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Rev. Fr. Geotech.
Numéro 168, 2021
Modélisation Physique en Géotechnique - Partie 2
Numéro d'article 3
Nombre de pages 14
DOI https://doi.org/10.1051/geotech/2021013
Publié en ligne 21 avril 2021

© CFMS-CFGI-CFMR-CFG, 2021

1 Introduction

The evaluation of lateral soil-pipe forces during large loading cycles is fundamental in pipeline design which is a pipe carrying up oil and gas from the wellheads on the seabed to the unit on the surface. Many authors (Cheuk et al., 2007a; Dingle et al., 2008; White and Cheuk, 2008; Merifield et al., 2009; Oliphant et al., 2009; Oliveira et al., 2010; Lee et al., 2011, Chatterjee et al., 2012; Kong et al., 2017, 2020; Cocjin et al., 2018; Rismanchian et al., 2019) have made contributions towards the understanding of soil-pipe interaction mechanisms on offshore pipelines.

Pipeline performance is affected by lateral movements (Morris and Webb, 1988; Wang et al., 2017; White et al., 2017) where a trench is formed by the lateral displacements of the pipe. These cyclic movements result in a combination of pipe-soil interaction at the trench wall (berm), and can lead to lateral forces being imposed on the pipe. Therefore, a significant lateral resistance of the soil is mobilized when the pipe is in contact with the soil berm (You et al., 2008; Rismanchian et al., 2019). Soil berms restrict the increase in lateral displacements in situations of high compression stresses along the pipe structure (Bruton et al., 2006), such as pipe buckling which is caused by the combination of temperature increase and axial restraints on the pipe.

The objective of this paper is to understand the behaviour of lateral clay-pipe interaction, particularly the large deformations associated with the berm formation process at the leading edge of the pipe during movement at given burial depths. In order to achieve this, a series of centrifuge tests was conducted to assess the relationship between horizontal force and lateral pipe displacement. Although cyclic tests have been undertaken, the analysis presented herein focuses on the first cycle, including the resistance associated with breakout and berm formation at specific burial depths. This burial depth parameterization is important because it simplifies the use of the results as input parameters in numerical analysis. This is the main reason why the burial depth of the pipe is imposed during the tests.

2 Literature background

Lateral resistance is associated with forces at breakout (Hb) and after breakout (Hr). Oliveira et al. (2010) proposed equation (1) to estimate the breakout horizontal forces acting on the pipe when subjected to lateral movements. According to the authors, the constant n0 is associated with the development of failure surfaces, which, in turn, represents the amount of mobilized resistance during breakout. For the very soft Guanabara Bay clay used by Oliveira et al. (2010), a value of n0 = 1.0 was assumed. (1)

The breakout resistance can also be calculated as the sum of a friction and a passive component (Hb = Hbf + Hbp), while the force after breakout (Hr) is basically the increase in lateral resistance due to formation and augmentation of a soil berm in front of the pipe, as it moves. The friction force is calculated as Hbf = µW’, where W’ is the submerged pipe weight and µ is the friction coefficient. Verley and Lund (1995), Bruton et al. (2006) and Dendani and Jaeck (2007) proposed the use of equation (2) to estimate the passive force Hbp. (2) where Su is the soil undrained shear strength, γ’ is the soil submerged unit weight, w is the pipe burial depth from the pipe invert to the soil surface and D is the pipe diameter. Each author has suggested different values for constants a, b and c.

According to Randolph (2012), depending on the relationship between the soil undrained shear strength (Su) and the pipe submerged weight (W’), the lateral force may decrease or increase in magnitude after breakout. In such cases, the pipe can be assigned as a light (W’/SuD < 2) or a heavy pipe (W’/SuD > 2), respectively. Pronounced breakout peaks may also be related to suction forces developed at the back of the pipe, at the onset of displacement.

