- Email: [email protected]
Effect of seabed instability on fixed offshore platforms
ARTICLE IN PRESS
Soil Dynamics and Earthquake Engineering 26 (2006) 1127–1142 www.elsevier.com/locate/soildyn
Effect of seabed instability on fixed offshore platforms Yasser E. Mostafaa,, M. Hesham El Naggarb a
Department of Irrigation & Hydraulics, Faculty of Engineering, Ain Shams University, Cairo, Egypt Geotechnical Research Centre, Faculty of Engineering, University of Western Ontario, London, Ont., Canada N6A 5B9
b
Accepted 10 December 2005
Abstract Storms, hurricanes, and earthquakes may cause seabed instability, especially if the seabed is weak. The seabed instability, manifested in movement of soil layers, exerts lateral forces that may cause large stresses in offshore foundations. The induced stresses may compromise the stability of the foundation and supported structure. The effect of seabed instability on a fixed offshore structure is examined in this study. The method used accounts for soil nonlinearity, dynamic soil resistance, and pile–soil–pile interaction within the stable soil layer. Dynamic p–y curves, dynamic t–z curves and q–z curves have been used to simulate the soil resistance in the lateral and axial directions. The effect of different parameters that influence the response of offshore structures to seabed instability is evaluated. The parameters considered include the value of soil movement, the sliding layer depth, the wave loading, the pile flexibility, the soil movement profile, and the axial loading at the pile head. The response predicted using the proposed analysis compared well with that calculated using a boundary element solution for a case history of a failed offshore platform. r 2006 Elsevier Ltd. All rights reserved.
1. Introduction Waves impose an oscillatory motion on the soft seabed sediments, which on sloping ground may lead to a mass transfer of soil down the slope. Also, the passage of a wave will impose a transient pressure change on the sea floor and this pressure change will be approximately sinusoidal in space and time [1]. The magnitude of this pressure change depends on the wavelength (time period), the water depth and the wave height. If the stresses induced from the differential pressure exceed the soil strength, significant displacements may occur. The most important factor that determines the wave pressure at which shear failure occurs is the soil strength. Even with sufficient soil strength, offshore structures may experience extensive damage due to the large lateral motions that occur at large depths, which may require the supporting foundations to be extended to greater depths [2]. Some case histories reported failure or damage that occurred to offshore structures due to hurricane-triggered Corresponding author.
E-mail addresses: [email protected] (Y.E. Mostafa), [email protected] (M. Hesham El Naggar). 0267-7261/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2005.12.010
submarine slides in the Mississippi River Delta [3–6]. Sterling and Strohbeck [6] discussed the reasons of failure of the South Pass 70 ‘‘B’’ Platform in Hurricane ‘‘Camille’’ occurred in 1969. They suggested that the platform did not fail by simple overload, but it had failed primarily owing to a major submarine slide extending to a considerable depth. They showed that what they called ‘‘B’’ structure could have withstood a soil slide of 9–12 m, but with the hurricane sea adding force to these slide forces, it was evident that the structure could not withstand a slide with that depth. Doyle [7] conducted experimental tests in a large model tank to study the effect of surface water waves on a soft clay soil under controlled conditions. Measurements of wave height and period, bottom pressure, and in situ soil shear strength were obtained to evaluate simple analytical methods for predicting seabed instability. In case of no bottom slope, the soil moved in an orbital path at the surface and the vertical component of movement decayed more rapidly than the horizontal component; in case of bottom slope, the soil moved with a net lateral translation. Therefore, the axial loading in the field due to soil instability may be minimal. Lee et al. [8] described the use of a modified nonlinear boundary element approach to analyze the response of
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offshore piles subjected to external soil movement. They investigated the effect of a number of pile and soil parameters on the behavior of a hypothetical single offshore pile. They suggested four modes of failure: (i) ‘‘flow’’ mode—flow of the slide past a stationary pile; (ii) ‘‘intermediate’’ mode—rotation of the pile with the soil at failure along the full length of the pile; ‘‘short pile’’ mode—translation of the pile with the sliding soil; and (iv) ‘‘long pile’’ mode—the maximum bending moment in the pile reaches the yield moment of the pile before complete development of the other three modes. They concluded that the ‘‘long pile’’ mode is the most common failure mode. However, the effect of seabed instability on the response of offshore structures supported on clusters of piles (pile groups) has not been studied. 2. Method of analysis The effect of seabed instability on a fixed offshore structure is examined accounting for soil nonlinearity, dynamic soil resistance, and pile–soil–pile interaction within the stable soil layer. The Kvitebjørn Platform shown in Fig. 1 has been considered in the study. The Kvitebjørn Platform is installed in the Norwegian section of the North Sea. The soil profile, including the design soil parameters is shown in Fig. 2a. The water depth in the field is 190 m, and the substructure is a steel jacket with four legs supported by vertical steel piles grouped symmetrically around each corner leg. The jacket is supported on sixteen piles with a diameter of 2.438 m arranged in symmetrical groups of four piles per corner leg. Each corner leg has an additional pile with a diameter of 1.372 m to be used for levelling (Fig. 2b and c). The total weight of the platform is 171,200 kN, and is designed to support a maximum operating topside weight of 225,000 kN [9]. Fig. 1. Three-dimensional view of the platform.
2.1. Lateral soil resistance
dashpot constants are calculated as
The soil resistance along the pile shaft is modeled using springs and dashpots whose constants are derived using dynamic p–y curves. The dynamic p–y curves for a single isolated pile are calculated using the equation proposed by El Naggar and Bentley [10] as
Pd ¼
n ! Ps ba2o þ kao oy=d Ps a þi y, y y
(1)
where Pd is the dynamic soil reaction at depth x (N/m), Ps the static soil reaction obtained from the static p–y curve at depth x (N/m), ao is dimensionless frequency ¼ od=V s , o the frequency of loading (rad/s), d the pile diameter (m), y the lateral pile deflection at depth x (m), and a (a ¼ 1 in this analysis), b, k, and n are constants that depend on the soil type. Considering Eq. (1), the nonlinear spring and
knl ¼
n Ps ba2o þ kao oy=d Ps a and cnl ¼ . y oy
(2)
2.1.1. Group effect The approach proposed by Mostafa and El Naggar [11] for calculating dynamic p–y curves for a pile in a group is used. In this approach, the dynamic p–y curve for a single isolated pile is multiplied by an appropriate p-multiplier (Pm) to calculate the dynamic p–y curve for a pile in a group, i.e. Pg ¼ Pm Pd ,
(3)
where Pg is the dynamic soil reaction at a certain depth for a pile in a group, Pm the p-multiplier and Pd the dynamic soil reaction at the same depth for an isolated single pile. The p-multipliers depend on the ratio of pile spacing to pile
ARTICLE IN PRESS Y.E. Mostafa, M. Hesham El Naggar / Soil Dynamics and Earthquake Engineering 26 (2006) 1127–1142
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Fig. 2. (a) Soil profile, (b) pile arrangement, (c) cross-section of the main and leveling piles
diameter (S/d) and the ratio of pile head displacement to pile diameter (y/d). Mostafa and El Naggar [11] provide an extensive set of charts for p-multipliers for piles in sand and clay for different spacing to diameter ratios. Using the p-multipliers, the group effect is accounted for, but the soil model includes dynamic p–y curves for individual piles
without interconnections resulting in significant efficiency in computations. The group effect is considered for the stable soil layers. The ratio of pile spacing to pile diameter (S/d) for the main piles of the Kvitebjørn Platform is 3.44. The leveling pile (pile 5 in Fig. 2b) is closer to pile 3, with a spacing of
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(S/d ¼ 2.35 m). The value of Pm ¼ 0.7 for piles 1, 2, and 4, and the value of Pm ¼ 0.55 for piles 3 and 5 are established from the charts presented in Mostafa and El Naggar [11]. Bransby [12] stated that the load transfer p–d curves for the case of passive lateral loading (piles displaced laterally due to soil movement) are different from the p–y curves for the case of active lateral loading. He concluded that p–d curves stiffen with reducing pile spacing, whereas p–y curves soften. Therefore, p–y curves for single piles were used to represent soil reactions in the sliding layers (i.e. group effect was not considered). In addition, dynamic p–y curves are used for the case of lateral soil movement as the dynamic p–y curves are stiffer than the static p–y curves. 2.2. Vertical soil resistance
on local pile deflection (t–z curves). The soil resistance at the pile toe is modeled using q–z curves. In this paper, t–z curves and q–z curves are constructed using the recommendations given by API (1993). Bea [13] stated that the dynamic axial soil resistance to pile movement due to wave loading and earthquakes (rate effect) is in the range of 1.2–1.8. Briaud and Garland [14] proposed a method to predict the behaviour of single piles in cohesive soil subjected to vertical loads applied at various rates. They proposed that the increase in pile capacity due to the effect of loading rate can be evaluated by n Qu1 t2 ¼ , (4) Qu2 t1
The soil resistance to the vertical movement of the pile is modeled using axial shear transfer functions that depend
in which Qu1 and Qu2 are the ultimate pile capacities reached in a time to failure t1 and t2, respectively, and n is a viscous exponent that varies from 0.02 for stiff clay to 0.10
10 -20
10 0
0.005 0.01 0.015 0.02 0.025
-0.0001
0
0.0001
0.0002
-50 Level (m)
Level (m)
-50
-20
-80 -110
-80 -110
-140
-140
-170
-170 SM=0.25 m
-200
-200
SM=0.5 m -230
-230 (a)
(b)
0 0.002
0.004
0.006
0.008
-5 0
-10
-10
-15
-15
-20
-20
Depth {m}
Depth {m}
-0.002 -5 0
0
-25 -30
0.0006
-30
SM=0.25 m
-35
-40
SM=0.5 m
-40
SM=0.25 m SM=0.5 m
-45
-50 (c)
0.0004
-25
-35
-45
0.0002
-50 (d)
Fig. 3. Effect of soil movement (SL ¼ 7.5 m) on: (a) platform displacement, (b) platform rotation, (c) pile displacement, and (d) pile rotation.
