Seismic responses of an offshore jacket-type platform incorporated with tuned liquid dampers

Abstract

In this article, the efficiency of tuned liquid damper in controlling the dynamic responses of offshore jacket-type platforms under earthquake excitation is investigated. This type of dampers consisting of a number of fluid-containing tanks can be installed on the topside of the platform. Hydrodynamic loads induced by the sloshing of the fluid inside the tank act as resistant forces against the vibration and can thus control the structural response. In this research, using finite element–based software package ANSYS, a jacket-type platform having dimensions appropriate for the Persian Gulf climate (case study: SPD1 platform) was modeled and then dynamically analyzed by the modal and time-history approaches subjected to the records of El Centro, Kobe, and Tabas earthquakes. The tuned liquid dampers were optimally designed and after the verification of FE results, the dynamic responses of the jacket-type platforms with and without the tuned liquid damper system were compared.

Keywords

dynamic analysis offshore jacket-type platform passive control seismic response tuned liquid damper

Introduction

One of the most important applications of offshore platforms is the oil/gas production from reservoirs below the sea bed. Fixed jacket-type platforms are widely used in offshore locations with the water depth of less than about 100 m. Although the jacket-type platform is not usually the best option for deeper waters, a number of jackets have been installed in water depths over 300 m. Jacket-type platforms are mainly fabricated from tubular members by welding one end of the branch member (brace) to the undisturbed surface of the main member (chord), resulting in what are known as tubular joints (Figure 1). Offshore platforms are subjected to environmental forces due to the sea waves, currents, wind, and earthquake. Hence, the seismic control of these structures can be useful to reduce the volume of the required construction materials, to increase the service life, and to enhance the reliability of the structure under the earthquake-induced loads and oscillations. Moreover, in the regions with low seismic hazard that also do not experience severe storms, most of the platforms are safe under the seismic forces and extreme loads due to design waves. In such conditions, the fatigue is the governing design factor. The utilization of a controlling system can also increase the fatigue life of the structure through narrowing the range of displacements.

Figure 1.

A typical offshore jacket-type platform: (a) structure during the service and (b) substructure.

The most common method for the control of structures subjected to earthquake-induced loads is using dampers or damping enhancer systems to absorb and dissipate the energy exerted to the structure. Based on their operation mechanism, damping systems are divided into three categories: active, semi-active, and passive dampers. Passive systems apply an indirect damping to the structure by renovation and improvement of the dynamic behavior of the structure. One of the most commonly used types of passive damping systems is tuned liquid damper (TLD) which is quite cost-effective and relatively easy to construct compared to the other kinds of passive dampers.

In this article, the efficiency of TLD in controlling the dynamic responses of offshore jacket platforms under earthquake excitation is investigated. This type of damping system consists of one or more tanks containing a fluid, generally water or oil, which can be installed on the topside (superstructure) of the platform. During the earthquake, hydrodynamic action induced by the sloshing of the water in the tank acts as a resistant force against the vibration and controls the structural response. In fact, due to the oscillation of the structure by the earthquake, the fluid inside the tank begins to oscillate in the opposite direction. During this process, most part of the fluid has a wave-like oscillatory motion, while the part adjacent to the tank’s floor experiences a rigid-type displacement and exerts impact pressures to the tank’s walls. In order to attain maximum decrease in the structural response, the oscillation frequency of the fluid inside the tank should be near the natural frequency of the structural free vibration which can be determined by performing a modal analysis. Hence, one of the objectives of this study is to adjust the frequency of fluid’s oscillation based on the natural frequency of the jacket structure. In other words, the aim is to find a frequency range in which the maximum decrease can be achieved in the amplitude of structural responses. In this research, using the finite element (FE) software ANSYS (version 14), a jacket-type platform having dimensions appropriate for the Persian Gulf climate (case study: SPD1 platform) was modeled and then dynamically analyzed by the modal and time-history approaches subjected to the records of El Centro, Kobe, and Tabas earthquakes. The TLD system was optimally designed and after the verification of FE results, the dynamic responses of the jacket-type platform with and without TLDs were compared.

