Experimental and Numerical Study on the Dragged Anchor–Trenchless Rock Berm Interaction

1. Introduction

Over the past decades, new energy reservoirs located offshore have been regularly discovered and industry needs to deliver the extracted oil and gas to the storage places, refineries, or processing plants located on land. For this, offshore pipelines play an important role in global economies and civil lives. Their protection from mechanical threats and damages means great value for industries and societies (Mustafina [2015]; Bartolini et al. [2018]). Among these threats, dragged anchors, dropped objects, sinking ships, etc. may cause severe mechanical damage or pipeline ruptures, specifically in areas with high/medium ship traffic.

Due to the importance of physical protection of pipelines during their lifetime, the risk of dragged anchors for submerged pipeline and their interaction has been addressed by Brown [1973], Mousselli [1978] and Hvam et al. [1990], and offshore codes and specifications by Australian Marine [1999] and DNV Offshore Standard [2000]. Macdonald et al. [2007] argued that even a small dent due to physical damage to the pipe body could result in a serious reduction in the strength of the weld and base metal. Although the risk of dropped/dragged anchors was considered by both researchers and manufacturers thoroughly, reported mechanical damages caused by ships’ activities (Mustafina [2015]; Bartolini et al. [2018]) proved that stricter regulations and further research are needed to provide better protection for submerged pipelines.

Improvement in the experimental laboratory facilities and numerical techniques encourages researchers to study the hazards of dragging anchors for buried pipelines. Some researchers executed numerical simulation to investigate the interaction of laid pipeline in the trenches–dragged anchor (Bartolini et al. [2018]; Sriskandarajah and Wilkins [2002]), the interaction of rock backfilled in the trench and dragged anchor (Wang et al. [2009]), the impact of dropped or falling objects on the pipes and the role of anchor weight on the level of pipeline damages (Yang et al. [2009]; Liu and Yang [2014]; Shin et al. [2020]) and minimum burial depth of pipelines according to weight of dropped objects (Zhuang et al. [2016]). Yu et al. [2016] examined the interaction of dropped anchors and the pipe in different subsea conditions. They showed that the pipe on the sandy soil subsea experiences smaller indentations compared with the pipe on the concrete and the softness of the seabed helps the pipe to dissipate the energy of impact. In addition, Gaudin et al. [2007] and Gaudin and Landon [2008] performed a series of centrifuge tests to investigate the performance of shape and geometry of rock berm protection due to anchor-dragging for laid pipelines in the trench. Yan et al. [2015] proposed an analytical method for rock backfill protection of pipelines and compared the results of experimental tests with an analytical solution. Their results show that the initially buried depth and the dragging distance of the anchor to the pipe do not influence the interaction of the anchor–rock berm.

Researchers showed that the stiffness of the rock berm has a direct impact on the dissipation of energy for dropped objects (Liu and Yang [2014]; Pichler et al. [2005]). In addition, the ability of soil covers to protect the pipe from dropped material increases by increasing the stiffness of covered soil. On the other hand, Hvam et al. [1990] argued that the performance of anchors depends on the stiffness of seabed soil, and in stiff soil, it could not work properly. While the anchor performance depends on both the anchor and the properties of the seabed, the role of seabed stiffness through dragged anchor–rock berm needs to address carefully. Zhuang et al. [2021] proposed a theoretical relationship for anchor–cohesive subsea materials and verified their relationship with experiments. The role of the undrained shear strength of clay on the trajectory of the anchor was examined (Grabe and Wu [2016]). However, the role of granular rock berm stiffness to diverge the dragged anchor and provide reasonable physical protection for trenchless laid pipelines needs to be investigated.

Due to environmental considerations, avoiding trench excavation in the seabed is of great interest. If the seabed stability criteria allows, trenchless pipeline laying and rock berm construction could be excellent alternatives from construction, economic, and environmental standpoints. In this research, four experimental tests have been carried out to capture the interaction of two types of rock berm with different material stiffness and dragged anchors with light and heavy weight in a spatial water tank. The results showed that rock berms sustain passive deformation and the size of the anchor plays an important role. To investigate various aspects of anchor–rock berm interaction in trenchless conditions, the effect of seabed stiffness, size of anchor, and stiffness of rock berm were studied numerically and were compared with experiments. These numerical simulations were executed to investigate the change of energy dissipations in the simulations, anchor force, and the depth of anchor penetration throughout the dragging path (i.e. trajectory of the anchor, Fig. 1). The results showed that numerical simulation could be a valuable method from engineering and scientific standpoint. The applied theoretical relationship for passive force shows good agreement with numerical and experimental tests and its results could be applied as the first estimate for the possible dragging force in the interaction of the anchor–rock berm.