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2.4. Platform
for soft clays. Briaud and Garland [14] stated that for values of n within the given range, the pile capacity will be 1.21–2.60 times the static capacity. In this paper, the t value in the dynamic t–z curves are taken to be 1.6 times its value in a static t–z curve. The soil profile considered in this study, the arrangement of pile groups and dimensions of piles are given in Fig. 2.
The structural members of the platform and the foundation piles are modeled using space frame elements in the Table 1 Values for associated current Depth below sea-level (m)
Current speed (m/s)
0 25 50 75 100 125 150 175 190
0.50 0.50 0.50 0.46 0.42 0.39 0.36 0.32 0.29
2.3. Soil movement The soil movement is modeled as prescribed horizontal displacements to the soil springs located in the sliding layer. The movement is assumed to increase monotonically until it reaches the maximum prescribed value in 20 s. The soil springs on the opposite side of the direction of soil movement and the dynamic t–z curves within the sliding layer are removed.
0
0 0
0.5
1
-0.5
-10
1
1.5
-20
Depth (m)
Depth (m)
0.5
-15
-30 -40 -50
-25 -30
-60
-35
-70
-40 SM=0.25 m
SM=0.25 m
-80
-45
SM=0.5 m
-90
SM=0.5 m
-50
(a)
(b)
0 -4
-2
-5
0 0
2
4
6
-0.1
-5
-10
-10
-15
-15
-20
-20
-25
Depth (m)
-6
Depth (m)
0
-10
-20
(c)
-5
0.1
0.2
0.3
0.4
-25
-30
-30
-35
-35
-40
-40
-45
-45
-50
0
SM=0.25 m SM=0.5 m
(d)
-50
Fig. 4. Effect of soil movement on the maximum stresses along the pile, (SL ¼ 7.5 m): axial force, (b) shear force, (c) bending moment, (d) distributed load.
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commercial software ASAS-NL [15]. The space frame element has two nodes, one at each end. Each node has six degrees of freedom, three translations and three rotations. The platform and the supporting piles are assumed to be linear elastic. 3. Results For all the analyses and results presented in this paper, the soil movement is assumed to be the same for all the piles supporting the platform. The damping ratio of the platform is assumed to be 2%. The weight of the platform deck is assumed to be the maximum operating topside weight (225,000 kN). 3.1. Effect of magnitude of soil movement The top layer (7.5 m thick) in the soil profile (Fig. 2a) consists of very soft clay, which is likely to slide due to
moderate storms or extreme currents. To examine the effect of soil movement on the response of the platform, three values of prescribed horizontal soil movements (SM) are selected: 0.25, 0.5 and 0.75 m. A transient loading with a peak displacement of 0.25, 0.5 or 0.75 m is applied (one at a time) to the three soil layers. The length of this ramp loading is 20 s and the natural period of the platform is about 4.15 s (i.e. no resonance conditions). No wave loading is considered in this case. Fig. 3a reveals that the displacement of the platform varies almost linearly along its height and that an increase in the soil movement from 0.25 to 0.5 m resulted in an increase in the platform displacement. Fig. 3b shows that there is considerable rotation especially at the lower part of the tower due to soil movement, which results in bending stresses that can compromise the integrity of the tower. However, the rotation increased slightly with an increase in SM from 0.25 to 0.5 m. Fig. 3c and 3d show that the soil
Displacement (m)
1.4 1.2
SL=7.5 m
1
SL=15 m
0.8 0.6 0.4 0.2 0 -0.2 0
10
20
30
40
50
60
-0.4 -0.6
(a)
Time (sec)
Velocity (m/s)
0.4 0.3
SL=7.5 m
0.2
SL=15 m
0.1 0 -0.1 0
10
20
30
40
50
60
-0.2 -0.3 -0.4 Time (sec)
(b)
Acceleration (m/s2 )
0.25 0.2
SL=7.5 m
0.15
SL=15 m
0.1 0.05 0 -0.05 0
10
20
30
40
50
60
-0.1 -0.15
(c)
Time (sec)
Fig. 5. Effect of sliding layer thickness on top nodal tower response (SM ¼ 0.5 m): displacement, (b) velocity, (c) acceleration.
ARTICLE IN PRESS Y.E. Mostafa, M. Hesham El Naggar / Soil Dynamics and Earthquake Engineering 26 (2006) 1127–1142
movement caused a maximum displacement of about 7 mm at the pile head, and a maximum rotation of about 0.0005 rad at the bottom of the sliding layer. Increasing SM from 0.5 to 0.75 m had almost no effect on the response of the platform. This means that the soil, which is soft clay, has reached its limiting pressure and it slid past the intact pile (i.e. flow mode). Therefore, the case of SM ¼ 0.75 m is not pursued any further. Fig. 4a shows that the axial force induced in the pile due to the soil movement varies almost linearly along its shaft. Figs. 4b and 4c show that the maximum shear force and bending moment occur at depth ¼ 12.5 m. Fig. 4d shows the distributed loads along the pile length (the loads on the springs and dashpots) due to the sliding soil. It can be noted from Fig. 4d that the maximum load occurs at a depth equal to 7.5 m (i.e., the sliding plane). Generally, the increase in soil movement increases the stresses along the pile shaft.
1133
3.2. Effect of thickness of sliding layer The thickness of the sliding layer of the soil is influenced by different conditions. To examine the effect of the thickness of the sliding layer, SL, two different values were considered SL ¼ 7.5 and 15 m. Due to the close association between initiation of seabed movement and the period of maximum wave action, the lateral soil force and the maximum lateral force generated by wave, and current action could occur concurrently [3]. Therefore, the combined effects of the soil movement and the wave forces due to the 100-year design wave are considered. The design wave height and wave period are taken to be 28.5 m and 15.3 s, respectively. The current loading as indicated in Table 1 is also accounted for. The soil properties considered in the analysis are: cu ¼ 15 kPa and e50 ¼ 0.02 for the top 7.5 m; cu ¼ 80 kPa 30
10 0 -20 0
0.2 0.4 0.6 0.8
1
1.2 1.4
0
0.002 0.004 0.006 0.008 0.01
-30 -60
-80
Level (m)
Level (m)
-50
-110
-90 SL=7.5 m -120
-140
SL=15 m
-150
-170 SL=7.5 m
-180
-200 SL=15 m
-210 (b)
-230 (a)
0 -5
0 0
0.1
0.2
0.3
0.4
0.5
-0.004 0 -10
-10
-20 -30 Depth {m}
Depth {m}
-15 -20 -25 -30 -35
SL=7.5 m
-50
-70
SL=15 m
-80
-45 -50
-40
-60
-40
(c)
0.004 0.008 0.012 0.016
SL=7.5 m SL= 15 m
-90 (d)
Fig. 6. Effect of sliding layer thickness (SM ¼ 0.5 m) on: (a) platform displacement, (b) platform rotation, (c) pile displacement, (d) pile rotation.
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and e50 ¼ 0.007 for the clay layer that extends from depth ¼ 7.5 m to depth ¼ 32 m, where cu is the undrained shear strength and e50 is the strain corresponding to one-half the maximum principal stress difference. The lateral soil movement, SM ¼ 0.5 m and is assumed to be uniform throughout the sliding layer. Fig. 5 shows the effect of the sliding layer thickness on the response of the top node of the platform. It is noted that an increase in the thickness of the sliding layer resulted in a significant increase in the top nodal displacement (400%). Figs. 6a and 6b show the variation of the platform displacement and rotation for SL ¼ 7.5 and 15 m. It is noted from the figures that the maximum displacement for SL ¼ 15 m is more than three times the displacement for
SL ¼ 7.5 m, and the rotation along the tower length in case of SL ¼ 15 m is almost double of the rotation in case of SL ¼ 7.5 m. The increase in the rotation of the lower part of the tower is rather large. This may lead to substantial bending stresses in the tower members in this region. Fig. 6c reveals the large increase in the displacement along the length of pile 1 as SL increased from 7.5 to 15 m, as would be expected. For SL ¼ 7.5 m, the displacement is very small and it vanishes at a depth about 15 m. For SL ¼ 15 m, the maximum displacement is about 0.42 m (y/d ¼ 17%). This displacement is considered to be quite high and it is beyond the conventional geotechnical definition of pile failure limits. The displacement for the latter case vanishes at a depth about 40 m.
0 -15
-10
-5
0 0
-10
-5
-10
0
5
10
-10
-20 -20 Depth (m)
Depth (m)
-30 -40 -50
-30
-40
-60 -50 SL=7.5 m
-70 -60 -80
SL=15 m
-90
(a)
-70
(b)
0
0
(c)
-40
-20
0
20
40
-0.5
60
0
-10
-10
-20
-20
-30 -40
Depth (m)
Depth (m)
-60
1.5
-40 -50
-60
-60
(d)
1
-30
-50
-70
0.5
-70
Fig. 7. Effect of sliding layer thickness on the maximum stresses along the pile length, (SM ¼ 0.5 m): (a) axial force, (b) shear force, (c) bending moment, (d) distributed load.
