1. Introduction
Submarine pipelines are important transportation infrastructures for offshore oil and gas industry. With the increasing construction of submarine pipelines and port development on coastlines, there are often cases where the landing part of a submarine pipeline crosses shipping lanes [
1]. Over 50 percent failure of the global submarine oil and gas pipeline rupture has been caused by the third party, and the ship anchoring operation is one of the most important causes [
2,
3]. The risk assessment of pipelines caused by falling anchors have been assessed in the DNVGL-RP-F107 code [
4]. Once an accidental causes damage in a pipeline, the economic loss is huge, and the pollution of sea water is severe as well. Therefore, it is necessary to analyze the dynamic response of a submarine pipeline exposed to the impact of a falling anchor and propose effective protection methods to prevent the damage in the design stage.
The subject of transverse impacts on submarine pipelines has received considerable attention in the literature. Yang et al. (2009) [
5] studied the dynamic response of a horizontal pipeline impacted by another swinging vertical pipeline. The effects of impacting position and ending fixed condition on the strain response and depressed depth of the horizontal pipeline were investigated. Arabzadeh and Zeinoddini (2011) [
6] established a coupled soil-structure-fluid finite element model to examine the effects of the pipeline bed flexibility on the dynamic pressure wave propagation inside the pipeline. Dou and Yu (2013) [
7] used a finite element analysis (FEA) software package, LSDYNA, to model the pressurized pipelines to investigate the crash and collapse mechanisms of pipelines subjected to lateral impact. Yu et al. (2016) [
8] conducted a three-dimensional numerical simulation to study the deformations of a pipeline due to transverse impacts from dropped anchors. The method has the advantages of higher-order resolution and low computational cost. Cui et al. (2018) [
9] studied the effects of the mass, height, and shape of a falling object; the pipeline laying conditions; the water depth; and other factors on the mechanical damage of a submarine pipeline (including the axial and circumferential strain response of the pipeline). The above-mentioned research was mainly focused on the direct impact on an exposing pipeline and its deformation response under various factors.
There are also a few studies on the dynamic response of a pipeline under cover layers. Wang et al. (2009) [
10] conducted 3D non-linear finite element (FE) analysis to study the interaction of dragging anchor with a pipeline protected by rock backfill. Ma et al. (2012) [
11] studied the effects of the thickness and the particle size gradation of the rock protection layer on the effectiveness of protecting a submarine pipeline based on the DNVGL-RP-F107 code. To estimate the energy dissipating capacity of a rock armor berm, Qiu et al. (2015) [
12] combined the discrete element method (DEM) and the finite element method (FEM) to analyze the dynamic response of pipelines exposed to impact loads. The calculated results of energy absorption by gravels agree well with those recommended by the DNVGL-RP-F107 code. Sun et al. (2018) [
2] analyzed the effects of seabed material, burial thickness, water depth, and dropping height on the strain history of the top surface of a submarine pipeline. Shin et al. (2020) [
3] conducted both experimental and finite element analysis of the soil–pipe–rock interactions to quantify the effects of seabed soil properties, anchor weight, dropping height, buried depth, and rock berm height on the strain of pipeline. Li et al. (2021) [
13] studied the effects of buried foundation materials (including clay, sand, and rock) and buried depth on the depression depth and residual equivalent stress of buried pipelines impacted by spherical falling objects. It was found that the layered backfilling method of multi-layer foundation materials can effectively improve the impact resistance of high-rise pipeline.
In addition to the traditional sand filling or rock berm above the pipeline using the pipeline protection method, more effective methods are required to protect pipelines from the damage of external forces. In this study, a series of physical model tests and theoretical analyses are conducted to study the dynamic response of a pipelines with various protection methods exposed to the impact of a falling anchor. Four protection methods are tested, and the strain and deformation are analyzed to investigate the effectiveness of the protection method. This paper comprises the following sections: the motivation and background of the study are stated in
Section 1; the experimental setup and methodology are given in
Section 2; the experimental results and discussions are presented in
Section 3; theoretical analysis on the strain and deformation of the pipeline is conducted in
Section 4; and concluding remarks are given in the final section.
4. Theoretical Analysis
The theoretical model for a pipeline laid on a soft seabed [
14], which considers the effect of the seabed stiffness on the deformation and stress of the pipeline, is applied in this study. Because the vertical deflection is much smaller than the horizontal length of the pipeline, the small deflection theory can be adopted.
The linear stiffness of the seabed is
kb and the bending stiffness of the pipeline is
EI. Due to the cushion effect of the protective layer, the action of the falling anchor can be represented by a uniform load
q with an acting length 2
a. Here, the acting length is defined as the length of the upper moving protective layer directly acting on the pipeline. In this study, the acting length is estimated as 10
d empirically, i.e., 2
a = 0.40 m, through analysis of the strain distribution along the pipeline. It is assumed that the deflection is symmetrical at the impact point. The coordinate is established and its center is set at the impact point, as shown in
Figure 10.
Then, the deflection and bending moment of the pipeline can be described in two sections (I and II), according to Xing et al. (2013), as shown in
Figure 10. Here, the horizontal dimension is normalized as
ξ =
x/
a and the normalized deflection is
Y(
ξ) =
y(
x)/
a with the bending moment
M1(
ξ).