2. Passive Pressure of Soil

The efficiency of vessel anchors relies on their interaction with the seabed and the magnitude of mobilized passive force in front of the anchor. Traditional formulations for calculating passive earth pressure such as Coulomb theory are mostly applicable in the case of support walls in plain strain condition. Reese et al. [1974] provided an equation for calculating the passive earth pressure of laterally loaded soldier beams in granular soils, considering a 3D passive zone behind the pile. Their proposed equation can be used in order to compare the analytical formulation with experimental and numerical results in terms of anchor traction force. Two assumptions have been applied to the passive force ($F_{\mathrm{\text{passive}}}$) formulation. First, we assumed the anchor is always fully penetrated into the soil. Second, cross-section of anchor is analogous to cross-section of soldier beam. Figure 2 shows the schematic passive zone behind a fully penetrated anchor using Reese et al. [1974] approach. The mobilized passive force could be calculated based on Eqs. (1)–(3).

where the term $\phi$ is soil internal friction angle and $\alpha$ varies between $\phi /3$ to $\phi$ for loose to dense sands, respectively. In Eq. (1), h, B, and ${\gamma }_s$ are height of the soil in front of anchor, width of anchor (see Fig. 2), and soil total density, respectively.

3. Experimental Tests

In this study, four experimental tests were carried out to study the role of rock berm material on the mechanical protection of trenchless buried pipeline against dragged anchors, the effects of anchor size in the anchor–rock berm interaction, and the performance of filled soil to provide adequate protection.

Simulation of the natural deposit in detail in a 1g model test is not possible and some modification and simplification need to be considered (Franke and Muth [1985]). Therefore, model tests show some deviations with respect to actual conditions and they suffer from the same deficiency as a theoretical analysis does, and idealized material behavior must be presumed. Soil behavior is dependent on stress level, stress path and strain rate. In addition, by dragging the anchor, it starts to generate passive resistance in the seabed and in the rock berm materials. The interface friction coefficient between very soft soil and steel, which is of high importance in calculating the passive forces, should be estimated with caution (Robinson et al. [2017]; Cathie and Wintgens [2001]). Therefore, scale effects occur when 1g model tests are used to predict prototype behavior. The scale of length $\lambda$ is defined as the ratio of corresponding lengths in the model test and in the prototype. This factor for big (heavy) and small (light) size (weight) anchors was approximately 1:20 and is analogous to 76.2kN and 18.9kN prototype anchor weights. By having scaling factor, other quantities such as weight and force in a 1g test can be compared with a relevant prototype. It must be mentioned that the concept of stiffness is difficult for a nonlinear material such as soil and in general, we have to permit the possibility that stiffness of our geotechnical material may or may not be under our control to some extent (Wood [2004]). Both anchors were made up with steel and the angle between flukes and shank was fixed to 33° (Fig. 3(a)).

In order to provide a loose silty sand seabed, Firoozkooh sand #101 (Imam and Fotowat [2018]; Maghvan et al. [2020]) was poured into the flume (Fig. 3(b)). This procedure allows us to provide high porosity in the soil. With high porosity in the silty sand, a loose layer of sedimentations and soft seabed could be expected (Naeij and Mirghasemi [2013]; Mirghasemi and Naeij [2015]). The pouring of fine sand was continued until the depth of the seabed reached about 15cm (Fig. 3(c)). In this study, the experiments were carried out in the water to keep the seabed, soft layer, and stiff layer in saturated conditions during anchor drop and anchor dragging. For the rock berm material, two different soil materials were selected. The softcover is made from subsea material (i.e. Firoozkooh sand #101). By increasing the particles size in granular soil, its shear strength increases and the magnitude of its Young modulus (elastic modulus, E) increases (Naeij and Mirghasemi [2013]; Look [2007]). Therefore, the stiff cover consisted of gravel particles. Both soil materials were considered granular soil. Figure 4 shows the grading curves of selected soils. The silty soil and the gravel are classified as SP-SM and GP, respectively according to the Unified Soil Classification Scheme (USCS). Table 1 presents details of the experimental tests. In this table, the first two letters S or R relate to soft or rigid layer of the rock berm from lower layer to the top layer, respectively and the S or B letter after minus sign (− shows small or big anchor type), respectively.