ARTICLE IN PRESS Y.E. Mostafa, M. Hesham El Naggar / Soil Dynamics and Earthquake Engineering 26 (2006) 1127–1142
3.3. Effect of wave and current loading combined with seabed instability
Displacement {m}
Fig. 6d shows the rotation along the shaft of pile 1 for the two cases. It is noted that the pile rotation increased significantly with the increase of SL. The pile head rotation for case of SL ¼ 15 m is almost four times its rotation for case of SL ¼ 7.5 m. In both cases, the maximum rotation along the pile length occurred just below the depth of the sliding layer. The axial force, shear force, bending moment and the distributed load along the shaft of pile 1 are presented in Fig. 7. The stresses increase significantly with an increase in SL. For SL ¼ 7.5 m, the maximum shear force and bending moment occur at depth about 12.5 m. For SL ¼ 15 m, the maximum shear force occurred below the mudline by about 17.5 and 40 m while the maximum bending moment occurred at a depth about 35 m below the mudline. The distributed load along the pile shaft is indicated in Fig. 7d. For SL ¼ 7.5 m, the maximum force occurred at depth ¼ 7.5 m, and the load vanished at depth ¼ 40 m. For SL ¼ 15 m, the distributed load increased with depth to a maximum at depth ¼ 15 m, then it decreased to almost zero, then increased again in the zone between depths of 40 and 60 m. It has to be noted that increasing the sliding depth more than 15 m resulted in divergence of the stresses (i.e., failure of the platform piles) which represents long pile failure mode.
1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 0 -0.4 -0.6
The lateral loading due to soil movement may occur while extreme storms take place and it may occur some time after the duration of the storm terminates. To investigate the effect of the wave and current loading combined with the seabed instability, a comparison is presented between the coupled wave and current loading and the lateral soil movement, and the lateral soil movement alone. The case of wave and current loading alone without the occurrence of seabed instability is also shown for the sake of comparison. SL is assumed to be 15 m and SM is assumed to be 0.5 m. Fig. 8a shows the top nodal response for the cases of seabed instability, instability combined with waves and currents, and waves and currents only. For the case of seabed instability only, the top nodal displacement increased almost monotonically till it reached its maximum then it almost stabilized and slightly oscillated around the peak value. As expected, the case of combined seabed instability and wave loading lead to a larger response. It can be noted from Fig. 9a that the case of seabed instability alone is less critical than the case of wave loading only. Fig. 8b shows that the displacement along the pile shaft
Instability Instability+waves Waves
10
20
30
0
50
60
0 0
0.1
0.2
0.3
0.4
0.5 -10
-20
-20
-30
-30 Depth {m}
Depth {m}
-10
-40 -50 -60 -70
Instability Instability + waves Waves
0
0.004
0.008
0.012
0.016
-40 -50 -60
Instability
-70
Instability+ waves
-80
-80
Waves
-90
-90
(b)
40
Time (sec)
(a)
1135
(c)
Fig. 8. Effect of wave loading (SL ¼ 15 m, SM ¼ 0.5 m) on: (a) top nodal tower response (b) pile displacement, (c) pile rotation.
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0
0 0
2
4
6
-6
8
-4
-2
0
2
4
6
8
-10 -10 -20 -20
-40
Depth (m)
Depth (m)
-30
-50
-30
-40
-60 -70 -80
-50
Instability Instability + waves Waves
-60
-90 (b)
(a) 0 -60
-40
-20
0
20
40
60
-10
Depth (m)
-20
-30
-40
-50
(c)
-60
Fig. 9. Effect of wave loading on the stresses along the pile shaft (SL ¼ 15 m, SM ¼ 0.5 m) (a) axial force, (b) shear force, (c) bending moment.
due to seabed instability was much greater than the displacement due to wave loading only. Also, the combined effect of instability and wave loading resulted in almost double the displacement in case of seabed instability only. Fig. 8c shows that the rotation at the pile head (tower base) was almost the same for cases of instability only and waves only. However, the rotation t the pile head due to the combined effect of both cases was about four times greater. The maximum rotation occurred at a depth of about 17.5 m below the mudline. Fig. 9a shows that the case of wave loading only caused a greater axial force along the pile shaft. The case of seabed instability decreased the compression on the piles due to the uplift induced on the piles. Fig. 9b reveals that the
seabed instability has more pronounced effect on the shear along the pile shaft. The maximum shear force occurred at 15 and 40 m below the mudline. Fig. 9c shows a significant increase in the bending moment due to the combined effect of the seabed instability and wave loading. The maximum bending moment for the case of wave loading only is about 7.5 MN m and it occurred at 12.5 m below the mudline. The maximum bending moments for the cases of seabed instability only and seabed instability and wave loading are 36 MN m and 52, respectively. These values occurred at the pile head. The maximum bending moment along the pile shaft occurred at 35 m below the mudline (i.e, at depth equivalent to about 40% of the pile length). At this depth,
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30 10 0 -20 0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0.002
0.004
0.006
0.008
0.01
-30 -50 Level (m)
Level (m)
-60 -80 -110
-90
-120
-140
-150
-170 LSM
LSM
-180
-200 USM
USM -210
-230 (b)
(a)
0
0 0.1
0.2
0.3
0.4
0.5
-0.004 0 -10
0.6
-20
-20
-30
-30 Depth {m}
Depth {m}
-0.1 0 -10
-40 -50
-40 -50 -60
-60 LSM
-70
-70
-90
LSM USM
USM
-80
-80 (c)
0.004 0.008 0.012 0.016 0.02
-90 (d)
Fig. 10. Effect of soil movement profile (SL ¼ 15 m, SM ¼ 1.5 m) on: (a) platform displacement, (b) platform rotation, (c) pile displacement, (d) pile rotation.
the thickness of the offshore piles is decreased substantially as indicated in Fig. 2c. Offshore piles installed in soft clays, should be designed with a due consideration of instability effects because the seabed instability may induce great bending moments at greater depths. These bending moments may exceed the yielding moment of the piles if the cross-section is reduced above the level of the maximum bending moment. 3.4. Effect of soil movement profile In the previous sections, the soil movement profile is assumed to be uniform through the sliding layer depth (USM). However, the sliding soil layer may have a linear slide pattern, LSM, (i.e., maximum soil movement value
occurs at the top of the sliding layer and the movement vanishes at the bottom of the sliding layer). In this section, a comparison between the effect of uniform and linear soil movement profiles on the response of the platform is presented. In both cases, the soil modulus is assumed to be the same (increasing with depth). The sliding layer depth is assumed to be 15 m and the maximum soil movement value is assumed to be 1.5 m. The uniform soil movement profile increases the response along the tower length and the pile length as indicated in Fig. 10. The effect of the shape of movement profile on the displacement and rotation of the piles are more pronounced. Fig. 11 shows that the uniform soil movement profile increases the shear stress, distributed load and bending moment along the pile shaft.
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0
0
Depth (m)
-8
-6
-4
-2
0
2
4
6
8 -1
0
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
1
2
3
LSM -60
LSM
-60
USM
USM
-70
-70
(a)
(b)
0 -80 -60 -40 -20
0
20
40
60
80
-10
Depth (m)
-20
-30
-40
-50 -60 LSM USM (c)
-70
Fig. 11. Effect of soil movement profile on the stresses along the pile shaft (SL ¼ 15 m, SM ¼ 1.5 m): (a) axial force, (b) shear force, (c) bending moment.
3.5. Effect of pile flexibility on the pile group response The lateral displacement of each pile in the group can be related to the pile flexural stiffness and the pile–soil–pile interaction. The lateral displacement of the soil layers is related to the soil modulus or stiffness and the free field soil movement [16]. The pile and soil stiffness can be related together by a factor called the relative pile flexibility (KR), which is a dimensionless parameter. The pile flexibility factor (KR) is defined as KR ¼
EPI P , E s L4
(5)
where Ep is the pile’s Young’s modulus ¼ (2.1 105 MPa for piles under consideration); Ip the pile’s moment of
inertia; Es the soil’s Young’s modulus; L the embedded pile length. The soil modulus is possibly the most difficult quantity to estimate for real soil as the method of installation of the piles may influence the value and the distribution of Es with depth. Ideally Es should be back calculated from the results of a full-scale in situ lateral load test or plate load tests at various depths [17]. From the Kvitebjørn soil investigation (Aker Engineering AS [9]), the maximum shear modulus Gmax is taken as 2300 times the undrained shear strength (cu) in the top 7.5 m, and as 1100 times the undrained shear strength in the subsequent soil layers (refer to Fig. 2a). The maximum Elastic modulus Emax is then calculated as E max ¼ 2ð1 þ nÞGmax , where n is the Poisson’s ratio. Assuming undrained conditions for clay layers and partly
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0 -6
-4
-2
0
2
4
6
-10 -20
Depth (m)
-30 -40 -50 -60
3.6. Effect of axial loading at the pile head
Pile 5
The effect of seabed instability on offshore piles has been investigated in the literature. However, many researchers did not take into consideration the axial loading transmitted from the offshore tower to the pile head and the pile head fixity condition while studying this problem. In this section, pile 1 is investigated in two cases. The first case is the pile head connected to a cap together with the heads of the other piles and supporting the offshore tower. The second case is the same pile, but without a cap and without any axial loading. The effect of seabed instability only is taken into consideration without the wave loading. SL is assumed to be 15 m and SM is assumed to be 0.5 m. Fig. 13a shows the time histories of the lateral displacement of the pile head in the two cases described above. It is noted from Fig. 13a that the existence of pile cap and axial loading significantly decrease the lateral displacement at the pile head. Figs. 13b and 13c indicate the shear stress and bending moment along the pile shaft in the two cases. It is noted that the axial loading substantially alters the shear along the pile shaft. Ignoring the axial loading at the pile head and the pile fixity conditions eliminates the bending moment at the pile head and significantly overestimates the bending moment along the pile shaft. It is also noted that the bending moment profiles along the pile shaft are similar in both cases.