White et al. (2017) present the following expression proposed by Cheuk and White (2010) to assess the lateral breakout peak force: (3)

3 Centrifuge tests set up

The Federal University of Rio de Janeiro (UFRJ) 1.6 m diameter beam centrifuge (Almeida et al., 2014; Lukiantchuki et al., 2018) comprises a strong box able to contain a 0.100 m wide, 0.300 m long and 0.180 m high soil sample. A dual axis (Z-X) electric linear actuator and drive system (Fig. 1) is able to apply downward and upward movements (Z axis) as well as horizontal movement along the length of a sample (X axis).

The main objective of these tests is to cyclically drive a rigid pipe section laterally forward and backward on a clay layer while keeping the vertical position constant. The rigid pipe section represents a plane strain condition. Similar tests were conducted by Bruton et al. (2008), Dingle et al. (2008) and White and Cheuk (2008).

The horizontal pipe is attached to a vertical rod that maintains the pipeline at a constant elevation (Fig. 1). A Measurement Specialities ELPF-T2M-100N load cell, with 0.25 N accuracy, placed on the rod above the pipe, measures the applied vertical force in real time. In order to assess the horizontal forces acting on the pipe, a full Wheatstone bridge, using four Micro-Measuremnents EA-13-062AQ-350 strain gauges, with 50 N maximum capacity was installed on a narrow section of the rod, which holds the pipe in position.

A scale factor of N = 33 was chosen as adequate for the simulations, in order to accommodate requirements regarding the size of the model pipe, the thickness of the clay layer, the magnitude of the applied load and to meet the technical capabilities of the centrifuge actuators. Table 1 presents the centrifuge scaling relationships for the most relevant parameters regarding this research.

Two pipe diameters of 9 mm and 15 mm in model scale were adopted for the tests, corresponding to typical pipeline diameters of 0.3 m and 0.5 m in prototype scale. Two tests were conducted per container with the same soil sample for the 9 mm diameter pipe, while one test was conducted per container with the same soil sample for the 15 mm diameter pipe. Figure 1 shows the test set up for the bigger pipe.

thumbnail Fig. 1

Test set-up for the 15 mm diameter pipe.

Schéma du montage pour le tuyau de 15 mm de diamètre.
Table 1

Centrifuge scaling relationships for a scale factor of N.

Facteurs d’échelle en centrifugeuse.

4 Soil parameters and clay layer preparation

An artificial kaolin clay soil was used for the tests to increase repeatability, since natural soils tend to be more variable. A series of soil characterization, X-ray diffraction, consolidation, and isotropic (CIU) and anisotropic (CAU) consolidated triaxial tests were undertaken to assess the geotechnical parameters, which are presented in Table 2.

The clay beds were built using the well-established clay lumps technique (Manivannan et al., 1998; Cheuk et al., 2007b; Oliveira et al., 2010; Rammah et al., 2014) with the kaolin at a water content of 1.5wL which was found to improve workability and facilitate collapse of the macro voids. Water content measurements taken after the tests show the suitability of this technique. The main purpose was to build both a weaker (Profile 1) and a stronger (Profile 2) clay layer with undrained strength values of around 4 kPa and 14 kPa at a 0.5 m depth in prototype scale, respectively (Fig. 2).

After placing the lumps in the strong box, a temporary surcharge of 19.7 kPa (Profile 1) and 118.4 kPa (Profile 2) was applied to the clay surface by means of a rigid platen and the centrifuge was accelerated to 100 × g until the clay reached 85% consolidation. A PDCR 81-8317 pore-pressure transducer from GE Druck Incorporated was used to monitor the pore-pressure dissipation during consolidation and an OADM 12U6460/S35A laser distance sensor from Baumer Electric was used to track the clay settlement.

After the consolidation phase, the centrifuge was stopped, the surcharge was removed and the clay layer was considered ready for the actuation phase. Based on a series of preliminary tests, a set of vertical forces was selected to lead, roughly, to embedment ratios of w/D = 25%, 50% and 75%. The respective embedment ratios were kept constant during the entire lateral actuations. Therefore, all tests are considered normally penetrated which means that the soil was not subjected to a force higher than the one experienced during installation.