The experiment method involved two stages; first, dropping the anchor from the surface of the water. The length of the flume allowed for dropping the anchors from 132.5cm, measured as the distance to the center of the laid pipeline. The results showed that this distance was enough to capture the smooth dragging force before its interaction with the rock berm. In the second stage, the dragging process started with constant speed. In this stage, a constant horizontal velocity equal to 5cm/s was applied to the chain of the anchors. The dragging direction was assumed perpendicular to the pipeline route.

Figure 5 presents the elevation view of the experimental models and relevant details of each test are introduced in Table 1.

The results of the interaction of small anchor with two-layer rock berm (Test No. 1) and rock berm made of the seabed (Test No. 2) are presented in Figs. 6 and 7, respectively. In both models, the small anchor dragging path has diverged from the pipeline and no hooking between fluke(s) and pipe occurred. These figures show a V shape cut and the trace of the small anchor from the top of the pipeline. After drafting the rock berm materials from the top of the pipe, both sides of sheared zone created stable slopes based on the internal friction angle and the drafted soil will spread asides during the downward movement of the anchor. Figure 6(b) shows scattered gravel particles in the path of the dragged anchor.

Figure 8 demonstrates the interaction of the big anchor and rock berm constructed with stiff material (Test No. 3). The point of initial drop, the trajectory path of the dragged anchor, and its interaction with the rock berm were highlighted in Fig. 8(a). Due to the drop of the anchor into the tank, an initial penetration of the anchor has occurred. Due to drag velocity applied to the chain, this penetration into the seabed continued until near the rock berm. After interaction with the rock berm, the shank of the anchor moved upward but this was not enough to prevent anchor hooking and fluke contact with the pipeline happened. Figure 8(b) shows the penetration of the heavy anchor into the two-layer rock berm and Fig. 8(c) presents the hooking of the fluke and the buried pipe (after extracting the soil).

Figure 9 presents the results of the big anchor and its interaction with a rock berm made of soft material (Test No. 4). The dragged path in the subsea and the interaction of the rock berm–big anchor are presented in Fig. 9(a). Contrary to the rock berm with stiff material (see Fig. 8), Figure 9(b) shows a complete penetration of the flukes and shank into the soft rock berm. Figures 9(c) and 9(d) illustrate the complete hooking of both flukes and buried pipe.

Comparison between Figs. 8(b)–8(c) and 9(b)–9(d) demonstrates that the stiff material of the rock berm changed the direction of shank movement and its stiffness was enough to prevent the chain from penetrating into the rock berm. However, this stiffness was not enough to fully change the trajectory of the big anchor to the top of the laid pipeline. In the soft material, the chain sheared the rock berm and the movement direction of the anchor remained unchanged. In addition, the soil mass of the soft rock berm in front of the anchor shows passive mobilization in the direction of anchor movement. However, this mobilization could not provide enough soil passive resistance to prevent the hooking of big anchor or to diverge the anchor in the vertical direction.

Test Nos. 3 and 4 show the interaction of rigid and soft rock berm with big anchor, respectively. In both models, the hooking between anchor and pipeline has occurred but the shape of hooking and the response of the rock berm to the anchor movement and its passive pressure show significant differences. From the difference between shank directions, passive deformation of rock berm soil in front of flukes, and the magnitude of anchor force, one may deduce that a stiffer rock berm or higher height of rock berm is needed in order to prevent anchor hooking.