-90
(a)
0 -60
-40
-20
0
20
40
60
-10 -20 -30 Depth (m)
the maximum value of bending moment for pile 5 is about 11 MN m (i.e., very close to its yielding moment). Therefore, the failure of pile 5 occurred before the failure of pile 1. This is attributed to the relative flexibility of the two piles. Significant difference occurred between the bending moment distributions along the pile shafts. This can be attributed to the relative flexibility of the two piles. The relatively stiffer pile 1 goes through larger rotation (curvature) that extends to a greater depth. It has to be noted that the pile–soil–pile interaction is neglected due the high level of loading and the long free length [11].
Pile 1 -70 -80
1139
-40 -50 -60 -70
Pile 1
-80
Pile 5
-90 (b) Fig. 12. Effect of seabed instability on piles of different relative flexibility (SL ¼ 15 m, SM ¼ 0.5 m): (a) shear force, (b) bending moment.
drained conditions for sand layer, n is taken to be 0.5 and 0.3 for clays and sands, respectively. KR is calculated from Eq. (5) to be 1.35 104 for piles 1, 2, 3, and 4, and 8.63 105 for pile 5. The case of seabed instability together with waves and current loading is investigated. The sliding layer depth is assumed to be 15 m. Since piles 1, 2, 4 have the same relative flexibility (KR) and spacing ratio (S/d), only the results for piles 1 and 5 are presented. Fig. 12 presents the shear force along the shafts of piles 1 and 5. It can be noted from this figure that the maximum shear force for pile 1 is about three times the maximum shear force for pile 5. Fig. 12 shows the large difference between the bending moment distribution along the shafts of piles 1 and 5. It is noted from Fig. 12 that the maximum bending moment for pile 5 occurred at 25 m below the mudline while the maximum bending moment for pile 1 occurred at 35 m below the mudline. Fig. 12 indicates that
4. Study of case history The South Pass 70 ‘‘B’’ platform was destroyed by Hurricane Camille in August 1969 [3–6]. Sterling and Strohbeck [6] suggested that the platform did not fail by simple overload, but it had failed due to a major submarine slide extending to a considerable depth, triggered by the hurricane. The failed main pile A-1 is a steel tube 1.22 m in diameter and a wall thickness of 19 mm and embedded length of 120 m [4]. The yield moment of the pile is computed to be about 5.18 MN m [8]. After the hurricane, the pile was found to have buckled severely at about 10 m below the mudline. Lee et al. [8] employed a boundary element method to predict the pile behaviour in this case history. The pile head was assumed to be fixed against rotation, but allowed to translate freely. It has been assumed that the hurricane triggered a uniform slide
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Displacement (m)
0.5 0.4 0.3 0.2 Fixed head
0.1
Free head 0 0
10
20
30 Time (sec)
(a)
40
0
2
4
-40
6
-20
0
-10
-10
-20
-20 Depth (m)
Depth (m)
-2
60
0
0 -4
50
-30
20
40
60
-30
-40
-40 Fixed head -50
-50 Free head
Free head
-60
(b)
Fixed head
-60
(c)
Fig. 13. Effect of pile head condition on the pile (SL ¼ 15 m, SM ¼ 0.5 m): (a) lateral head displacement, (b) shear force, (c) bending moment.
movement extending to 10 m depth as Bea and Audibert [5] reported that one pile of a similar platform in the area had been displaced due to a slide to a depth of 10 m. The soil profile used in the analysis is shown in Fig. 14a. In the present study, the same method of analysis presented in Section 2 is employed to predict the pile stresses in this case history. The same assumptions made by Lee et al. [8], are adopted. The present analysis shows that the pile yields at a soil movement of 0.5 m at a depth of about 10.2 m below mudline, which agrees with the observed buckling position of about 10 m. Fig. 14b and 14c show a comparison between the results of the present analysis and the results presented by Lee et.al. [8]. The figures show that there is a good match between the deflection along the pile shaft and the deflection given by Lee et al. [8], but the latter slightly overestimates the maximum pile deflection. It can also be noted from this figure that the shear force and bending moment along the pile shaft have the same trend and reasonable match for both analyses except for the top 7.5 m. The maximum positive bending moment and shear force are close in both cases. Lee et al. [8] found that the pile yields at a total soil movement of 0.48 m, which is very close to the corresponding value in the present study.
5. Conclusions The response of offshore platforms to lateral soil movement is investigated. The parameters of soil movement examined include the magnitude of soil movement, thickness of sliding layer, soil movement profile, the wave loading and the pile flexibility. The following conclusions are drawn: 1. The thickness of the sliding layer is more critical than the magnitude of the soil movement for the range of parameters considered in this study. 2. The effect of seabed instability on the response and stresses at the platform base and along the pile shaft is more severe than the effect of extreme wave and current loadings only. The platform response due to waves and current loadings is higher than its response due to seabed instability only. The case of combined seabed instability together with waves and current loadings leads to the most critical response and stresses for the platform. 3. The behaviour of the foundation piles in the example considered under the seabed instability is dominated by the ‘‘long pile’’ failure mode. In this case, the pile yield moment governs the design. However, the
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Fig. 14. Platform 70 B: (a) soil data for Mississippi River Delta [5], (b) predicted pile deflection, (c) predicted shear force, and (d) predicted bending moment.
performance of the foundation piles under soil movement of a limited thickness-sliding layer was dominated by the ‘‘flow mode’’. 4. Offshore piles installed in soft clays that may be subjected to soil movement should be designed with due consideration of seabed instability effects. The soil movement may induce large bending moments at a depth much greater than the depth of the sliding layer. These bending moments may exceed the yield moment of the pile if its cross-section is reduced at the level of the maximum bending moment. 5. The axial load and the fixity conditions at the pile head significantly affect the response of the pile to soil movement. Thus, they must be considered in any meaningful analysis of seabed instability. 6. The uniform soil movement profile leads to a slightly higher response and stresses in the platform than the linear soil movement profile.
Acknowledgement The authors wish to thank Dr. Torstein Alm of Aker Maritime for providing the data for the Kvitebjørn Platform used in this study.
References [1] Henkel DJ. The role of waves in causing submarine landslides. Geotechnique 1970;20(1):75–80. [2] Wright SG, Dunham RS. Bottom stability under wave induced loading. Fourth annual offshore technology conference, vol.1, paper no. OTC 1603; 1972. p. 853–62. [3] Bea RG. How sea floor slides affect offshore structures. Oil Gas J 1971;29:88–92. [4] McClelland B, Cox WR. Performance of pile foundations for fixed offshore structures. Proceddings, BOSS’76, international conference on behaviour of off-shore structures, vol. 2. University of Trondheim, Norway; 1976. p. 528–44.
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[5] Bea RG, Audibert JME. Offshore platforms and pipelines in Mississippi River Delta. J Geotechn Eng Div, ASCE 1980;106(GT8): 853–69. [6] Sterling GH, Strohbeck EE. The failure of the South Pass 70 ‘‘B’’ Platform in Hurricane Camille. Proceedings of the 5th offshore technology conference, vol. 2, paper OTC 1898; 1973. p. 719–30. [7] Doyle EH. Soil-wave tank studies of marine soil instability. Fifth Annual offshore technology conference, vol. 2, paper no. OTC 1901; 1973. p. 753–66. [8] Lee CY, Poulos HG, Hull TS. Effect of seabed instability on offshore pile foundations. Can Geotechn J 1991;28:729–37. [9] Aker Engineering AS. Kvitebjørn Jacket EPC, Design Premises and Design Brief-Foundation. Documents no. C193-AV- N-RA-0001 and C193-AV-N-RA-0005; 2000. [10] El Naggar MH, Bentley K. Dynamic analysis for laterally loaded piles and dynamic p–y curves. Can Geotechn J 2000;37(6):1166–83.
[11] Mostafa YE, El Naggar MH. Dynamic analysis of laterally loaded pile groups in sand and clay. Can Geotechn J 2002;39(6):1358–83. [12] Bransby MF. Difference between load-transfer relationships for laterally loaded pile groups: active p–y or passive p–d. J Geotechn Eng 1996;122(12):1015–8. [13] Bea RG. Dynamic response of piles in offshore platforms. Dynamic response of Pile Foundations: analytical aspects. Proceeding of a session sponsored by the Geotechnical Engineering Division at the ASCE National Convention; 1980. [14] Briaud JL, Garland E. Loading rate method for pile response in clay. J Geotechn Eng, ASCE 1985;111(3):319–35. [15] ASAS-NL. Version 13.01, WS Atkins Engineering Software; 2001. [16] Chen LT, Poulos HG. Piles subjected to lateral soil movements. J Geotechn Geoenviron Eng, ASCE 1997;123(9):802–11. [17] Poulos HG. Analysis of piles in soil undergoing lateral movement. J Soil Mech Found Div, ASCE 1973;99(SM5):391–406.
