Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings

ENGEO-04431; No of Pages 13 Engineering Geology xxx (2016) xxx–xxx

Contents lists available at ScienceDirect

Engineering Geology journal homepage: www.elsevier.com/locate/enggeo

Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings Kanmin Shen a, Lizhong Wang a, Zhen Guo a,⁎, Dong-sheng Jeng b a b

Key Laboratory of Offshore Geotechnics and Material of Zhejiang Province, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China Griffith School of Engineering, Griffith University Gold Coast Campus, QLD 4222, Australia

a r t i c l e

i n f o

Article history: Received 30 June 2016 Received in revised form 17 November 2016 Accepted 5 December 2016 Available online xxxx Keywords: Suction anchor Floating offshore wind turbine Cyclic loading Oscillatory pore-pressure Residual pore-pressure Pullout capacity

a b s t r a c t The suction anchor is an effective option for the anchor foundations of floating offshore wind turbines (FOWTs). During its long-term service, in addition to the static pretension load, the suction anchor is subjected to a series of cyclic loads that are caused by waves, currents and the continuous motions of the floating structure. Thus, excess pore-pressure will accumulate within the soil around the embedded anchor, and the anchor capacity tends to be reduced. In this paper, by introducing the oscillatory and residual mechanisms, a novel numerical model is proposed to predict the instantaneous variations and accumulations of excess pore-pressures around a suction anchor that is subjected to long-term vertical cyclic loads. The results indicate that excess pore-pressure builds up mainly in the shallow soil near the external anchor wall. As a consequence, the effective soil stress in this region decreases along with the interface friction between the external wall and the soil. Detailed parametric studies reveal that the accumulation of excess pore-pressure is obvious for a larger load magnitude and smaller load period. With a lower permeability, smaller shear modulus or smaller relative density of the seabed soil, the porepressure accumulation outside the anchor increases significantly. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Wind is a rapidly growing renewable energy source both onshore and offshore for the last decade. Vast sea areas in China with stronger and steadier winds show a potential to develop offshore wind turbines (OWTs) in the future. Currently, offshore wind turbines are always supported by the monopiles but limited to a shallow water depth up to approximately 30 m. For deep water, only floating platform systems are expected to be economically and technically feasible. The foundation design for FOWTs in varying water depths is shown in Fig. 1. Mooring line stabilized Tension Leg Platform (TLP) is one of effective choices for FOWTs in water depths exceeding 50 m. The TLP consists of a floating structure connected to the seafloor with by a group of mooring lines or tendons attached to the anchor foundations (Ronalds, 2002). The reserve buoyancy for the floater is transferred to the suction anchors embedded in the seabed (Sclavounos et al., 2010). Suction anchor is made of steel and resembles a large over-turned bucket. The typical length of a suction anchor ranges from 5 to 30 m, with a length-diameter ratio of 3 to 6 (Randolph and Gourvenec, 2011). Compared with other anchors (e.g., drag embedded anchor, pile anchor), the advantages of suction anchors include the accommodation of a variety of soil conditions (clay or ⁎ Corresponding author. E-mail addresses: [email protected] (K. Shen), [email protected] (L. Wang), [email protected] (Z. Guo), d.jeng@griffith.edu.au (D. Jeng).

sand), accurate positioning, and the ease of installation and retrieval for reutilization. As shown in Fig. 2, during the installation process, the suction anchor penetrates into the seabed by its dead weight and by applying suction in sequence until it reaches the target depth below the seabed surface. After anchor installation and set-up (full dissipation of excess porepressure), the mooring line is gradually tensioned to remove the line slack. A specific degree of pretension load is always required to provide adequate constraint to the floating structure. The capacity of the embedded anchor must be large enough to sustain the loads passed from the attached mooring line. Most previous works (DNV, 2005; Houlsby and Byrne, 2005; Guo et al., 2014) have studied the monotonic capacity of suction anchors. For the drained condition, the vertical pullout resistance of a suction anchor only consists of its submerged self-weight and the soil frictions on the external and internal sides of the caisson wall (Deng and Carter, 1999; Randolph and House, 2002). This is the minimum pullout capacity of a suction anchor that determines the safe load limit of an embedded suction anchor. In fact, a suction anchor in service is subjected to long-term cyclic vertical loads produced by waves, currents and the continuous motions of the floating structure. This kind of cyclic load is mainly composed of wave-frequency and low-frequency components, which may last for a few hours, days or even weeks (Clukey et al., 1995). Therefore, the load cycles can be counted by thousands. Under this long-term effect of cyclic loads, the excess pore-pressure will build up within the soil

http://dx.doi.org/10.1016/j.enggeo.2016.12.001 0013-7952/© 2016 Elsevier B.V. All rights reserved.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

2

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

Fig. 1. Foundations for the OWTs with varying water depths.