For section II:
where
q0,
q1, and
λ0 are calculated from the static load of the anchor, as follows:
Then, the strain on the surface of the pipeline can be approximated based on a beam theory with the bending moments from Equations (2) and (4):
It is noted that for a falling anchor, a dynamic amplified coefficient
kd should be multiplied on the values from above equations. For different protection methods, the dynamic load coefficients are different, which can be obtained through calibration from the measured results.
Figure 11 shows the comparisons between measured and theoretical values of strain along the pipeline. Through calibration, the dynamic amplified coefficient for the four protective layers are
kd = 21, 16, 13, and 8, respectively, as shown in
Table 1. The measured and theoretical values are also listed in
Table 1. It is observed that the theoretical model can effectively describe the distribution of strain on the pipeline exposed to the impact of a falling anchor. Then, the deformation of the pipeline can be calculated by Equations (3) and (5) with the dynamic amplified coefficient
kd, as shown in
Figure 12. The maximum deflections at the middle of the pipeline are 0.088 m, 0.068 m, 0.055 m, and 0.034 m for the four protection methods, as shown in
Table 1.
Based on the theory of material mechanics (Wang and Kang, 2008), the dynamic amplified coefficient for a fixed-end beam can be approximated by:
where Δ
st is the static deflection at the middle of the pipeline, which can be obtained from Equation (2) at
ξ = 0;
vT is the velocity of the upper protective layer associated with the anchor impacting on the pipeline. In this study,
vT can be calculated based on the energy conversation principle.
According to DNV-RP-F107, the total energy before impacting on the seabed includes the kinetic energy of the falling anchor and the energy from the added hydrodynamic mass, i.e.,
where
Ca is the added mass coefficient and is taken as 1.0;
V is the volume of the anchor; and
v0 is the falling velocity before impacting on the seabed. In this study,
v0 is analyzed from the high-speed video record and has a value of 3.27 m/s for a 1.0 m falling height.
After the anchor impacts on the seabed, a part of energy is absorbed by the protective layer, and then the anchor becomes further associated with a part of the protective layer impacting on the pipeline at a velocity
vT, i.e.,
where
Ee is the kinetic energy of the anchor and the moving protective layer (i.e., the shadow area in
Figure 10):
where
mp is mass of the moving protective layer. In the present study, the moving protective layer has a length of 2
a (10
d = 0.4 m), a width of
d (0.04 m), and a thickness of 0.13 m. The density of the moving protective layer is taken as 2200 kg/m
3. Thus,
mp is calculated as 4.58 kg.
Ep is the energy absorbed by the protective layer, and can be described as (DNVGL-RP-F107):
where
γ′ is the submerged weight of the fill material, assumed to be 11,000 N/m
3, according to the DNVGL-RP-F107 code;
W is the width of the anchor, with a value of 0.1 m;
z is the penetration depth, which is measured from the experiments and has a mean value of 0.029 m; and
Nr is the bearing capacity coefficients of the protective layer.
According to DNVGL-RP-F107, the bearing capacity coefficients for a rock cover (P1) is empirically selected as
Nr = 99. Combining Equations (12)–(14), the bearing capacity coefficients for other three protective layer (P2–P4) are
Nr = 138, 169, and 196, as shown in
Table 1. Based on above analyses, the protective method P4 has the best performance to protect the pipeline, i.e., having the minimum strain on the pipeline and minimum effective length. It is noted that the effectiveness of the protective method is determined based on mechanical properties of materials in this study. As for the economy of different protective methods, it has not been considered because the submarine pipeline is a very important facility for offshore engineering, and the safe operation of the pipeline is usually at the first place in some important areas under the channel bottom.
5. Conclusions
In this study, the impact of a falling anchor on a buried submarine pipeline is physically modelled and the strain responses of the pipeline are monitored with a series of fiber Bragg grating (FBG) sensors. Four protective methods on the pipeline, including pure rock, concrete mattress + rock, concrete mattress + rubber pad + rock layer, and compound flexible pad + rock, are tested. In the test, the anchor dropped from a certain height and attacks on the middle point of the pipeline. The peak value and the distribution of the impact along the pipelines are analyzed. The experimental results indicate that the maximum strain on the pipeline is located at the falling point, and then decreases along the axis of the pipeline to two sides. The affected length of the falling anchor on the pipeline can be up to 30~40 times that of the pipeline diameters. The absolute values of the strain on the upper surface of the pipeline are almost the same to those on the bottom surface, which can be treated as pure bending behavior. The strain on the upper surface at the middle point of the pipeline has the maximum negative value and has positive values on the other points. On contrary, the strain on the bottom surface at the middle point has a positive value and those on the other points on the bottom surface have negative values. This indicates that the bending of the pipeline at the colliding point is downward, while the bending of the pipeline at other points are upward due to support from the surrounding soil. It can be further described with a theoretical model for a pipeline laid on an elastic seabed. By curve-fitting the experimental results, the bearing capacity coefficients for the four protection methods are quantitatively determined as Nr = 99, 138, 169, and 196, respectively.
By comparing the maximum value of the strain on the middle of the pipeline, the effectiveness of the different protective methods is sorted (the first is the best) as follows: compound flexible pad + rock > concrete mattresses + rubber pad + rock layer > concrete mattresses + rock > pure rock. The protection method of the compound flexible pad + rock can provide the best protection with the lowest strain and affected length on the pipeline. It is also noted that the materials of the protective layer, such as the concrete mattresses, rubber pad, and compound flexible pad, cannot entirely satisfy the elastic similarity in model making, which may affect the test results to a certain extent. Therefore, in practical engineering, the influence of this difference on pipeline protection should be considered.