Soil Dynamics and Earthquake Engineering 26 (2006) 1127–1142 www.elsevier.com/locate/soildyn
Effect of seabed instability on fixed offshore platforms Yasser E. Mostafaa,, M. Hesham El Naggarb a
Department of Irrigation & Hydraulics, Faculty of Engineering, Ain Shams University, Cairo, Egypt Geotechnical Research Centre, Faculty of Engineering, University of Western Ontario, London, Ont., Canada N6A 5B9
b
Accepted 10 December 2005
Abstract Storms, hurricanes, and earthquakes may cause seabed instability, especially if the seabed is weak. The seabed instability, manifested in movement of soil layers, exerts lateral forces that may cause large stresses in offshore foundations. The induced stresses may compromise the stability of the foundation and supported structure. The effect of seabed instability on a fixed offshore structure is examined in this study. The method used accounts for soil nonlinearity, dynamic soil resistance, and pile–soil–pile interaction within the stable soil layer. Dynamic p–y curves, dynamic t–z curves and q–z curves have been used to simulate the soil resistance in the lateral and axial directions. The effect of different parameters that influence the response of offshore structures to seabed instability is evaluated. The parameters considered include the value of soil movement, the sliding layer depth, the wave loading, the pile flexibility, the soil movement profile, and the axial loading at the pile head. The response predicted using the proposed analysis compared well with that calculated using a boundary element solution for a case history of a failed offshore platform. r 2006 Elsevier Ltd. All rights reserved.
1. Introduction Waves impose an oscillatory motion on the soft seabed sediments, which on sloping ground may lead to a mass transfer of soil down the slope. Also, the passage of a wave will impose a transient pressure change on the sea floor and this pressure change will be approximately sinusoidal in space and time [1]. The magnitude of this pressure change depends on the wavelength (time period), the water depth and the wave height. If the stresses induced from the differential pressure exceed the soil strength, significant displacements may occur. The most important factor that determines the wave pressure at which shear failure occurs is the soil strength. Even with sufficient soil strength, offshore structures may experience extensive damage due to the large lateral motions that occur at large depths, which may require the supporting foundations to be extended to greater depths [2]. Some case histories reported failure or damage that occurred to offshore structures due to hurricane-triggered Corresponding author.
E-mail addresses: [email protected] (Y.E. Mostafa), [email protected] (M. Hesham El Naggar). 0267-7261/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2005.12.010
submarine slides in the Mississippi River Delta [3–6]. Sterling and Strohbeck [6] discussed the reasons of failure of the South Pass 70 ‘‘B’’ Platform in Hurricane ‘‘Camille’’ occurred in 1969. They suggested that the platform did not fail by simple overload, but it had failed primarily owing to a major submarine slide extending to a considerable depth. They showed that what they called ‘‘B’’ structure could have withstood a soil slide of 9–12 m, but with the hurricane sea adding force to these slide forces, it was evident that the structure could not withstand a slide with that depth. Doyle [7] conducted experimental tests in a large model tank to study the effect of surface water waves on a soft clay soil under controlled conditions. Measurements of wave height and period, bottom pressure, and in situ soil shear strength were obtained to evaluate simple analytical methods for predicting seabed instability. In case of no bottom slope, the soil moved in an orbital path at the surface and the vertical component of movement decayed more rapidly than the horizontal component; in case of bottom slope, the soil moved with a net lateral translation. Therefore, the axial loading in the field due to soil instability may be minimal. Lee et al. [8] described the use of a modified nonlinear boundary element approach to analyze the response of
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offshore piles subjected to external soil movement. They investigated the effect of a number of pile and soil parameters on the behavior of a hypothetical single offshore pile. They suggested four modes of failure: (i) ‘‘flow’’ mode—flow of the slide past a stationary pile; (ii) ‘‘intermediate’’ mode—rotation of the pile with the soil at failure along the full length of the pile; ‘‘short pile’’ mode—translation of the pile with the sliding soil; and (iv) ‘‘long pile’’ mode—the maximum bending moment in the pile reaches the yield moment of the pile before complete development of the other three modes. They concluded that the ‘‘long pile’’ mode is the most common failure mode. However, the effect of seabed instability on the response of offshore structures supported on clusters of piles (pile groups) has not been studied. 2. Method of analysis The effect of seabed instability on a fixed offshore structure is examined accounting for soil nonlinearity, dynamic soil resistance, and pile–soil–pile interaction within the stable soil layer. The Kvitebjørn Platform shown in Fig. 1 has been considered in the study. The Kvitebjørn Platform is installed in the Norwegian section of the North Sea. The soil profile, including the design soil parameters is shown in Fig. 2a. The water depth in the field is 190 m, and the substructure is a steel jacket with four legs supported by vertical steel piles grouped symmetrically around each corner leg. The jacket is supported on sixteen piles with a diameter of 2.438 m arranged in symmetrical groups of four piles per corner leg. Each corner leg has an additional pile with a diameter of 1.372 m to be used for levelling (Fig. 2b and c). The total weight of the platform is 171,200 kN, and is designed to support a maximum operating topside weight of 225,000 kN [9]. Fig. 1. Three-dimensional view of the platform.
2.1. Lateral soil resistance
dashpot constants are calculated as
The soil resistance along the pile shaft is modeled using springs and dashpots whose constants are derived using dynamic p–y curves. The dynamic p–y curves for a single isolated pile are calculated using the equation proposed by El Naggar and Bentley [10] as
Pd ¼
n ! Ps ba2o þ kao oy=d Ps a þi y, y y
(1)
where Pd is the dynamic soil reaction at depth x (N/m), Ps the static soil reaction obtained from the static p–y curve at depth x (N/m), ao is dimensionless frequency ¼ od=V s , o the frequency of loading (rad/s), d the pile diameter (m), y the lateral pile deflection at depth x (m), and a (a ¼ 1 in this analysis), b, k, and n are constants that depend on the soil type. Considering Eq. (1), the nonlinear spring and
knl ¼
n Ps ba2o þ kao oy=d Ps a and cnl ¼ . y oy
(2)
2.1.1. Group effect The approach proposed by Mostafa and El Naggar [11] for calculating dynamic p–y curves for a pile in a group is used. In this approach, the dynamic p–y curve for a single isolated pile is multiplied by an appropriate p-multiplier (Pm) to calculate the dynamic p–y curve for a pile in a group, i.e. Pg ¼ Pm Pd ,
(3)
where Pg is the dynamic soil reaction at a certain depth for a pile in a group, Pm the p-multiplier and Pd the dynamic soil reaction at the same depth for an isolated single pile. The p-multipliers depend on the ratio of pile spacing to pile
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Fig. 2. (a) Soil profile, (b) pile arrangement, (c) cross-section of the main and leveling piles
diameter (S/d) and the ratio of pile head displacement to pile diameter (y/d). Mostafa and El Naggar [11] provide an extensive set of charts for p-multipliers for piles in sand and clay for different spacing to diameter ratios. Using the p-multipliers, the group effect is accounted for, but the soil model includes dynamic p–y curves for individual piles
without interconnections resulting in significant efficiency in computations. The group effect is considered for the stable soil layers. The ratio of pile spacing to pile diameter (S/d) for the main piles of the Kvitebjørn Platform is 3.44. The leveling pile (pile 5 in Fig. 2b) is closer to pile 3, with a spacing of
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(S/d ¼ 2.35 m). The value of Pm ¼ 0.7 for piles 1, 2, and 4, and the value of Pm ¼ 0.55 for piles 3 and 5 are established from the charts presented in Mostafa and El Naggar [11]. Bransby [12] stated that the load transfer p–d curves for the case of passive lateral loading (piles displaced laterally due to soil movement) are different from the p–y curves for the case of active lateral loading. He concluded that p–d curves stiffen with reducing pile spacing, whereas p–y curves soften. Therefore, p–y curves for single piles were used to represent soil reactions in the sliding layers (i.e. group effect was not considered). In addition, dynamic p–y curves are used for the case of lateral soil movement as the dynamic p–y curves are stiffer than the static p–y curves. 2.2. Vertical soil resistance
on local pile deflection (t–z curves). The soil resistance at the pile toe is modeled using q–z curves. In this paper, t–z curves and q–z curves are constructed using the recommendations given by API (1993). Bea [13] stated that the dynamic axial soil resistance to pile movement due to wave loading and earthquakes (rate effect) is in the range of 1.2–1.8. Briaud and Garland [14] proposed a method to predict the behaviour of single piles in cohesive soil subjected to vertical loads applied at various rates. They proposed that the increase in pile capacity due to the effect of loading rate can be evaluated by n Qu1 t2 ¼ , (4) Qu2 t1
The soil resistance to the vertical movement of the pile is modeled using axial shear transfer functions that depend
in which Qu1 and Qu2 are the ultimate pile capacities reached in a time to failure t1 and t2, respectively, and n is a viscous exponent that varies from 0.02 for stiff clay to 0.10
10 -20
10 0
0.005 0.01 0.015 0.02 0.025
-0.0001
0
0.0001
0.0002
-50 Level (m)
Level (m)
-50
-20
-80 -110
-80 -110
-140
-140
-170
-170 SM=0.25 m
-200
-200
SM=0.5 m -230
-230 (a)
(b)
0 0.002
0.004
0.006
0.008
-5 0
-10
-10
-15
-15
-20
-20
Depth {m}
Depth {m}
-0.002 -5 0
0
-25 -30
0.0006
-30
SM=0.25 m
-35
-40
SM=0.5 m
-40
SM=0.25 m SM=0.5 m
-45
-50 (c)
0.0004
-25
-35
-45
0.0002
-50 (d)
Fig. 3. Effect of soil movement (SL ¼ 7.5 m) on: (a) platform displacement, (b) platform rotation, (c) pile displacement, and (d) pile rotation.