Afterward, the pipe is moved laterally forward and backward for a distance equivalent to three diameters in each direction for 12 complete cycles (Fig. 1). The fastest possible actuation velocities are v = 0.86 mm/s and v = 1.44 mm/s for the 15 mm and 9 mm diameter pipes, respectively, which corresponds to a non-dimensional velocity of V’ = vD/cv = 20. This velocity is fast enough to characterize undrained behaviour and yet slow enough to avoid any viscous effect while conforming to the capability of the equipment (Randolph and Hope, 2004; Schneider et al., 2007; Oliveira et al., 2011). Prototype velocities of pipe movements are reported to lie within the undrained behaviour range (Bruton et al., 2006).

After the actuation, in order to assess the undrained strength profile of the clay layer, T-bar penetration tests were carried out in each container (Fig. 1). Figure 2 presents the T-bar curves for the minimum, mean, and maximum Su profiles for all tests. Although some variation was observed, particularly for shallow depths in Profile 2, the minimum and maximum curves are reasonably close to each other showing good repeatability. These Su profiles are in the range of lightly overconsolidated clay sediments found in the Brazilian continental basin (Cardoso and Silveira, 2010; Cardoso et al., 2015). Lateral forces in each test were normalized by the undrained strength value at the test embedment depth, therefore the observed scatter was duly considered.

Table 2

Geotechnical parameters of the kaolin soil used in the study

Paramètres géotechniques du kaolin

thumbnail Fig. 2

Undrained strength from T-bar penetrometer for: (a) Profile 1; (b) Profile 2.

Cohésion non drainée (T-bar) pour : (a) le profil 1 ; (b) le profil 2.

5 Test results

Table 3 presents the centrifuge test characteristics and results from the 16 tests in Profile 1 and 15 tests in Profile 2 where w is the pipe embedment measured from the bottom of the pipe, D is the pipe diameter and w/D is the embedment ratio. The actual embedment ratios are not exactly the target values of 25%, 50% and 75%, but they were considered close enough.

Figures 3 and 4 show typical lateral and vertical forces-displacement responses for w/D = 25% and 75%. Regarding the lateral force, initially, the breakout resistance is mobilized within a displacement of around 0.1D. Following the breakout, a slight increase in lateral resistance is observed, which is associated to a soil berm formation in front of the pipe. The lateral force continues to increase until the pipe reaches the maximum pre-established displacement of 3D, which is around the order of magnitude associated with lateral movements of pipelines (Bruton et al., 2006). As the pipe reverses its movement, a smaller berm is also formed when it returns to its initial position. With the cycles, the maximum lateral force decreases at both ends while the force values approach zero at the midpoint. The decrease in lateral resistance is associated with the lack of soil in front of the pipe, which is almost completely scraped away by the pipe during the previous cycles.

When it comes to the vertical forces, the first cycle for w/D = 25% shows an increase of about 100%, while for w/D = 75% the force stayed nearly constant. Regarding the following cycles, vertical forces were only different from zero close to the initial and final pipe positions, where the berms are located.

The results show the behaviour of a pipe with its initial embedment kept constant throughout the lateral cycles (25%, 50% and 75%). This means that the pipe cannot be correctly classified as light or heavy since the vertical force tends to decrease as the pipe scrapes the soil and forms the berm. In the first cycle, as the pipe continuously moves, the lateral residual force increases and then stabilizes to reach a final value associated to the specific burial depth.

Figure 5 shows typical normalized lateral breakout force versus normalized displacement response for different pipe diameters and soil profiles. Test results are compared to predictions by Verley and Lund (1995), Bruton et al. (2006), Dendani and Jaeck (2007) and Cheuk and White (2010). In general, to allow comparison between equations based on constant vertical load tests and the results presented in this work, the measured vertical load values associated with each breakout lateral forces were used to calculate the predicted values at this point. The results showed good agreement, most closely matching those presented by Dendani and Jaeck (2007).