near the anchor. The accumulated excess pore-pressure can reduce the effective soil stress, thus reducing the interface friction between the anchor wall and the surrounding soil. Consequently, the pullout capacity of suction anchor is reduced. Kelly et al. (2006a,b) carries out model tests of suction caissons under vertical monotonic and cyclic loading, as well as a comparison with field data, showing the positive pore pressure increases with the rate of cycling. Zhu et al. (2013) presents the 1 g laboratory cyclic loading tests with approximately 10,000 cycles to investigate the long-term lateral cyclic response of suction bucket foundations in sand. In order to predict excess pore-pressure response of offshore foundations and its effect on the bearing capacity, two numerical methodologies are adopted with different advantages. The first one is to apply advanced constitutive soil models to describe the plastic volumetric strain and stiffness of soil element within every load cycle, which require complex constitutive equations and numerous parameters. Thieken et al. (2014) describe the numerical simulation of suction bucket under variable tension loadings in sand. Cerfontaine et al. (2015) adopt the Prevost elasto-plastic model to estimate the response of a suction caisson embedded in dense sand under monotonic and cyclic vertical loading. Applications of these advanced models can be limited due to the determination of parameters and massive calculation steps involving hundreds or thousands of load cycles. The other approach is a semi-analytical method based on simplified constitutive model

incorporated with laboratory tests to evaluate the effects of cyclic loading. Taiebat and Carter (2000) present a method for the development of pore-pressure build up in seabed to predict the liquefaction analysis of a tank during a storm with time duration of 6 h. The semi-analytical method is efficient for cyclic response of offshore foundations facing numerous load cycles. To accurately predict the responses of the pore-pressure around the suction anchor, two mechanisms (the oscillatory and residual mechanisms) are used to simulate the instantaneous variation and accumulation of excess pore-pressures, respectively. Based on these two mechanisms, a novel numerical model is proposed for an embedded suction anchor under long-term vertical cyclic loadings. In this paper, the development and characteristics of the excess pore-pressure along the caisson wall are first studied, and then, the influences of different load and seabed parameters are investigated in detail. 2. Theoretical formulations As shown in Fig. 3, there are two different mechanisms controlling the pore-pressure responses in the seabed soil (Zen and Yamazaki, 1990): the oscillatory and residual mechanisms. Therefore, the overall pore water pressure p can be expressed as p ¼ posc þ pres

ð1Þ

Fig. 2. Suction anchors used for a moored FOWT.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

3

Fig. 3. Pore-pressure mechanisms (Jeng, 2013).

Fig. 5. Vertical loads acting on the anchor.

where posc is the oscillatory pore-pressure caused by the reversible deformation of the soil skeleton, and pres represents the period-averaged residual pore-pressure, which is defined by

∂ 1 ∂ ∂ where Laplace operator ∇2 ¼ ð∂r 2 þ r ∂r þ ∂z2 Þ, u and w are the soil displacements at the horizontal r-axis and vertical z-axis, respectively, G is the soil shear modulus, μ is the Poisson ratio, k is the permeability coefficient, n is the porosity, γw is the unit weight of water, εV is the reversible volume deformation of the soil skeleton, which can be expressed as

pres ¼

1 T

Z

tþT

ð2Þ

pdt t

where T is the period of cyclic loading and t is the time. In essence, pres is the result of accumulated residual deformation of the soil skeleton under cyclic loadings. Assuming the seabed soil to be a homogeneous isotropic porous medium, Biot (1941) gives the governing equations. Under the axisymmetric coordinates (r, z, ϕ), the equations are expressed as: G ∂εV u ∂p G∇ u þ −G 2 ¼ osc 1−2μ ∂r r ∂r 2

εV ¼

2

∂u u ∂w þ þ ∂r r ∂z

ð6Þ

and the compressibility coefficient of the pore water β is equal to β¼

1 1−Sr þ Kw P w0

ð7Þ

ð3Þ

G∇2 w þ

G ∂εV ∂posc ¼ 1−2μ ∂z ∂z

ð4Þ

∇2 posc −

γw nβ ∂posc γ w ∂εV ¼ k k ∂t ∂t

ð5Þ

(a) Sketchof 3D model

2

in which Kw = 2× 109 N/m2 is the bulk modulus of water, Pw0 is the sum of the hydrostatic pressure and atmospheric pressure, and Sr is the saturation of the seabed soil. The shear stress within the soil is limited by Mohr-Coulomb criterion, and the shear strength τf′ is expressed as: τ0f ¼ c0 þ σ 0n  tanδ

ð8Þ

(b) FEM meshes

Fig. 4. Axisymmetric model in three dimensional and axisymmetric coordinates. (a) Sketch of 3D model. (b) FEM meshes.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

4

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

Table 1 Parameters of the numerical model. Category

Designation

Values

Anchor

Anchor diameter, D wall thickness, tf Anchor length, L Submerged self-weight, W′ Elastic modulus, Ea Poisson ratio, μa Unit weight, γs Shear modulus, G Poisson ratio, μ Frictional angle, δ Permeability coefficient, k Porosity, n Saturability, Sr Maximum void ratio, emax Minimum void ratio, emin Relative density of soil, Dr Static load ratio, SLR Cyclic load ratio, CLR Cyclic load period, T