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2.4. Platform
for soft clays. Briaud and Garland [14] stated that for values of n within the given range, the pile capacity will be 1.21–2.60 times the static capacity. In this paper, the t value in the dynamic t–z curves are taken to be 1.6 times its value in a static t–z curve. The soil profile considered in this study, the arrangement of pile groups and dimensions of piles are given in Fig. 2.
The structural members of the platform and the foundation piles are modeled using space frame elements in the Table 1 Values for associated current Depth below sea-level (m)
Current speed (m/s)
0 25 50 75 100 125 150 175 190
0.50 0.50 0.50 0.46 0.42 0.39 0.36 0.32 0.29
2.3. Soil movement The soil movement is modeled as prescribed horizontal displacements to the soil springs located in the sliding layer. The movement is assumed to increase monotonically until it reaches the maximum prescribed value in 20 s. The soil springs on the opposite side of the direction of soil movement and the dynamic t–z curves within the sliding layer are removed.
0
0 0
0.5
1
-0.5
-10
1
1.5
-20
Depth (m)
Depth (m)
0.5
-15
-30 -40 -50
-25 -30
-60
-35
-70
-40 SM=0.25 m
SM=0.25 m
-80
-45
SM=0.5 m
-90
SM=0.5 m
-50
(a)
(b)
0 -4
-2
-5
0 0
2
4
6
-0.1
-5
-10
-10
-15
-15
-20
-20
-25
Depth (m)
-6
Depth (m)
0
-10
-20
(c)
-5
0.1
0.2
0.3
0.4
-25
-30
-30
-35
-35
-40
-40
-45
-45
-50
0
SM=0.25 m SM=0.5 m
(d)
-50
Fig. 4. Effect of soil movement on the maximum stresses along the pile, (SL ¼ 7.5 m): axial force, (b) shear force, (c) bending moment, (d) distributed load.
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commercial software ASAS-NL [15]. The space frame element has two nodes, one at each end. Each node has six degrees of freedom, three translations and three rotations. The platform and the supporting piles are assumed to be linear elastic. 3. Results For all the analyses and results presented in this paper, the soil movement is assumed to be the same for all the piles supporting the platform. The damping ratio of the platform is assumed to be 2%. The weight of the platform deck is assumed to be the maximum operating topside weight (225,000 kN). 3.1. Effect of magnitude of soil movement The top layer (7.5 m thick) in the soil profile (Fig. 2a) consists of very soft clay, which is likely to slide due to
moderate storms or extreme currents. To examine the effect of soil movement on the response of the platform, three values of prescribed horizontal soil movements (SM) are selected: 0.25, 0.5 and 0.75 m. A transient loading with a peak displacement of 0.25, 0.5 or 0.75 m is applied (one at a time) to the three soil layers. The length of this ramp loading is 20 s and the natural period of the platform is about 4.15 s (i.e. no resonance conditions). No wave loading is considered in this case. Fig. 3a reveals that the displacement of the platform varies almost linearly along its height and that an increase in the soil movement from 0.25 to 0.5 m resulted in an increase in the platform displacement. Fig. 3b shows that there is considerable rotation especially at the lower part of the tower due to soil movement, which results in bending stresses that can compromise the integrity of the tower. However, the rotation increased slightly with an increase in SM from 0.25 to 0.5 m. Fig. 3c and 3d show that the soil
Displacement (m)
1.4 1.2
SL=7.5 m
1
SL=15 m
0.8 0.6 0.4 0.2 0 -0.2 0
10
20
30
40
50
60
-0.4 -0.6
(a)
Time (sec)
Velocity (m/s)
0.4 0.3
SL=7.5 m
0.2
SL=15 m
0.1 0 -0.1 0
10
20
30
40
50
60
-0.2 -0.3 -0.4 Time (sec)
(b)
Acceleration (m/s2 )
0.25 0.2
SL=7.5 m
0.15
SL=15 m
0.1 0.05 0 -0.05 0
10
20
30
40
50
60
-0.1 -0.15
(c)
Time (sec)
Fig. 5. Effect of sliding layer thickness on top nodal tower response (SM ¼ 0.5 m): displacement, (b) velocity, (c) acceleration.
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movement caused a maximum displacement of about 7 mm at the pile head, and a maximum rotation of about 0.0005 rad at the bottom of the sliding layer. Increasing SM from 0.5 to 0.75 m had almost no effect on the response of the platform. This means that the soil, which is soft clay, has reached its limiting pressure and it slid past the intact pile (i.e. flow mode). Therefore, the case of SM ¼ 0.75 m is not pursued any further. Fig. 4a shows that the axial force induced in the pile due to the soil movement varies almost linearly along its shaft. Figs. 4b and 4c show that the maximum shear force and bending moment occur at depth ¼ 12.5 m. Fig. 4d shows the distributed loads along the pile length (the loads on the springs and dashpots) due to the sliding soil. It can be noted from Fig. 4d that the maximum load occurs at a depth equal to 7.5 m (i.e., the sliding plane). Generally, the increase in soil movement increases the stresses along the pile shaft.
1133
3.2. Effect of thickness of sliding layer The thickness of the sliding layer of the soil is influenced by different conditions. To examine the effect of the thickness of the sliding layer, SL, two different values were considered SL ¼ 7.5 and 15 m. Due to the close association between initiation of seabed movement and the period of maximum wave action, the lateral soil force and the maximum lateral force generated by wave, and current action could occur concurrently [3]. Therefore, the combined effects of the soil movement and the wave forces due to the 100-year design wave are considered. The design wave height and wave period are taken to be 28.5 m and 15.3 s, respectively. The current loading as indicated in Table 1 is also accounted for. The soil properties considered in the analysis are: cu ¼ 15 kPa and e50 ¼ 0.02 for the top 7.5 m; cu ¼ 80 kPa 30
10 0 -20 0
0.2 0.4 0.6 0.8
1
1.2 1.4
0
0.002 0.004 0.006 0.008 0.01
-30 -60
-80
Level (m)
Level (m)
-50
-110
-90 SL=7.5 m -120
-140
SL=15 m
-150
-170 SL=7.5 m
-180
-200 SL=15 m
-210 (b)
-230 (a)
0 -5
0 0
0.1
0.2
0.3
0.4
0.5
-0.004 0 -10
-10
-20 -30 Depth {m}
Depth {m}
-15 -20 -25 -30 -35
SL=7.5 m
-50
-70
SL=15 m
-80
-45 -50
-40
-60
-40
(c)
0.004 0.008 0.012 0.016
SL=7.5 m SL= 15 m
-90 (d)
Fig. 6. Effect of sliding layer thickness (SM ¼ 0.5 m) on: (a) platform displacement, (b) platform rotation, (c) pile displacement, (d) pile rotation.
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and e50 ¼ 0.007 for the clay layer that extends from depth ¼ 7.5 m to depth ¼ 32 m, where cu is the undrained shear strength and e50 is the strain corresponding to one-half the maximum principal stress difference. The lateral soil movement, SM ¼ 0.5 m and is assumed to be uniform throughout the sliding layer. Fig. 5 shows the effect of the sliding layer thickness on the response of the top node of the platform. It is noted that an increase in the thickness of the sliding layer resulted in a significant increase in the top nodal displacement (400%). Figs. 6a and 6b show the variation of the platform displacement and rotation for SL ¼ 7.5 and 15 m. It is noted from the figures that the maximum displacement for SL ¼ 15 m is more than three times the displacement for
SL ¼ 7.5 m, and the rotation along the tower length in case of SL ¼ 15 m is almost double of the rotation in case of SL ¼ 7.5 m. The increase in the rotation of the lower part of the tower is rather large. This may lead to substantial bending stresses in the tower members in this region. Fig. 6c reveals the large increase in the displacement along the length of pile 1 as SL increased from 7.5 to 15 m, as would be expected. For SL ¼ 7.5 m, the displacement is very small and it vanishes at a depth about 15 m. For SL ¼ 15 m, the maximum displacement is about 0.42 m (y/d ¼ 17%). This displacement is considered to be quite high and it is beyond the conventional geotechnical definition of pile failure limits. The displacement for the latter case vanishes at a depth about 40 m.
0 -15
-10
-5
0 0
-10
-5
-10
0
5
10
-10
-20 -20 Depth (m)
Depth (m)
-30 -40 -50
-30
-40
-60 -50 SL=7.5 m
-70 -60 -80
SL=15 m
-90
(a)
-70
(b)
0
0
(c)
-40
-20
0
20
40
-0.5
60
0
-10
-10
-20
-20
-30 -40
Depth (m)
Depth (m)
-60
1.5
-40 -50
-60
-60
(d)
1
-30
-50
-70
0.5
-70
Fig. 7. Effect of sliding layer thickness on the maximum stresses along the pile length, (SM ¼ 0.5 m): (a) axial force, (b) shear force, (c) bending moment, (d) distributed load.