Figure 6 presents a comparison between some of the tests and the envelope curves proposed by Lee et al. (2011) based on sideswipe (constant w/D) and probe (constant force) tests. The results are in accordance with the respective envelopes showing that the horizontal (H) and vertical (V) forces reach very quickly the yield surface, where a hardening phase begins associated with a berm formation in front of the pipe. All forces were normalized by the maximum vertical force for each test (Vmax).

The decay of normalized lateral and vertical forces relative to the number of cycles is shown in Figure 7. In the first cycle, the pipe forms a trench as it moves laterally, scraping the soil and pushing it to form a berm. With each following cycle, the pipe keeps scraping lesser amounts of soil and depositing it in the berm. As a result, the lateral forces acting on the pipe continuously decline until reaching a constant value, as well as the vertical forces. This mechanism will be better understood in the following section.

Table 3

Centrifuge tests program.

Programme d’essais en centrifugeuse.

thumbnail Fig. 3

Typical lateral force (a) and vertical force (b) versus lateral displacement test curves for 25% embedment ratio.

Courbes d’essai typiques de la force latérale (a) et de la force verticale (b) en fonction du déplacement latéral pour un rapport d’encastrement de 25 %.
thumbnail Fig. 4

Typical lateral force (a) and vertical force (b) versus lateral displacement test curves for 75% embedment ratio.

Courbes d’essai typiques de la force latérale (a) et de la force verticale (b) en fonction du déplacement latéral pour un taux d’encastrement de 75 %.
thumbnail Fig. 5

Normalized lateral breakout forces versus normalized embedment.

Forces de rupture latérales normalisées en fonction de l’encastrement normalisé.
thumbnail Fig. 6

Comparison between test results and envelopes proposed by Lee et al. (2011).

Comparaison entre les résultats des tests et les enveloppes proposées par Lee et al. (2011).
thumbnail Fig. 7

Normalized lateral and vertical forces decay in the berm with cycles.

Evolution des forces latérales et verticales normalisées dans la berme au fil des cycles.

6 Procedure to assess the normalized lateral force

Based on the physical modelling results, a simplified procedure is presented to estimate the normalized lateral force. The main parameters associated with the lateral movement are: the pipe diameter (D), the pipe length (L), the undrained shear strength (Su), the burial depth (w) and the lateral displacement (u). The correct identification of these parameters is essential to understand the failure mechanisms taking place in the soil.

The normalized lateral force at breakout (Nh1 = Hb/(Su ⋅ D ⋅ L)) is a direct function (Fig. 8) of the embedment ratio (w/D), while the increase in normalized lateral force due to berm formation (Nh2 = Hr/(Su ⋅ D ⋅ L)) is a direct function (Fig. 8) of the normalized lateral displacement (u/D). Therefore, the total normalized lateral force (Nh = (Hb + Hr)/(Su ⋅ D ⋅ L)) can be factored as the sum of these two parts. (4)

Hb in Nh1 equation presented above can be calculated using equation (1) while Nh2 can be estimated by means of Rankine’s classical plastic failure mechanism of a smooth retaining wall, adapted for the berm in front of the pipe. (5) where γ is the soil unit weight and Ds is the height from the bottom of the pipe to the centre of gravity of the berm, assuming berms as semi-circular forms (Fig. 9).

It is important to note that the lateral force, considering breakout and berm, is a function of both normalized burial depth and normalized displacement.

Figure 8 presents a comparison between the experimental horizontal breakout values and the model proposed by Oliveira et al. (2010). The authors used n0 = 1.0 for the very soft Guanabara Bay clay, which has different soil properties when compared to the artificial kaolin clay used herein. Figure 8 shows that experimental values from the present study fit equation (1) well by adopting n0 = 0.5.