5m 0.2 m 12 m 3.1 × 105 N 2.1×1011 Pa 0.35 2×104 N/m3 5 × 106 Pa 0.33 30° 1×10−5 m/s 0.3 0.985 1.2 0.4 0.5 15% 10% 20 s

Seabed

Load

where σn′ is the effective normal stress, δ is the friction angle and the cohesive strength c′ = 0 for cohesionless soil. For the residual pore-pressure pres, the one-dimensional (1D) equation was derived from Biot's consolidation equation (Sumer and Fredsøe, 2002),

where τ0 is the amplitude of shear stress and σ0′ is the initial mean effective stress in the soil. αr and βr are functions of the soil relative density Dr = (emax − e)/(emax − emin), in which e is the current void ratio, and emax and emin are the maximum and minimum void ratios, respectively. Based on test data for cohesionless soil from Alba et al. (1976), empirical expressions of αr and βr are given by α r ¼ 0:34Dr þ 0:084

ð12Þ

βr ¼ −0:37Dr þ 0:46

ð13Þ

As an extension, Zhao et al. (2013) proposed a two-dimensional plain strain model for the development of residual pore-pressure. The accuracy and reliability of this model have been verified by Jeng and Zhao (2014) and Zhao et al. (2014). This paper makes further efforts to its application in the axisymmetric coordinate system, ∂pres ¼ cv ∇2 pres þ f r ðr; zÞ ∂t

where pres represents the residual pore-pressure caused by structure vibration, ρw is the density of seawater, and cv is the consolidation coefficient in the axisymmetric coordinates, cv ¼

Gk 2ð1 þ μ Þ γw 3ð1−2μ Þ

ð9Þ

in which cv1 is the coefficient of 1D consolidation and is defined by cv1

Gk 2ð1−μ Þ ¼ γ w ð1−2μ Þ

ð10Þ

and the source term fr represents the total amount of excess pore-pressure generated per unit time and per unit volume of soil. A linear expression of fr for sandy seabed has been proposed by Seed and Rahman (1978), 

fr ¼

σ 00 τ0 T αr σ 0

1=βr

ð11Þ

(a) Entire geo-stress field

ð15Þ

and in the axisymmetric coordinate system, fr(r, z) can be expressed as

2

∂pres ∂ pres þ fr ¼ cv1 ∂t ∂z2

ð14Þ

f ðr; zÞ ¼

  σ 00 jτðr; zÞj 1=βr α r σ 00 T

ð16Þ

where τ(r, z) is the shear stress amplitude at the calculation point, which can be gained from the calculation of the oscillatory pore-presσ 0 þσ 0 þσ 0θ

sure, and σ 00 ¼ r 3z the calculation point.

is the mean effective normal stress of soil at

3. Implementation of numerical model By using the FEM software COMSOL Multiphysics 5.0, the numerical model for a suction anchor embedded in the seabed is built to simulate its behavior under cyclic loading in service. As shown in Fig. 4(a), this model is established in the axisymmetric coordinate system, with the

(b) Zoom view near the wall

Fig. 6. Geo-stress field after anchor pretension. (a) Entire geo-stress field. (b) Zoom view near the wall.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

symmetry axis through the center of the anchor. The whole computation domain, namely the rectangle ABCD, contains two parts that are the suction anchor and the seabed soil. The anchor is built as a linearly elastic material. As shown in Fig. 4(b), the width of boundary AB is 3 times the diameter of the suction anchor, and the depth AD is 3.3 times the anchor length. 3.1. Boundary conditions The boundary conditions of computation domain ABCD are set as follows: (1) boundary BE: the seabed surface is considered as a kind of zero excess pressure boundary, which means that the oscillatory and residual pore-pressures posc = pres = 0; (2) boundary BC: u = 0, ∂posc/∂r = ∂pres/∂r = 0; (3) boundary CD: u = w = 0, ∂posc/∂z = ∂pres/∂z = 0; (4) boundary AD: the axisymmetric boundary; (5) boundaries AE and EF: the anchor-soil interfaces, along which the displacement is continuous and the interfaces are impermeable, u = uA, w = wA, ∂posc/∂r = ∂pres/∂r = 0, where uA and wA are the displacements of the anchor in the horizontal and vertical directions.