4. Finite Element Analysis

To provide a more detailed insight into the anchor–rock berm interaction, a series of Coupled Eulerian–Lagrangian (CEL) models have been executed. In conventional mesh-based Lagrangian finite element model, the mesh nodes are attached to the material and deformation in the material leads to change of mesh shape as well as nodes coordination. The material boundary will always coincide with element boundary in Lagrangian simulation (Fig. 10(a)). Contrary to Lagrangian FEM, Eulerian simulation is a finite element analysis in which the nodes of finite element mesh are fixed in space (i.e. the displacement of nodes is zero). In this type of finite element simulation, under loading, Eulerian materials deform, but the mesh keeps its initial shape. Therefore, this method could be very effective when the material undergoes very large deformation, flow, or damage and the mesh in Lagrangian simulation will distort excessively. In Eulerian simulation, a void domain (i.e. red domain in Fig. 10(b) should be defined at the beginning of simulation to let the deformed material pass through the mesh according to the applied forces. Because of this, the material boundary does not coincide with element boundary. The purpose of the void domain is to capture the material flow during the deformation. Due to the severe deformation of the soil materials through anchor dragging, CEL simulations have been executed in this study.

ABAQUS (Simulia [2014]) 3D nonlinear finite element models have been performed and each model consisted of the anchor and pipeline as Lagrangian domains and seabed and rock berm as Eulerian domains. Figure 11 shows different part instances of the finite element model.

To simulate the anchor–soil interaction, three stages were introduced. First, the gravitational load was applied in each model to provide the initial stress state in the seabed and rock berm. Then, the anchor was allowed to drop freely from a height of 10m and penetrate into the seabed. In the last stage, a specific horizontal dragging velocity was applied to the end of the shank. The pipeline section was modeled with shell elements. A perfectly elastic constitutive model was attributed to the pipeline. All soil domains were modeled with Eulerian meshes. Based on a series of mesh sensitivity analysis (Table 3), variable mesh sizes were applied to Eulerian domain in order to keep the balance between energy, time, and accuracy. The domains near the center of the rock berm were simulated with the finest mesh and the size of mesh was increased by moving toward boundaries. Different material constitutive parameters were assigned to each soil layer. The anchors were modeled as steel material with brick elements. Table 2 shows relevant numerical parameters of all parts. Like the prototype anchor in the experimental tests, the spreading angle of 33° was fixed between the anchor shank and the flukes.

To include the force transmission between different materials and the interface between the Lagrangian parts and Eulerian domains, general contact algorithm was selected and the magnitude of friction coefficient (${tan}^{-1}\phi /3$) was applied. Due to dropping the anchor, initial penetration may affect the anchor dragging force and its flukes position with respect to the rock berm. The length of the flume (Fig. 3(c)) allowed us to drop the anchor from 132.5cm distance to the center of laid pipeline. The results showed that this distance was enough to capture smooth dragging force before its interaction with rock berm. The velocity of the Eulerian domain boundaries was fixed to zero and impermeable to prevent the loss of material.

Three steel anchor sizes (Small, Medium, and Big) with elastic constitutive material parameters of steel have been modeled. Two heights of rock berm from the top of steel pipe (2m and 2.5m for two- and three-layer rock berms) with different combinations of the presented soil materials in Table 2 (Seabed, Stiff) were simulated with Mohr—Coulomb constitutive model parameters for very loose silty sand (Imam and Fotowat [2018]; Maghvan et al. [2020]) and very loose sand (Look [2007]).

Similar to engineering practices, the first layer of rock berm was constructed with soft soil in all experimental and numerical models. This provides an absorbent soil layer around the pipeline. The height of this layer was 1m from the top of the pipe and the heights of the second and third layers (for models with three-layer rock berm) were 1m and 0.5m, respectively. For all presented results, the first three letters (S, R) relate to the layers of the rock berm. The letter after rock berm layers shows the anchor type (S, M, B). The top layers of seabed usually consist of sediments and soft silty materials. Therefore, we applied soft seabed (i.e. $E=1.2$Mpa) in the simulations and for simulations with different seabed properties, the magnitude of Young modulus was mentioned.