Nh2 was evaluated based on the increase in the lateral resistance due to formation and augmentation of a berm in front of the pipe, as it moves. The normalized passive force Nh2 is given by (6)

As shown in Figure 9, Ds increases with: the pipe diameter D; the non-dimensional displacement u/D; and an increasing rate per length constant assigned as a. The more direct way to take into account all of these parameters is through a simple multiplication of them, which leads to equation (7) and consequently to equation (8). (7) (8)

Therefore, Nh can be written as: (9)

Comparisons between lateral normalized force (Nh) data and the proposed equation are presented in Figures 10 and 11, for Profiles 1 and 2, respectively, with n0 = 0.50 and a = 0.10. The experimental results fit the model better in Profile 1 than in Profile 2, but in both cases, the trends are the same and the predictions are reasonable.

Figure 12 shows a comparison between the calculated and experimental values of the normalized lateral force (Nh) for both profiles. The values are quite close, with a slightly higher scatter in Profile 2.

thumbnail Fig. 8

Comparison between Oliveira et al. (2010) (data and linear fit) and lateral normalized force data at breakout.

Comparaison entre Oliveira et al. (2010) (données et ajustement linéaire) et les données de force latérale normalisée à la rupture.
thumbnail Fig. 9

Proposed model of berm increase with u/D.

Modèle proposé d’accroissement de la berme avec u/D.
thumbnail Fig. 10

Comparisons between experimental values (points) and the proposed model for Lateral Normalized Forces (lines) – Profile 1.

Comparaisons entre les valeurs expérimentales (points) et le modèle proposé pour les forces latérales normalisées (lignes) – Profil 1.
thumbnail Fig. 11

Comparisons between experimental values (points) and the proposed model for Lateral Normalized Forces (lines) – Profile 2.

Comparaisons entre les valeurs expérimentales (points) et le modèle proposé pour les forces latérales normalisées (lignes) – Profil 2.
thumbnail Fig. 12

Comparisons between experimental and proposed model values.

Comparaisons entre les valeurs expérimentales et les valeurs du modèle proposé.

7 Conclusions

A series of 31 centrifuge tests was conducted in artificial kaolin clay to study the behaviour of lateral clay-pipe interaction focusing on large deformations associated with the berm formation process in front of the pipe during the movement. The tests were conducted for pipe diameters of 0.3 m and 0.5 m, and embedment ratios from 16% to 84%.

The normalized lateral breakout forces were compared with predictions from Verley and Lund (1995), Bruton et al. (2006), Dendani and Jaeck (2007) and Cheuk and White (2010), showing a good agreement. The tests also proved to be in accordance with envelope curves proposed by Lee et al. (2011) showing that the forces reach very quickly the yield surface, where a hardening phase begins associated with a berm formation in front of the pipe.

A simplified procedure was presented to estimate the normalized lateral force, taking into account the breakout resistance and the increase in the force due to berm formation. The breakout resistance was calculated using the equation proposed by Oliveira et al. (2010) while the increase in the force from the berm was estimated by means of Rankine’s classical approach to the plastic failure mechanism of a smooth retaining wall, adapted for the berm in front of the pipe. Comparisons between the experimental data and the equation proposed in this work show good correlation but further investigation is needed to validate this approach. Furthermore, both normalized lateral forces and forces in the berm decayed rapidly with the cycles showing significant degradation in soil confinement capacity.

List of notations

a: Constant value

b: Constant value

c: Constant value

cv: Coefficient of consolidation

CAU: Consolidated Anisotropic Undrained

CIU: Consolidated Isotropic Undrained

D: Pipe diameter

Ds: Height from the bottom of the pipe to the centre of gravity of the berm

H: Horizontal force

Hb: Breakout force

Hr: After breakout force

Hbf: Friction breakout force

Hbp: Passive breakout force

L: Pipe length

N: Scale factor

Nh: Normalized lateral force

Nh1: Normalized lateral force at breakout

Nh2: Normalized lateral force at berm

nₒ: Constant value

Su: Soil undrained shear strength

UCS: Soil Unified Classification System

u: Lateral displacement

v: Velocity of actuation

V: Vertical force

V’: Non-dimensional velocity

Vmax: Maximum vertical force

w: Pipe burial depth from the pipe invert to the soil surface

W’: Submerged pipe weight

wL: Soil liquid limit

wP: Soil plastic limit

X: “x” axis

Z: “z” axis

γ: Soil unit weight

γ’: Soil submerged unit weight

µ: Friction coefficient

Acknowledgements

The authors would like to acknowledge FINEP and TECHNIP for the financial support and the interest in this study. This research was financed in part by the “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior” (CAPES) and by CNPq, Brazilian Research Council.

