the above detrimental effects. Simplified relations are developed to aid pipeline design.
The safe and economical design of buried pipes subjected to lateral motion requires an accurate knowledge of the subgrade reaction. Too often values of the coefficient of horizontal subgrade reaction, k//S//h, reported in the literature are used without understanding the author's intentions and without thought as to whether or not the conditions in the particular application are compatible to those in the literature. A survey of the available literature discloses that the numerical values and formulations proposed were such as to underestimate the soil restraint against flexible culverts and laterally loaded piles. These values are inadequate for the safe design of buried pipes laterally displaced by settlement, thermal expansion, earthquake shaking or wave action. The results of a laboratory testing program show the complex soil-conduit interaction and the associated failure mechanisms. An analytical method is presented to determine the load-displacement curve for any size pipe embedded at any given depth. A moderate size in-situ test was performed, which confirmed that the results of the laboratory model tests could be successfully applied to in-situ conditions.
Finite element (FE) analyses of pipeline-soil interaction for pipelines buried in dense sand subjected to lateral ground displacements are presented in this paper. Analysis is performed — using the Arbitrary Lagrangian-Eulerian (ALE) method available in Abaqus/Explicit FE software — in the plane strain condition using the Mohr-Coulomb (MC) and modified Mohr-Coulomb (MMC) models. The MMC model considers a number of important features and properties of stress-strain and volume change behaviour of dense sand including the nonlinear pre-and post-peak behaviour with a smooth transition and the variation of the angle of internal friction and dilation angle with plastic shear strain, loading conditions (triaxial or plane strain), density, and mean effective stress. Comparing FE and experimental results, it is shown that the MMC model can better simulate the force-displacement response for a wide range of lateral displacements of the pipe for different burial depths, although the peak force on the pipe could be matched using theMCmodel. Examining the progressive development of zones of large inelastic shear deformation (shear bands), it is shown that the mobilized angle of internal friction and dilation angle vary along the length of the shear band; however, constant values are used in the MC model. A comprehensive parametric study is also performed to investigate the effects of pipeline diameter, burial depth, and soil properties. Many important aspects in the force-displacement curves and failure mechanisms are explained using the present FE analyses. © 2016, National Research Council of Canada. All Rights Reserved.
A large-deformation numerical methodology is applied to simulate the interaction effects for a pipeline installed in a trench backfilled with loosely deposited dry sand, focusing on shallow buried pipelines subjected to lateral displacements relative to the surrounding soil. Based on the backfill–pipeline deformation mode under shallow embedment conditions, described in previous experimental studies, analyses are performed while considering only the critical state shear strength parameters of the backfill. The numerical methodology is validated against experimental full-scale test measurements from the literature, for pipelines buried in uniform dry loose and medium sand. Parametric analyses are performed to generate approximate formulas and charts for calculating (i) the maximum force on the pipeline and (ii) the minimum trench dimensions to eliminate interaction with the surrounding natural ground. Application of the proposed approach in the prediction of independent full-scale test results for a pipeline embedded in a shallow trench demonstrates its effectiveness, and underlines the effect of trench dimensioning on the response of the pipeline.
The response of a buried pipeline to seismic waves is controlled by differential movements along its length. The axial movement of the pipeline is restrained by friction forces at the soil-pipe interface. Tests performed by others on a full scale pipe indicate that the relationship between the soil resistant force and relative displacement (i.e., between the soil and the pipe) is linear at small displacements. This soil resistant force reaches a ``plateau'' when shippage of the pipe with respect to the soil occurs. This suggests that the axial soil-pipe interaction can be modeled by discrete spring-sliders distributed along the pipeline. The initial stiffness of these spring-sliders is the subject of this technical note. First, previous studies evaluating this initial soil axial stiffness are reviewed. Then, results from the field tests are used to backcalculate the value of the initial soil stiffness. On the basis of the results obtained, a range of values is proposed to estimate the initial soil axial stiffness.
An analytical scheme using the finite-element method is proposed for interaction between slide-prone soils and piles in single-row anti-slide structures. Results are presented for calculation and analysis of the stress-strain state of slide-prone soils interacting with the piles.