5

3.2. Loads acting on the suction anchor The vertical loads acting on the suction anchor are illustrated in Fig. 5. As described in the previous section, the loads in the service condition of a suction anchor are divided into three categories: the static pretension load, the wave-frequency cyclic load, named as “Cyclic load 1”, and the low-frequency cyclic load named as “Cyclic load 2”. In this simulation, the uplift force on the anchor is set to be larger than the submerged weight but smaller than the pullout capacity. The calculation time for the cyclic loading is set to 3 h as the common duration of a certain storm state. The cyclic load ratio (CLR), which is the ratio of load amplitude Ac to the static pullout resistance of suction anchor Vs, represents the degree of applied cyclic load amplitude. The static load ratio (SLR) is defined by the stress level of pretension divided by the pullout resistance Vs. For simplification, the cyclic load curve is set to be sinusoidal with a period of T. The load acting on the anchor is expressed as: Load ¼ V s  SLR þ V s  CLR  sin

2π ðt−t 0 Þ T

ð17Þ

When the suction anchor is subjected to a vertical pullout load, there are three main failure modes: reverse bearing failure, bottom tension

(a) t1=t0+0.0

(b) t2=t0+T/4

(c) t3=t0+2×T/4

(d) t4=t0+3×T/4

Fig. 7. Oscillatory pore-pressure variations in a typical period. (a) t1 = t0 + 0.0. (b) t2 = t0 + T ∕ 4. (c) t3 = t0 + 2 × T ∕ 4. (d) t4 = t0 + 3 × T ∕ 4.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

6

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

(a) Points along the anchor wall

(b) along the external wall

(c) along the internal wall

Fig. 8. Variations of soil shear stress τrz along the anchor wall. (a) Points along the anchor wall. (b) Along the external wall. (c) Along the internal wall.

failure and sliding failure (Thorel et al., 2005). Among these, the sliding failure mode is prone to drained condition and corresponds to the minimum pullout capacity of suction anchor. In this case, the static pullout capacity Vs of the suction anchor can be estimated as the sum of the submerged self-weight W′ and the total interface friction F between the anchor wall and the seabed soil, Vs ¼ W0 þ F

ð18Þ

where the friction force F can be divided into the internal and external portions, F ¼ F int þ F ext Z F int ¼

0

Z F ext ¼

L

ð19Þ

σ 0v dz  ðK tanδÞðπDi Þ

ð20Þ

σ 0v dz  ðK tanδÞðπDo Þ

ð21Þ

L 0

where L is the anchor depth, σv′ is the effective vertical stress, Di and Do represent the internal and external diameters of the anchor,

respectively, K stands for the lateral pressure coefficient, and δ is the mobilized friction angle between the anchor wall and the soil. 3.3. Calculation procedure In this paper, to simulate the actual responses of suction anchor during the period of service, the calculation involves three steps in sequence: (1) Generate the initial geo-stress field. The seabed soil is consolidated under its self-weight, without consideration of the pore-pressure accumulation. (2) Pretension of the suction anchor. First, the suction anchor embedded in the seabed is built to be wished in place. The interfaces between the anchor wall and the soil are set to be rough. Then, some level of pretension force is applied and causes the stress relieve around the anchor. It is assumed that the time is sufficient long for full dissipation of the excess pore-pressure induced by the anchor pretension. Thus, the geo-stress field σ0′, considering the pretension of the suction anchor, is obtained. (3) Apply one-way cyclic tensile loading. A kind of cyclic uplift force is applied to the suction anchor with a fixed load period and

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

(a) 200s, 10T

(b) 400s, 20T

(c) 600s, 30T

(d) 1200s, 60T

(e) 3600s, 180T

(f) 10800s, 540T

7

Fig. 9. Residual pore-pressure variations. (a) 200 s, 10 T. (b) 400 s, 20 T. (c) 600 s, 30 T. (d) 1200s, 60 T. (e) 3600 s, 180 T. (f) 10,800 s, 540 T.

amplitude. Both the development of the oscillatory and residual pore-pressures are obtained at this step. 4. Simulation results and interpretations The parameters for suction anchor, seabed soil and loads are listed in Table 1. The anchor geometry size is specified in reference to the stocky suction anchors used in the Timor Sea (Randolph and Gourvenec, 2011). In this case, the calculated static pullout capacity Vs is 7.1 × 106 N, nearly 23 times the submerged weight. With a static load ratio SLR = 15%, the anchor is kept tensile. The cyclic load ratio CLR = 10% and the period is set to 20 s. The geo-stress σ 00 ¼

σ 0r þσ 0z þσ 0θ 3

in the seabed soil after anchor

pretension is shown in Fig. 6. The pretension mainly affects the geostress near the anchor wall, especially at the tip. The empirical coefficients αr and βr in Alba et al. (1976) are calibrated with a shear stress ratio στh0 between 0.1 and 0.3. The initial lateral earth pressure is calculatv

ed by K =1 − sin δ. The estimated peak shear stress is limited by MohrCoulomb criterion and the peak shear stress ratio στh0 is equal to 0.289 and v

coincident with the test. Fig. 7 shows the variations of the oscillatory pore-pressure around the anchor with an interval of T/4 in a typical period T. The negative pore-pressure mainly appears inside the anchor caisson and changes periodically with applied cyclic loadings. Previous tests by Guo et al. (2014) indicated that when the suction anchor is pulled vertically, the

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

8

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

(a) On the external side

(b) On the internal side

Fig. 10. Normalized pore-pressure along the anchor wall. (a) On the external side. (b) On the internal side.