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Cite this article as: Pablo Cesar Trejo, Jose Renato M.S. Oliveira, Márcio S.S. Almeida, Maria C.F. Almeida, Mario A. Vignoles. A procedure to estimate the lateral force in clay-pipe interaction after breakout. Rev. Fr. Geotech. 2021, 168, 3.

All Tables

Table 1

Centrifuge scaling relationships for a scale factor of N.

Facteurs d’échelle en centrifugeuse.

In the text
Table 2

Geotechnical parameters of the kaolin soil used in the study

Paramètres géotechniques du kaolin

In the text
Table 3

Centrifuge tests program.

Programme d’essais en centrifugeuse.

In the text

All Figures

thumbnail Fig. 1

Test set-up for the 15 mm diameter pipe.

Schéma du montage pour le tuyau de 15 mm de diamètre.
In the text
thumbnail Fig. 2

Undrained strength from T-bar penetrometer for: (a) Profile 1; (b) Profile 2.

Cohésion non drainée (T-bar) pour : (a) le profil 1 ; (b) le profil 2.
In the text
thumbnail Fig. 3

Typical lateral force (a) and vertical force (b) versus lateral displacement test curves for 25% embedment ratio.

Courbes d’essai typiques de la force latérale (a) et de la force verticale (b) en fonction du déplacement latéral pour un rapport d’encastrement de 25 %.
In the text
thumbnail Fig. 4

Typical lateral force (a) and vertical force (b) versus lateral displacement test curves for 75% embedment ratio.

Courbes d’essai typiques de la force latérale (a) et de la force verticale (b) en fonction du déplacement latéral pour un taux d’encastrement de 75 %.
In the text
thumbnail Fig. 5

Normalized lateral breakout forces versus normalized embedment.

Forces de rupture latérales normalisées en fonction de l’encastrement normalisé.
In the text
thumbnail Fig. 6

Comparison between test results and envelopes proposed by Lee et al. (2011).

Comparaison entre les résultats des tests et les enveloppes proposées par Lee et al. (2011).
In the text
thumbnail Fig. 7

Normalized lateral and vertical forces decay in the berm with cycles.

Evolution des forces latérales et verticales normalisées dans la berme au fil des cycles.
In the text
thumbnail Fig. 8

Comparison between Oliveira et al. (2010) (data and linear fit) and lateral normalized force data at breakout.

Comparaison entre Oliveira et al. (2010) (données et ajustement linéaire) et les données de force latérale normalisée à la rupture.
In the text
thumbnail Fig. 9

Proposed model of berm increase with u/D.

Modèle proposé d’accroissement de la berme avec u/D.
In the text
thumbnail Fig. 10

Comparisons between experimental values (points) and the proposed model for Lateral Normalized Forces (lines) – Profile 1.

Comparaisons entre les valeurs expérimentales (points) et le modèle proposé pour les forces latérales normalisées (lignes) – Profil 1.
In the text
thumbnail Fig. 11

Comparisons between experimental values (points) and the proposed model for Lateral Normalized Forces (lines) – Profile 2.

Comparaisons entre les valeurs expérimentales (points) et le modèle proposé pour les forces latérales normalisées (lignes) – Profil 2.
In the text
thumbnail Fig. 12

Comparisons between experimental and proposed model values.

Comparaisons entre les valeurs expérimentales et les valeurs du modèle proposé.
In the text

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