Although the elastoplastic behavior of loose silty sand and coarse gravel is complicated (Javanmardi et al. [2018]), in this study, the Mohr–Coulomb model was taken as the soil layers’ constitutive model. It can preferably simulate the elastic-perfectly plastic deformation of the soil (Carter et al. [2010]) under impact load and calculates its deformation during anchor drop or passive shear resistance dragging, and it was applied to simulate the geotechnical damage characteristic. Liu and Yang [2014] stated that unstable phenomenon did not occur in large deformed calculations and the precision was high enough for impact simulations. Similar elastic-perfectly plastic constitutive soil model was applied for penetration of rigid cone into the soil (Carter et al. [2010]). Liu and Yang [2014] compared the results of their numerical simulations with full-scale test curves from Pichler et al. [2005] and showed that considering the plastic behavior of soil can accurately reflect the actual behavior of soil-stiff material impact.

Liu and Yang [2014] proposed Eq. (4) based on Hertz collision theory for elastic materials and showed that by increasing the mass of a dropped object (i.e. mass of anchor, $m_a)$, the magnitude of impact force increases (Eq. (4)). In Eq. (4), $E_s$ and ${\mu }_s$ are soil Young modulus and Poisson ratio, respectively and $H_d$ is the height of the drop.

According to Eqs. (4) and (5), the weight of the anchor has a direct influence on its drop energy and its penetration into the seabed. The higher its weight, the deeper an anchor penetrates. Equation (5) shows the relationship between the impact force of dropped anchor and the magnitude of its penetration into the soil (${\delta }_{\mathrm{\text{pen}}}$). Zhuang et al. [2016] found that the anchor weight is the largest influencing factor on the required burial depth of the submarine pipelines. In this equation, $k_s$ is spring constant and its value depends on anchor shape, area of contact, and soil. By increasing the interaction surface between the soil and anchor, the penetration of a specific anchor will decrease. After applying the horizontal velocity to the shank and initiation of dragging, the passive soil pressure will mobilize in the soil and this passive force can be calculated according to Eq. (1).

Equations (1)–(5) demonstrate that the interaction of anchor–rock berm depends on many factors. Due to the complexity of this problem which relates to the short duration of interaction, local large deformation, and plastic deformation of the soils, a comparison between dissipated energy could bring new insights for soil simulations and its deformation in different problems (Naeij et al. [2019]; Naeij and Soroush [2021]; Naeij et al. [2021]). When the conventional contact theories do not take the effect of buried depth of pipeline or soil plastic energy dissipation into account, elastoplastic numerical models could be an excellent approach for measuring the energy dissipation in different conditions.

The movement of the anchor in the model will create internal ($E_I$) and kinetic ($E_k$) energy. Equation (6) shows that internal energy can be integrated by calculating strain rate ($\dot{\epsilon }$) and stress tensor ($\sigma$) in all domains (V) in the model. By decomposing the strain rate into the elastic (${\dot{\epsilon }}^{\mathrm{\text{el}}}$) and plastic (${\dot{\epsilon }}^{\mathrm{\text{pl}}}$) strain rate, the elastic energy, and plastic dissipated energy can be calculated according to Eq. (9). It must be noted that in this study only Eulerian materials show plastic deformation. Therefore, a comparison between plastic energy in different simulations could be a reasonable measure for soil plastic deformation. Equation (10) shows the magnitude of kinetic energy in the model, and it computes for all deformable materials.

4.1. Verification of numerical simulations

The experiments in our study have been carried out using loose saturated sand in the flume. This brought some difficulties into our measurements, as the detached sand particles got suspended in the flume leading to opaque brown water. However, many aspects of anchor–rock berm interaction such as penetration of anchor into seabed and different layers of rock berm, the drafting of rock berm materials in front of anchor, and anchor hooking were captured by our numerical model qualitatively (Fig. 12).

Figure 13 shows the anchor forces for experimental tests due to dragging of small (S) and big (B) anchors. The experimental tests were performed in a 1g tank. To consider the scale effects, the anchor force was multiplied in ${\left(\frac{L_{\mathrm{\text{prototype}}}}{L_{\mathrm{\text{model}}}}\right)}^3$. The anchor force of all experimental tests was compared with their relevant numerical tests. The anchor force for Test Nos. 3 and 4 were presented before hooking. Due to anchors hooking, the magnitude of anchor load increases dramatically, and it went beyond the limitation of load set up. However, in numerical simulation, the anchor force changed in position above the pipe (i.e. see the results of SS-B and SS-S). The results of anchor force due to passive mobilization of seabed or rock berm were calculated according to Eq. (1) and were presented in black dots.