Fig. 11. Normalized friction force on the wall.

passive pore-pressure inside the anchor works to keep the interior soil plug moving together with the anchor. The peak of negative pressure is located at the bottom of suction anchor. As shown in Fig. 8(a), twelve points are selected from the depth of 1/ 6 L to L below the mudline with an interval of 1/6 L along the internal and external walls. Fig. 8(b) and (c) respectively gives the variations

(a) On the external side

of the soil shear stress τrz along inner and outer surface of the caisson in two load cycles. The shear stress fluctuates with the same period of the applied cyclic load, and the amplitude increases along with the increase in the embedment depth. The maximum shear stress occurs at the depth of 1 L on both sides of the anchor wall. Except for the anchor tip, the shear stress is relatively small inside the anchor. Fig. 9 shows the residual pore-pressure distributions at 200 s (10 T), 400 s (20 T), 600 s (30 T), 1200 s (60 T), 3600 s (180 T) and 10,800 s (540 T). With a load period of 20 s, the numbers of load cycles are 10, 20, 30, 60, 180 and 540, respectively. The residual pore-pressure increases with an increase in loading time. The residual pore-pressure first appears in the shallow layer of the seabed soil on the external side of anchor wall. Then, the residual pore-pressure gradually develops downwards along the anchor wall. The distribution area of the residual pore-pressure also expands horizontally at the external side. In contrast, there is no obvious pore-pressure accumulated at the internal side of the anchor wall. Under continuous cyclic loadings, the development of residual pore-pressure is fast at the beginning, and then becomes much slower. There is a tendency for the residual pore-pressure to reach a steady state rather than continue increasing. After 3 h under certain loading conditions, the normalized residual pore-pressure (pres⁎ = pres ∕ σ0′) distributions along the external and internal walls are shown in Fig. 10. The time interval between each curve coincides with that in Fig. 9(a)–(f). As shown in Fig. 10(a), the residual pore-pressure appears on the entire external side at the end of calculation. The residual pore-pressure achieves 0.65 of the initial effective

(b) On the internal side

Fig. 12. Normalized residual pore-pressure with different amplitudes. (a) On the external side. (b) On the internal side.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

Fig. 13. Normalized friction change with different amplitudes.

stress in the shallow layer (depth of 0.1 L), but decreases rapidly as the depth increases further. At the lower tip of the anchor wall, the residual pore-pressure does not exceed more than 0.03 times the effective stress. The development of residual pore-pressure in the first hour is more significant than in the latter 2 h. On the internal side, the residual porepressure is much smaller and not obvious in the first hour. The accumulation of pore-pressure first takes place in the shallow layer of the external seabed, and then gradually develops downwards along the external wall. After it reaches the lower end, the residual pore-pressure begins to diffuse upwards to the caisson top, which is set to be impermeable. It is acknowledged that the residual pore-pressure around the anchor can reduce the soil effective stress. Consequently, the friction between the anchor wall and the seabed soil is reduced. In order to investigate the effect of the accumulated pore-pressure on the anchor pullout capacity, the changes in the frictions on both sides are shown in Fig. 11. By assuming that the lateral pressure coefficient K and mobilized friction angle δ are not affected by the residual pore-pressure, the interface frictions are calculated according to Eqs. (19)–(21). The frictions are normalized by the initial values, according to the normalized internal friction F*int = Fint ∕ Fint0. The normalized external friction F*ext = Fext ∕ Fext0 and the normalized total friction F* = F ∕ F0, in which Fint, Fext and F are the internal, external and total frictions after

(a) On the external side

9

Fig. 15. Normalized friction change with different periods.

applying the cyclic load, respectively. And Fint0, Fext0 and F0 are the internal, external and total frictions before applying the cyclic load, respectively. The reduction in the wall friction is not significant on the internal wall but is significant on the external wall. In this case, the total friction on the caisson wall decreases down by approximately 7.5%, whereas the internal friction decreases by 2.5% and the external friction decreases by 12.5%. 5. Parameter analysis In this section, the effects of the cyclic load and seabed parameters are studied, including the amplitude and period of the cyclic load, and the shear modulus and permeability of the seabed soil. 5.1. Effects of load parameters The movements of the floating structure in deep water usually consist of two parts: the wave-frequency motion and slow-frequency drift. These two components induce cyclic loads acting on the anchor through the tensioned mooring line. The amplitude and period of the cyclic loads change with different cyclic motions of the floating structure. To study the effects of load amplitude and period, different load combinations are adopted in the simulations.

(b) On the internal side

Fig. 14. Normalized residual pore-pressure with different periods. (a) On the external side. (b) On the internal side.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

10

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

(a) On the external side

(b) On the internal side

Fig. 16. Normalized residual pore-pressure with different permeability coefficients. (a) On the external side. (b) On the internal side.