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3.3. Effect of wave and current loading combined with seabed instability
Displacement {m}
Fig. 6d shows the rotation along the shaft of pile 1 for the two cases. It is noted that the pile rotation increased significantly with the increase of SL. The pile head rotation for case of SL ¼ 15 m is almost four times its rotation for case of SL ¼ 7.5 m. In both cases, the maximum rotation along the pile length occurred just below the depth of the sliding layer. The axial force, shear force, bending moment and the distributed load along the shaft of pile 1 are presented in Fig. 7. The stresses increase significantly with an increase in SL. For SL ¼ 7.5 m, the maximum shear force and bending moment occur at depth about 12.5 m. For SL ¼ 15 m, the maximum shear force occurred below the mudline by about 17.5 and 40 m while the maximum bending moment occurred at a depth about 35 m below the mudline. The distributed load along the pile shaft is indicated in Fig. 7d. For SL ¼ 7.5 m, the maximum force occurred at depth ¼ 7.5 m, and the load vanished at depth ¼ 40 m. For SL ¼ 15 m, the distributed load increased with depth to a maximum at depth ¼ 15 m, then it decreased to almost zero, then increased again in the zone between depths of 40 and 60 m. It has to be noted that increasing the sliding depth more than 15 m resulted in divergence of the stresses (i.e., failure of the platform piles) which represents long pile failure mode.
1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 0 -0.4 -0.6
The lateral loading due to soil movement may occur while extreme storms take place and it may occur some time after the duration of the storm terminates. To investigate the effect of the wave and current loading combined with the seabed instability, a comparison is presented between the coupled wave and current loading and the lateral soil movement, and the lateral soil movement alone. The case of wave and current loading alone without the occurrence of seabed instability is also shown for the sake of comparison. SL is assumed to be 15 m and SM is assumed to be 0.5 m. Fig. 8a shows the top nodal response for the cases of seabed instability, instability combined with waves and currents, and waves and currents only. For the case of seabed instability only, the top nodal displacement increased almost monotonically till it reached its maximum then it almost stabilized and slightly oscillated around the peak value. As expected, the case of combined seabed instability and wave loading lead to a larger response. It can be noted from Fig. 9a that the case of seabed instability alone is less critical than the case of wave loading only. Fig. 8b shows that the displacement along the pile shaft
Instability Instability+waves Waves
10
20
30
0
50
60
0 0
0.1
0.2
0.3
0.4
0.5 -10
-20
-20
-30
-30 Depth {m}
Depth {m}
-10
-40 -50 -60 -70
Instability Instability + waves Waves
0
0.004
0.008
0.012
0.016
-40 -50 -60
Instability
-70
Instability+ waves
-80
-80
Waves
-90
-90
(b)
40
Time (sec)
(a)
1135
(c)
Fig. 8. Effect of wave loading (SL ¼ 15 m, SM ¼ 0.5 m) on: (a) top nodal tower response (b) pile displacement, (c) pile rotation.
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0
0 0
2
4
6
-6
8
-4
-2
0
2
4
6
8
-10 -10 -20 -20
-40
Depth (m)
Depth (m)
-30
-50
-30
-40
-60 -70 -80
-50
Instability Instability + waves Waves
-60
-90 (b)
(a) 0 -60
-40
-20
0
20
40
60
-10
Depth (m)
-20
-30
-40
-50
(c)
-60
Fig. 9. Effect of wave loading on the stresses along the pile shaft (SL ¼ 15 m, SM ¼ 0.5 m) (a) axial force, (b) shear force, (c) bending moment.
due to seabed instability was much greater than the displacement due to wave loading only. Also, the combined effect of instability and wave loading resulted in almost double the displacement in case of seabed instability only. Fig. 8c shows that the rotation at the pile head (tower base) was almost the same for cases of instability only and waves only. However, the rotation t the pile head due to the combined effect of both cases was about four times greater. The maximum rotation occurred at a depth of about 17.5 m below the mudline. Fig. 9a shows that the case of wave loading only caused a greater axial force along the pile shaft. The case of seabed instability decreased the compression on the piles due to the uplift induced on the piles. Fig. 9b reveals that the
seabed instability has more pronounced effect on the shear along the pile shaft. The maximum shear force occurred at 15 and 40 m below the mudline. Fig. 9c shows a significant increase in the bending moment due to the combined effect of the seabed instability and wave loading. The maximum bending moment for the case of wave loading only is about 7.5 MN m and it occurred at 12.5 m below the mudline. The maximum bending moments for the cases of seabed instability only and seabed instability and wave loading are 36 MN m and 52, respectively. These values occurred at the pile head. The maximum bending moment along the pile shaft occurred at 35 m below the mudline (i.e, at depth equivalent to about 40% of the pile length). At this depth,
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1137
30 10 0 -20 0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0.002
0.004
0.006
0.008
0.01
-30 -50 Level (m)
Level (m)
-60 -80 -110
-90
-120
-140
-150
-170 LSM
LSM
-180
-200 USM
USM -210
-230 (b)
(a)
0
0 0.1
0.2
0.3
0.4
0.5
-0.004 0 -10
0.6
-20
-20
-30
-30 Depth {m}
Depth {m}
-0.1 0 -10
-40 -50
-40 -50 -60
-60 LSM
-70
-70
-90
LSM USM
USM
-80
-80 (c)
0.004 0.008 0.012 0.016 0.02
-90 (d)
Fig. 10. Effect of soil movement profile (SL ¼ 15 m, SM ¼ 1.5 m) on: (a) platform displacement, (b) platform rotation, (c) pile displacement, (d) pile rotation.
the thickness of the offshore piles is decreased substantially as indicated in Fig. 2c. Offshore piles installed in soft clays, should be designed with a due consideration of instability effects because the seabed instability may induce great bending moments at greater depths. These bending moments may exceed the yielding moment of the piles if the cross-section is reduced above the level of the maximum bending moment. 3.4. Effect of soil movement profile In the previous sections, the soil movement profile is assumed to be uniform through the sliding layer depth (USM). However, the sliding soil layer may have a linear slide pattern, LSM, (i.e., maximum soil movement value
occurs at the top of the sliding layer and the movement vanishes at the bottom of the sliding layer). In this section, a comparison between the effect of uniform and linear soil movement profiles on the response of the platform is presented. In both cases, the soil modulus is assumed to be the same (increasing with depth). The sliding layer depth is assumed to be 15 m and the maximum soil movement value is assumed to be 1.5 m. The uniform soil movement profile increases the response along the tower length and the pile length as indicated in Fig. 10. The effect of the shape of movement profile on the displacement and rotation of the piles are more pronounced. Fig. 11 shows that the uniform soil movement profile increases the shear stress, distributed load and bending moment along the pile shaft.
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1138
0
0
Depth (m)
-8
-6
-4
-2
0
2
4
6
8 -1
0
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
1
2
3
LSM -60
LSM
-60
USM
USM
-70
-70
(a)
(b)
0 -80 -60 -40 -20
0
20
40
60
80
-10
Depth (m)
-20
-30
-40
-50 -60 LSM USM (c)
-70
Fig. 11. Effect of soil movement profile on the stresses along the pile shaft (SL ¼ 15 m, SM ¼ 1.5 m): (a) axial force, (b) shear force, (c) bending moment.
3.5. Effect of pile flexibility on the pile group response The lateral displacement of each pile in the group can be related to the pile flexural stiffness and the pile–soil–pile interaction. The lateral displacement of the soil layers is related to the soil modulus or stiffness and the free field soil movement [16]. The pile and soil stiffness can be related together by a factor called the relative pile flexibility (KR), which is a dimensionless parameter. The pile flexibility factor (KR) is defined as KR ¼
EPI P , E s L4
(5)
where Ep is the pile’s Young’s modulus ¼ (2.1 105 MPa for piles under consideration); Ip the pile’s moment of
inertia; Es the soil’s Young’s modulus; L the embedded pile length. The soil modulus is possibly the most difficult quantity to estimate for real soil as the method of installation of the piles may influence the value and the distribution of Es with depth. Ideally Es should be back calculated from the results of a full-scale in situ lateral load test or plate load tests at various depths [17]. From the Kvitebjørn soil investigation (Aker Engineering AS [9]), the maximum shear modulus Gmax is taken as 2300 times the undrained shear strength (cu) in the top 7.5 m, and as 1100 times the undrained shear strength in the subsequent soil layers (refer to Fig. 2a). The maximum Elastic modulus Emax is then calculated as E max ¼ 2ð1 þ nÞGmax , where n is the Poisson’s ratio. Assuming undrained conditions for clay layers and partly
ARTICLE IN PRESS Y.E. Mostafa, M. Hesham El Naggar / Soil Dynamics and Earthquake Engineering 26 (2006) 1127–1142
0 -6
-4
-2
0
2
4
6
-10 -20
Depth (m)
-30 -40 -50 -60
3.6. Effect of axial loading at the pile head
Pile 5
The effect of seabed instability on offshore piles has been investigated in the literature. However, many researchers did not take into consideration the axial loading transmitted from the offshore tower to the pile head and the pile head fixity condition while studying this problem. In this section, pile 1 is investigated in two cases. The first case is the pile head connected to a cap together with the heads of the other piles and supporting the offshore tower. The second case is the same pile, but without a cap and without any axial loading. The effect of seabed instability only is taken into consideration without the wave loading. SL is assumed to be 15 m and SM is assumed to be 0.5 m. Fig. 13a shows the time histories of the lateral displacement of the pile head in the two cases described above. It is noted from Fig. 13a that the existence of pile cap and axial loading significantly decrease the lateral displacement at the pile head. Figs. 13b and 13c indicate the shear stress and bending moment along the pile shaft in the two cases. It is noted that the axial loading substantially alters the shear along the pile shaft. Ignoring the axial loading at the pile head and the pile fixity conditions eliminates the bending moment at the pile head and significantly overestimates the bending moment along the pile shaft. It is also noted that the bending moment profiles along the pile shaft are similar in both cases.