Figure 13 demonstrates that the magnitude of anchor force in normal seabed geometry condition increases with the dimension of anchor. The interaction of two-layer rock berm and anchors increases the magnitude of anchor force. All anchors experience their maximum drag force slightly before maximum height of rock berm. To calculate the analytical passive force (Eq. (1)), soil parameters of different layers were averaged. The reported numerical and experimental results show that the results of numerical simulations and theoretical formulation are very close for big anchor during the dragging in the seabed and before hooking (SR-B and SS-B). However, there are slight differences between them during the dragging in the seabed sand and interaction with rock berm material (Fig. 13). The maximum discrepancy between numerical and experimental results is related to the initiation of dragging. This may have happened because we applied very loose silty sand as the seabed. When the anchor drop, it will penetrate into the soft sand. The behavior of loose sand is very sensitive to its porosity and the impact of anchor will reduce its porosity. Due to impact of anchor and the seabed, the soft soil will be compacted and it will show stiffer response to the deformation at the beginning of anchor dragging compared to a numerical simulation with elastic-perfectly plastic constitutive model for silty sand. Furthermore, we increased the velocity of anchors in 1s in the numerical simulations to reduce the dynamic effects due to initiation of anchor movement. But in the experimental test, constant speed was applied to the anchors from the beginning. In addition, including water above the seabed in the numerical model (i.e. in void domain in Eulerian mesh) may decrease the differences. However, the run time of numerical simulations will increase excessively.

When comparing the numerical results with the results of the 1g tests, it must be considered that confinement and stress levels have direct impact on the behavior of granular soil (Lauder [2011]) and it is hard to capture these parameters in the numerical simulation of soil domain. Not only the scale effect, but also kinetic effects associated with discontinuous soil mass in model tests similar to anchor dragging and soil drifting require statements about displacements as well as strains, and care is required in predicting large scale response on the basis of the results of small model tests (Stone and Wood [1992]). It must be noted that the speed of dragged anchor may cause some dynamic effects in the simulations which cannot be explained by the transient formulation employed in our FEM model.

4.2. Stiffness of seabed

Figures 14(a) and 14(b) show the anchor trajectory (i.e. maximum flukes’ penetration) and anchor dragging force for the models with two-layer rock berm (SR). Comparing the initial penetrations of the big anchor into the seabed in Fig. 14(a) demonstrates that by increasing the magnitude of seabed elastic modulus (Young modulus, Es), the magnitude of initial penetration of anchor with constant shape, weight, and the contact area between soil and anchor will decrease (see Eqs. (4) and (5)). The weight and contact area of the small- and medium-sized anchors are smaller than the big anchor and the magnitude of initial penetration will decrease. In addition, the initial penetrations decrease for dropped anchors on the stiff seabed. However, by starting the movement of anchors, the anchor in the stiff seabed could not keep its penetration. Comparing the minimum clearance between the toe of anchor fluke (TAF) and the top of pipeline shows that the stiffness of the seabed helped the big anchor to pass from the top of pipe with more clearance.

Figure 14(b) presents the magnitude of anchor forces. The minimum anchor force belongs to the big anchor dragging on the stiff seabed and its maximum value belongs to the big anchor dragging on the soft seabed. Hvam et al. [1990] mentioned that in the stiff soil the flukes could not bring enough soil passive resistance because of insufficient penetration. According to Eq. (1), decreasing the depth of penetration will decrease the magnitude of $F_{\mathrm{\text{passive}}}$. Figure 14(c) demonstrates the penetration of anchors after free fall.