5.1.1. Load amplitude In this study, the adopted load amplitudes increase from 2.5% to 15% of the static pullout capacity Vs, with an interval of 2.5%. The load period of cyclic loading is set to 20 s. For a three-hour computation, the final normalized residual pore-pressures along the anchor wall with different load amplitudes are shown in Fig. 12. Accordingly, the change in the normalized total friction is shown in Fig. 13. The amplitude of the applied cyclic load has obvious effects on the accumulation of excess pore-pressure around the anchor. On the external side, the residual pore-pressure under a load ratio of 2.5% is the smallest. With larger amplitude, the residual pore-pressure increases and develops downwards along the anchor wall. When the cyclic load ratio reaches 12.5%, the residual pore-pressure reaches its initial effective stress at the depth of 0.07 L, and the seabed soil can be liquefied in the circumstance. With a cyclic load ratio of 15%, the residual porepressure develops deeper to 0.15 L. On the internal side, the residual pore-pressure becomes more significant with a larger cyclic loading, especially in the shallow layer. With the largest CLR, the residual porepressure can reach the initial effective stress under the caisson top. As shown in Fig. 13, the wall friction can decrease to 0.85 of its initial value with a cyclic load ratio of 15%. The development tends to become steady after 3 h with a small ratio, but the increasing tendency remains for a large ratio.

Fig. 17. Normalized friction with different permeability coefficients.

5.1.2. Load period With cyclic load ratio CLR of 10%, and static load ratio SLR of 15%, the load periods are 5 s, 10 s, 20 s, 40 s and 60 s. The calculated residual pore-pressures along the anchor wall are shown in Fig. 14, and the change in normalized friction is shown in Fig. 15. For the same load duration, a smaller period leads to a greater increase in the residual porepressure along the anchor wall. This may be due to more load cycles for a smaller period. After 3 h of cyclic loading, the residual pore-pressure expands to a larger depth on the external wall. With a period of 5 s, the residual pore-pressure reaches the initial effective stress within the depth of 0.12 L, but the peak value of pore-pressure is only 0.17 times that of the initial effective stress for a cycle period of 60 s. The normalized residual pore-pressure on the internal side is not significant compared with the external side. With the period of 5 s, the peak value reaches 0.95 under the anchor top but decreases fast with the depth. As a consequence, the friction decrease changes with the residual pore-pressure as shown in Fig. 15. With same load amplitude, the highfrequency cyclic load tends to cause a bigger decrease in the pullout resistance of the suction anchor. The friction can be reduced to 0.84 times the initial value with a period of 5 s. 5.2. Effects of seabed parameters 5.2.1. Soil permeability In this section, different seabed soil permeability coefficients (k = 10−4, 5 × 10−5, 10−5, 5 × 10−6, 10−6 m/s) are used in the simulation. The normalized residual pore-pressures p∗res = pres/σ0′ on the external and internal sides at the end of the simulation are plotted in Fig. 16(a) and (b), respectively. The effect of soil permeability on the anchor friction force is shown in Fig. 17. Based on Eqs. (14)–(15), the residual pore-pressure accumulates with a smaller permeability. A smaller consolidation coefficient cv makes it more difficult for pore-pressure to diffuse from the high-magnitude region to the low-magnitude region. Therefore, as the permeability coefficient decreases, the excess pore-pressure appears and expands to a larger depth on the external side of the caisson, as shown in Fig. 16(a). With the smallest permeability coefficient of 1 × 10−6 m/s, the residual pore-pressure reaches the effective stress in the shallow seabed (approximately 0.22 L). However, the distribution of the internal porepressure is small and complex, as shown in Fig. 16(b). The first source of the internal excess pore-pressure is the shear stress in the inside soil plug, under the effect of cyclic loads. The other one is the diffusion from the excess pore-pressure near the wall tip, where the pore-pressure is relatively high. The magnitude of the excess pore-pressure outside the anchor is large, which can lead to a great reduction in the

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

(a) On the external side

11

(b) On the internal side

Fig. 18. Normalized residual pore-pressure with different shear modulus. (a) On the external side. (b) On the internal side.

wall friction. With the permeability of 1 × 10−6 m/s, the friction force decreases to 0.75 times its initial value. 5.2.2. Shear modulus The shear modulus G of the seabed soil ranges from 108 Pa for dense sand to 106 Pa for loose sand or silt. Thus, different shear moduli (G = 106, 5 × 106, 107, 5 × 107 and 108 Pa) are used in this section to study the features of the residual pore-pressure. The distributions of the residual pore-pressures on both sides are shown in Fig. 18, and the decrease of the friction force with time is plotted in Fig. 19. As shown in Fig. 18(a), the magnitude and influence depth of the accumulated pore-pressure on the external wall are strongly affected by the shear modulus of the seabed soil. With a smaller shear modulus, the consolidation coefficient cv in Eqs. (14)–(15) decreases, which makes the accumulation of the pore-pressure easier on the external side, but suppresses the diffusion of high excess pore-pressure. As a result, the pore-pressure inside the anchor wall is negligible at a shear modulus of 106 Pa. Because the external residual pore-pressure contributes more to the reduction of friction, the total friction is smaller with a smaller modulus, as shown in Fig. 19. With the smallest modulus, the normalized friction force decreased the most, to approximately 0.77. 5.2.3. Relative density In order to investigate the effect of relative density Dr on the porepressure accumulation, the permeability and shear modulus are