-90
(a)
0 -60
-40
-20
0
20
40
60
-10 -20 -30 Depth (m)
the maximum value of bending moment for pile 5 is about 11 MN m (i.e., very close to its yielding moment). Therefore, the failure of pile 5 occurred before the failure of pile 1. This is attributed to the relative flexibility of the two piles. Significant difference occurred between the bending moment distributions along the pile shafts. This can be attributed to the relative flexibility of the two piles. The relatively stiffer pile 1 goes through larger rotation (curvature) that extends to a greater depth. It has to be noted that the pile–soil–pile interaction is neglected due the high level of loading and the long free length [11].
Pile 1 -70 -80
1139
-40 -50 -60 -70
Pile 1
-80
Pile 5
-90 (b) Fig. 12. Effect of seabed instability on piles of different relative flexibility (SL ¼ 15 m, SM ¼ 0.5 m): (a) shear force, (b) bending moment.
drained conditions for sand layer, n is taken to be 0.5 and 0.3 for clays and sands, respectively. KR is calculated from Eq. (5) to be 1.35 104 for piles 1, 2, 3, and 4, and 8.63 105 for pile 5. The case of seabed instability together with waves and current loading is investigated. The sliding layer depth is assumed to be 15 m. Since piles 1, 2, 4 have the same relative flexibility (KR) and spacing ratio (S/d), only the results for piles 1 and 5 are presented. Fig. 12 presents the shear force along the shafts of piles 1 and 5. It can be noted from this figure that the maximum shear force for pile 1 is about three times the maximum shear force for pile 5. Fig. 12 shows the large difference between the bending moment distribution along the shafts of piles 1 and 5. It is noted from Fig. 12 that the maximum bending moment for pile 5 occurred at 25 m below the mudline while the maximum bending moment for pile 1 occurred at 35 m below the mudline. Fig. 12 indicates that
4. Study of case history The South Pass 70 ‘‘B’’ platform was destroyed by Hurricane Camille in August 1969 [3–6]. Sterling and Strohbeck [6] suggested that the platform did not fail by simple overload, but it had failed due to a major submarine slide extending to a considerable depth, triggered by the hurricane. The failed main pile A-1 is a steel tube 1.22 m in diameter and a wall thickness of 19 mm and embedded length of 120 m [4]. The yield moment of the pile is computed to be about 5.18 MN m [8]. After the hurricane, the pile was found to have buckled severely at about 10 m below the mudline. Lee et al. [8] employed a boundary element method to predict the pile behaviour in this case history. The pile head was assumed to be fixed against rotation, but allowed to translate freely. It has been assumed that the hurricane triggered a uniform slide
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Displacement (m)
0.5 0.4 0.3 0.2 Fixed head
0.1
Free head 0 0
10
20
30 Time (sec)
(a)
40
0
2
4
-40
6
-20
0
-10
-10
-20
-20 Depth (m)
Depth (m)
-2
60
0
0 -4
50
-30
20
40
60
-30
-40
-40 Fixed head -50
-50 Free head
Free head
-60
(b)
Fixed head
-60
(c)
Fig. 13. Effect of pile head condition on the pile (SL ¼ 15 m, SM ¼ 0.5 m): (a) lateral head displacement, (b) shear force, (c) bending moment.
movement extending to 10 m depth as Bea and Audibert [5] reported that one pile of a similar platform in the area had been displaced due to a slide to a depth of 10 m. The soil profile used in the analysis is shown in Fig. 14a. In the present study, the same method of analysis presented in Section 2 is employed to predict the pile stresses in this case history. The same assumptions made by Lee et al. [8], are adopted. The present analysis shows that the pile yields at a soil movement of 0.5 m at a depth of about 10.2 m below mudline, which agrees with the observed buckling position of about 10 m. Fig. 14b and 14c show a comparison between the results of the present analysis and the results presented by Lee et.al. [8]. The figures show that there is a good match between the deflection along the pile shaft and the deflection given by Lee et al. [8], but the latter slightly overestimates the maximum pile deflection. It can also be noted from this figure that the shear force and bending moment along the pile shaft have the same trend and reasonable match for both analyses except for the top 7.5 m. The maximum positive bending moment and shear force are close in both cases. Lee et al. [8] found that the pile yields at a total soil movement of 0.48 m, which is very close to the corresponding value in the present study.
5. Conclusions The response of offshore platforms to lateral soil movement is investigated. The parameters of soil movement examined include the magnitude of soil movement, thickness of sliding layer, soil movement profile, the wave loading and the pile flexibility. The following conclusions are drawn: 1. The thickness of the sliding layer is more critical than the magnitude of the soil movement for the range of parameters considered in this study. 2. The effect of seabed instability on the response and stresses at the platform base and along the pile shaft is more severe than the effect of extreme wave and current loadings only. The platform response due to waves and current loadings is higher than its response due to seabed instability only. The case of combined seabed instability together with waves and current loadings leads to the most critical response and stresses for the platform. 3. The behaviour of the foundation piles in the example considered under the seabed instability is dominated by the ‘‘long pile’’ failure mode. In this case, the pile yield moment governs the design. However, the
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Fig. 14. Platform 70 B: (a) soil data for Mississippi River Delta [5], (b) predicted pile deflection, (c) predicted shear force, and (d) predicted bending moment.
performance of the foundation piles under soil movement of a limited thickness-sliding layer was dominated by the ‘‘flow mode’’. 4. Offshore piles installed in soft clays that may be subjected to soil movement should be designed with due consideration of seabed instability effects. The soil movement may induce large bending moments at a depth much greater than the depth of the sliding layer. These bending moments may exceed the yield moment of the pile if its cross-section is reduced at the level of the maximum bending moment. 5. The axial load and the fixity conditions at the pile head significantly affect the response of the pile to soil movement. Thus, they must be considered in any meaningful analysis of seabed instability. 6. The uniform soil movement profile leads to a slightly higher response and stresses in the platform than the linear soil movement profile.
Acknowledgement The authors wish to thank Dr. Torstein Alm of Aker Maritime for providing the data for the Kvitebjørn Platform used in this study.
References [1] Henkel DJ. The role of waves in causing submarine landslides. Geotechnique 1970;20(1):75–80. [2] Wright SG, Dunham RS. Bottom stability under wave induced loading. Fourth annual offshore technology conference, vol.1, paper no. OTC 1603; 1972. p. 853–62. [3] Bea RG. How sea floor slides affect offshore structures. Oil Gas J 1971;29:88–92. [4] McClelland B, Cox WR. Performance of pile foundations for fixed offshore structures. Proceddings, BOSS’76, international conference on behaviour of off-shore structures, vol. 2. University of Trondheim, Norway; 1976. p. 528–44.
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[5] Bea RG, Audibert JME. Offshore platforms and pipelines in Mississippi River Delta. J Geotechn Eng Div, ASCE 1980;106(GT8): 853–69. [6] Sterling GH, Strohbeck EE. The failure of the South Pass 70 ‘‘B’’ Platform in Hurricane Camille. Proceedings of the 5th offshore technology conference, vol. 2, paper OTC 1898; 1973. p. 719–30. [7] Doyle EH. Soil-wave tank studies of marine soil instability. Fifth Annual offshore technology conference, vol. 2, paper no. OTC 1901; 1973. p. 753–66. [8] Lee CY, Poulos HG, Hull TS. Effect of seabed instability on offshore pile foundations. Can Geotechn J 1991;28:729–37. [9] Aker Engineering AS. Kvitebjørn Jacket EPC, Design Premises and Design Brief-Foundation. Documents no. C193-AV- N-RA-0001 and C193-AV-N-RA-0005; 2000. [10] El Naggar MH, Bentley K. Dynamic analysis for laterally loaded piles and dynamic p–y curves. Can Geotechn J 2000;37(6):1166–83.
[11] Mostafa YE, El Naggar MH. Dynamic analysis of laterally loaded pile groups in sand and clay. Can Geotechn J 2002;39(6):1358–83. [12] Bransby MF. Difference between load-transfer relationships for laterally loaded pile groups: active p–y or passive p–d. J Geotechn Eng 1996;122(12):1015–8. [13] Bea RG. Dynamic response of piles in offshore platforms. Dynamic response of Pile Foundations: analytical aspects. Proceeding of a session sponsored by the Geotechnical Engineering Division at the ASCE National Convention; 1980. [14] Briaud JL, Garland E. Loading rate method for pile response in clay. J Geotechn Eng, ASCE 1985;111(3):319–35. [15] ASAS-NL. Version 13.01, WS Atkins Engineering Software; 2001. [16] Chen LT, Poulos HG. Piles subjected to lateral soil movements. J Geotechn Geoenviron Eng, ASCE 1997;123(9):802–11. [17] Poulos HG. Analysis of piles in soil undergoing lateral movement. J Soil Mech Found Div, ASCE 1973;99(SM5):391–406.