Figures 14(a) and 15(b) illustrate cumulative plastic energy dissipation (Eq. (9)) and induced kinetic energy (Eq. (10)) due to the dragging of anchors in the models with different seabed stiffnesses, respectively. Figure 15(a) shows the model with big anchor and soft seabed dissipates the maximum plastic energy and the model with big anchor and stiff seabed brings minimum value of dissipated energy because of soils plastic deformation. The magnitude of the dissipated plastic energy is compatible with the amount of anchor penetration into the soil. When the anchor penetrates the seabed or interacts with the rock berm, it causes passive shear deformation in the soil elements. The deeper the anchor enters the soil domains; the magnitude of plastic deformation of soil elements will increase. This proves that the magnitude of soil elements with plastic deformation in the model with big anchor and stiff seabed is fewer in models with small- and medium-sized anchors with the soft seabed. This shows that the interaction between stiff seabed and anchor is weaker than others. Therefore, a stiff seabed allows the anchor to move easily and pass through the rock berm with weak interaction.

Figure 15(b) shows that the interaction of anchors with rock berm increases the kinetic energy of models when the anchor reaches the rock berm, and this augmentation of kinetic energy continues until the drafted material is scattered (see Fig. 6). Figure 15 illustrates that decreasing the size of anchor leads to diminishing the magnitude of kinetic energy and drafted soil material. For anchors of the same size, the model with stiff seabed tolerates less kinetic energy.

From Figs. 14 and 15 one could deduce that the stiffness of the seabed has direct influence on the penetration of the dropped anchors and the interaction of rock berm–anchors. The ability of rock berm to protect trenchless laid pipeline (pipeline anchor clearance) will decrease when the stiffness of seabed soil reduces, i.e. the softer the seabed soil, the thicker armor rock protection on the pipeline is required. This is since in soft seabed conditions more penetration of anchor occurs.

4.3. Size of anchor

According to the experimental tests, the size of the anchors had a significant effect on the interaction of rock berm–anchor and the ability of soil for bringing reliable physical protection. Figure 16 shows the interaction of two-layer rock berm (SR) with small, medium, and big anchors. Figures 16(a) and 16(c) are comparable with experimental Test Nos.1 and 3, respectively.

Figure 16(a) illustrates that the rock berm brought a reasonable distance between the TAF and the top of pipe. In addition, similar to the results of Test No. 1 (Fig. 6), the drafted path of the anchor (i.e. the void space behind the anchor fluke) proves that the anchor path diverged to the top of pipe with adequate slope. Therefore, the rock berm thickness and stiffness were enough to avoid small anchor hooking. Figures 16(b) and 16(c) show that by increasing the size of the anchor, the potential of the rock berm to bring a substantial physical cover and clearance between TAF and the top of pipe decreases. Like Test No. 3 (Fig. 8), the hooking between the anchor fluke and the pipeline occurred and, in this condition, severe mechanical damage to the pipeline is expected.

Figure 17 shows the trajectory line of TAF for rock berm with configuration and anchors of different sizes. Figure 17 shows that the vertical dislocation of TAF from the start of interaction with rock berm material until the top of pipe for the big anchor is more than two other anchors. But the interaction started from a deeper point. When the dragged anchor reaches the rock berm, the accumulation of soil in front of the anchor fluke increases, and the slope of the trajectory line of TAF increases.

4.4. Height of rock berm

Figures 18(a)–18(f) show the interaction of the three-layer rock berm with 2.5-m soil above the top of pipe (SRR) and the big anchor. In these figures, a section from one fluke was selected to show the deformation of the seabed and the big anchor penetration into it (Fig. 18(a)). The big anchor starts to interact with rock berm layers (Fig. 18(b)). Due to dragging and producing passive shear deformation in the soil, it accumulated soft soil in front of its flukes. Comparison between Figs. 18(c) and 18(d) with Fig. 16(c) illustrates that adding an extra-stiff layer (with height equal to 0.5m) brought enough clearance between TAF and the top of pipe. The size of anchor and the stiffness of the seabed are identical for both models. Figures 18(e) and 18(f) show that after passing the top of pipe, the vertical position of TAF will decrease and it starts to move toward the seabed. In addition, the amount of drafted soil in front of flukes decreases. Like Fig. 6, the drafted materials are scattered in the path of anchor and the magnitude of soil passive resistance and anchor force reduces.