Fig. 19. Normalized friction force with different shear modulus.

assumed to be constant (coincident with the base case) despite the change in relative density. Different relative densities are chosen in this case (Dr = 0.3, 0.4, 0.5, 0.6 and 0.7), and the corresponding empirical expressions αr and βr in Eq. (11) are calculated by Eqs. (12)–(13). The normalized pore-pressure distribution and friction force are plotted in Figs. 20 and 21. As shown in Fig. 20, the pore pressure builds up faster in both external and internal sides with a smaller relative density. In loose sands with relative density Dr = 0.3 or 0.4, the shallow layer will be liquefied. The reduction in Fig. 21 caused by the residual porepressure is more significant with smaller relative density as well. The normalized friction goes down to 0.5 and 0.77 when the relative density Dr = 0.3 and 0.4. In real soil, the smaller relative density will increase the permeability and decrease the shear modulus. The former one will reduce the accumulation of residual pore-pressure and the latter one will accelerate the accumulation. 6. Conclusion This paper has proposed a novel numerical model to investigate the pore-pressure response around a suction anchor for the FOWTs in service. The suction anchor is embedded in a porous seabed and subjected to continuous vertical cyclic loading. Under the action of cyclic loading, there are two parts of excess pore pressure, namely the oscillatory and residual pore-pressures. The development and distribution of these two kinds of pore-pressure were first studied, and then the reduction in wall friction was estimated. Parameter studies were performed to assess the influences of the load and seabed parameters. Some useful conclusions are as follows: (1) The oscillatory pore-pressure mainly appears inside the caisson and changes periodically with the action of cyclic loading. The peak of the negative pressure is always located at the bottom of the suction anchor. Under the long-term effects of cyclic loading, the residual pore-pressure first accumulates in the upper soil layer outside the anchor. It gradually spreads both outward and downward to a larger area. This pore-pressure accumulation begins rapidly and tends to remain steady after 3 h. (2) The existence of residual pore-pressure can decrease the effective stress in the seabed, and consequently reduces the interface friction between the caisson and seabed soil. The reduction is more significant on the external side than the internal side. The reduction increases rapidly in the first hour, and remains relatively steady in the latter 2 h. (3) The characteristics of the cyclic load, including the load amplitude and period, affect the magnitude and influence depth of the residual pore-pressure in the seabed. Cyclic loading with a

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

12

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

(a) On the external side

(b) On the internal side

Fig. 20. Normalized residual pore-pressure with different relative densities. (a) On the external side. (b) On the internal side.

larger amplitude or shorter period can obviously increase the distribution of the pore-pressure and reduce the wall friction as well. (4) The characteristics of the seabed soil, including the seabed permeability, shear modulus, and relative density affect the accumulation trend of the residual pore-pressure. With lower permeability or smaller shear modulus, it is easier for the residual pore-pressure to develop under cyclic loadings, but also makes the diffusion of pore-pressure from the high-magnitude region to low-magnitude region much more difficult. The residual pore-pressure can develop fast outside the anchor wall, but the internal residual pore-pressure is quite small. The obvious reduction in friction for lower permeability and smaller shear modulus is mainly due to the significant external residual pore-pressure. If the soil permeability and shear modulus keep constant, the porepressure is easier to accumulate in loose soil with smaller relative density, and reduce more in interface friction. 7. Discussion From the simulation results, the residual pore-pressure is easily accumulated in shallow soil, although the shear stress is constrained by the Mohr-Coulomb criteria. In the base case, the normalized residual pore-pressures pres ∕ σ0′ archives 0.65 within a small depth of 0.1 L and decreases with the embedment depth. Numerical experiment is

Fig. 21. Normalized friction force with different relative densities.

conducted to seek the reason of the concentration near the surface. The initial effective stress is manually set to be a uniform constant value at all depth, which is equal to the effective overburden stress in the middle of the wall length L. So the accumulation of residual is only controlled by the shear stress. A comparison of the normalized residual pore-pressure along the external wall is shown in Fig. 22. There is no obvious residual pore-pressure near the seabed surface in the numerical experiment compared to the base case. The reason of the peak normalized residual pore-pressure in shallow soil is the source term fr becomes large due to low effective stress σ0′. In addition, the magnitude of porepressure is normalized using the effective stress σ0′, which makes the normalized value even obvious. Acknowledgement The authors are grateful to the support from International Science & Technology Cooperation Program of China (2015DFE72830), National Natural Science Foundation of China (Grant no. 51325901, 51209183 and no. 51279176), Zhejiang Provincial Natural Science Foundation of China (LY15E090002), and the Fundamental Research Funds for the Central Universities (2015QNA4023).