4.5. Stiffness of rock berm

The experimental results show that the soil condition in rock berm–anchor interaction is analogous to the soil passive stresses. The anchor tends to bulldoze the rock berm. Therefore, the stiffness of rock berm material plays an important role in the rock berm–dragged anchor interaction. The stiffness of rock berm comes from its height or the stiffness of its material. When the compaction of material in the water is impossible, using soil with coarse grain or adding the height of the rock berm could be practical options. Figure 19(a) shows the trajectory line of TAF of big anchor interacted with rock berm with different configurations on the soft seabed and Fig. 19(b) presents their anchor forces. Figure 19(a) illustrates that the maximum clearance between TAF and the top of pipe occurs in the model with maximum rock berm stiffness in this study (see Fig. 19) and the model with two soft layers (analogous to Test No. 4 and Fig. 9) shows a fully hooked anchor fluke. In all models, the interaction of the big anchor and rock berms provides upward anchor motion. Figure 19(b) demonstrates that the maximum anchor force belongs to the model with maximum height of stiff soil (SRR) and the minimum force belongs to the model with two soft layers (SS). This figure shows that the magnitude of anchor forces after applying velocity to the shank and during the interaction of the big anchor and soft seabed is similar and it changes based on the stiffness of rock berm. In addition, the anchor force for the model with a stiff layer (SR) is bigger than the anchor force for the model with three soft layers (SSS) and among the rock berms with the same height, the thickness of the stiff layer has direct influence on the magnitude of anchor force (SRR>SSR>SSS and SRN>SSN).

We applied constant velocity to the anchor (similar to experiments) in the numerical simulations and the anchor continued its movement after hooking. Figure 20 shows the deformation and the magnitude of Mises stress in pipeline before (a), during (b), (c), and after hooking (d). Due to applying constant velocity to the anchor, it continues its movement after creating a contact with pipe and this causes excessive local stress on the body of pipe. Contrary to numerical simulation, the experimental set ups (i.e. hydraulic jack, electric motor, force meter, and chain) had limited capacity and it was not possible to drag the anchor after hooking. Figure 20 shows that the anchor imposes high deformation in the pipe due to hooking and the applied numerical simulation is capable to capture the interaction between pipe and anchor.

5. Conclusion

When pipelines are laid in nearshore region, due to areas of shipping activities, they are vulnerable to shipping activities. Physical damages such as buckling of the pipeline due to lateral anchor-hooking forces cause high repair costs and environmental pollution. A series of 1g experimental and numerical tests were carried out to investigate the complex interaction between the soil cover of trenchless buried pipelines, anchors, and seabed. Although we compared the anchor force as a main calculable feature through the interaction between anchor and soil (seabed and rock berm) with an acceptable range of discrepancies, the reported numerical and experimental results show that many aspects of interaction such as the drafting of rock berm materials in front of anchor, penetration of anchor into seabed and different layers of rock berm, and anchor hooking were addressed in the numerical models similar to relevant experiments.

Due to severe deformation of dragging path in the seabed and interaction of rock berm–anchor, the CEL finite element method, an advanced numerical time-integration scheme has been employed to accurately predict the nonlinear elastoplastic response of the soil domains.

The results of experimental tests show that the dimension (weight) of the anchor has significant role in the interaction of the rock berm–anchor. With a constant dragging speed, the clearance of TAF and top of pipe strongly depends on the size of the anchor and inadequate rock berm height leads to hooking or contact of big anchors and pipeline. In addition, the anchor mobilizes passive deformation in the rock berm, and the anchor flukes draft the rock berm materials. Applying stiff material helps to improve the functionality of rock berm.

The results of numerical simulations demonstrate that penetration of the anchor into the seabed is a key factor in the design of trenchless rock berm. When the penetration depth of anchor decreases, the magnitude of imposed passive force due to the dragging anchor will decrease. Decreasing the penetration of the anchor allows it to slide more easily. Therefore, the performance of rock berm to provide mechanical protection of pipeline will increase. The numerical results also show that by increasing the height of rock berm, its ability for diverging the anchor increases, and for rock berm with the same height, increasing the stiffness of material helps to bring bigger distance between the anchor and pipeline.

Acknowledgments

The authors would like to express their deepest gratitude to Dr. M.R. Koohkan for his valuable comments in anchor preparation and dragging force of marine vessels.