Fig. 22. Normalized residual pore-pressure on external wall in numerical experiment.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001

K. Shen et al. / Engineering Geology xxx (2016) xxx–xxx

References Alba, P.D., Seed, H.B., Chan, C.K., 1976. Sand liquefaction in large-scale simple shear tests. J. Geotech. Geoenviron. Eng. ASCE 102 (GT9), 909–927. Biot, M.A., 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 26 (2), 155–164. Cerfontaine, B., Collin, F., Charlier, R., 2015. Numerical modelling of transient cyclic vertical loading of suction caissons in sand. Géotechnique 65 (12). Clukey, E.C., Morrison, M.J., Garnier, J., Corté, J.F., 1995. The response of suction caissons in normally consolidated clays to cyclic TLP loading conditions. Offshore Technology Conference, Richardson, TX (United States). Deng, W., Carter, J.P., 1999. Vertical pullout behaviour of suction caissons. Research Report, Centre for Geotechnical Research. The University of Sydney. Det Norske Veritas (DNV), 2005. Geotechnical design and installation of suction anchors in clay. Recommended Practice. DNV- RP-E303. Guo, Z., Wang, L.Z., Yuan, F., 2014. Set-up and pullout mechanism of suction caisson in a soft clay seabed. Mar. Georesour. Geotechnol. 32 (2), 135–154. Houlsby, G.T., Byrne, B.W., 2005. Design procedures for installation of suction caissons in sand. Proceedings of the ICE-Geotechnical Engineering. 158(3), pp. 135–144. Jeng, D.S., 2013. Porous Models for Wave-Seabed Interactions. Germany. Springer, Heidelberg. Jeng, D.S., Zhao, H.Y., 2014. Two-dimensional model for accumulation of pore pressure in marine sediments. J. Waterw. Port Coast. Ocean Eng. 141 (3), 04014042. Kelly, R.B., Houlsby, G.T., Byrne, B.W., 2006a. A comparison of field and laboratory tests of caisson foundations in sand and clay. Géotechnique 56 (9), 617–626. Kelly, R.B., Houlsby, G.T., Byrne, B.W., 2006b. Transient vertical loading of model suction caissons in pressure chamber. Géotechnique 56 (10), 665–675. Randolph, M., Gourvenec, M.R.S., 2011. Offshore Geotechnical Engineering. CRC Press. Randolph, M.F., House, A.R., 2002. Analysis of suction caisson capacity in clay. Offshore Technology Conference. Offshore Technology Conference.

13

Ronalds, B.F., 2002. Deepwater facility selection. Offshore Technology Conference. Offshore Technology Conference. Sclavounos, P.D., Lee, S., DiPietro, J., Potenza, G., Caramuscio, P., De Michele, G., 2010. Floating offshore wind turbines: tension leg platform and taught leg buoy concepts supporting 3–5 MW wind turbines. European Wind Energy Conference EWEC, pp. 20–23. Seed, H.B., Rahman, M.S., 1978. Wave-induced pore pressure in relation to ocean floor stability of cohesionless soils. Mar. Georesour. Geotechnol. 3 (2), 123–150. Sumer, B.M., Fredsøe, J., 2002. The Mechanics of Scour in the Marine Environment. World Scientific, Singapore. Taiebat, H.A., Carter, J.P., 2000. A semi-empirical method for the liquefaction analysis of offshore foundations. Int. J. Numer. Methods Eng. 24, 991–1011. Thieken, K., Achmus, M., Schröder, C., 2014. On the behavior of suction buckets in sand under tensile loads. Comput. Geotech. 60, 88–100. Thorel, L., Garmier, J., Rault, G., Bisson, A., 2005. Vertical uplift capacity of suction caisson in clay. Proceedings of the First International Symposium on Frontiers on Offshore Geotechnics. University of West Australia, Perth, pp. 273–279. Zen, K., Yamazaki, H., 1990. Mechanism of wave-induced liquefaction and densification in seabed. Soils Found. 30 (4), 90–104. Zhao, H., Jeng, D.S., Zhang, H., Zhang, J., 2013. Two-dimensional model for wave-induced pore pressure accumulation in marine sediments. ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers. Zhao, H.Y., Jeng, D.S., Guo, Z., Zhang, J.S., 2014. Two-dimensional model for pore pressure accumulations in the vicinity of a buried pipeline. J. Offshore Mech. Arct. Eng. 136, 1–16 (042001). Zhu, B., Byrne, B., Houlsby, G.T., 2013. Long-term lateral cyclic response of suction caisson foundations in sand. J. Geotech. Geoenviron. 139 (1), 73–83.

Please cite this article as: Shen, K., et al., Numerical investigations on pore-pressure response of suction anchors under cyclic tensile loadings, Eng. Geol. (2016), http://dx.doi.org/10.1016/j.enggeo.2016.12.001