Literature review

The TLD system as a passive control method was used for the first time at 1909. This particular system was consisted of two partially full water tanks installed on a ship (Den Hartog, 1956). Sakai et al. (1989) proposed TLDs for the control of structural vibration in cable bridges. Carrier and Miles (1960) studied the efficiency of using TLD systems with annular shape for the damping of oscillations in satellites and space shuttles.

The first studies on the applications of the TLD in civil engineering structures were conducted, at late 1980s and early 1990s, by Modi and Welt (1987), Kareem and Sun (1987), and Fujino and Sun (1992), among others. Various geometrical shapes have been considered for TLDs among which the cube, cylinder, and cone are the most common ones. Gao and Kwok (1987) investigated the efficiency of U- and V-shaped tuned liquid column dampers for the control of structural vibration and studied the optimum design of this type of dampers to achieve maximum decrease in the structural response subjected to harmonic excitation. Vandiver and Mitome (1987) investigated the effects of a liquid storage tank on the dynamic response of an offshore platform subjected to wind loading. Yamamoto and Kawahara (1999) studied the effects of wave–structure interaction on the control of structural vibration using a TLD system.

Yalla and Kareem (2000) determined the optimum values of design parameters for the tuned liquid column damper in a system subjected to random vibrations due to sound waves. Olson and Reed (2001) studied a 30° sloped-bottom TLD system. Casciati et al. (2003) studied conical TLDs. Tait (2008) experimentally investigated the behavior of a single-degree-of-freedom structure equipped with the TLD subjected to harmonic and random excitations. Using the results of the experimental tests, they proposed a relation for the calculation of the damping induced by a TLD system. The results obtained from this relation have a good agreement with the output of relations developed by other researchers for the damping induced by tuned mass dampers. If the TLD system is designed optimally, damping may increase 5%–15% in an average sense. This amount of increase in damping can have substantial effect on the dynamic response of the structure. Zahrai et al. (2012) studied a new kind of TLD with some installed rotatable baffles experimentally. The main idea behind installing such baffles was to compensate the effects of probable mistuning of the TLD and also it was an effort toward making the TLD more controllable, that is, a semi-active damper. Love and Tait (2013) conducted shake table experiments on a rectangular and chamfered tank subjected to unidirectional base excitation. Next, structure–TLD system tests were conducted and it was found that the model can predict the structural and TLD responses. The simulated and experimental results showed that the TLD tank transfers energy between orthogonal structural sway modes. Love and Tait (2015) employed a linearized equivalent mechanical model of the structure–TLD system to determine the root mean square (RMS) responses of the structural displacement and the TLD fundamental sloshing mode wave height. Structure–TLD system tests and nonlinear simulations were used to evaluate the model.

It can be concluded from above paragraphs that very few studies are available in the literature on the application of TLDs in offshore structures. As far as the authors are aware, the efficiency and optimum design of TLDs for the control of structural vibration in offshore jacket-type platforms subjected to earthquake excitation have not been extensively studied. Hence, the results of this research can be helpful to fill this gap.

Concepts of a TLD system

As mentioned earlier, in a TLD as a passive control system, hydrodynamic loads due to the sloshing of the water in the tank act as resistant forces against the structural vibration. A TLD system consists of a number of tanks containing a fluid (usually water) that is installed on top of the structure. The sloshing of the water in the tank absorbs and dissipates the energy exerted to the structure by the earthquakes, gusts, and storm waves. The sloshing in the tank during the oscillation of the structure generates pressure differences that consequently lead to the generation of shearing forces on the tank floor. Figure 2 shows a tall building incorporated with a TLD system.

Figure 2.

One Rincon Hill residential tower incorporated with a TLD system.

For the optimum design of a TLD system, that is, in order to attain the maximum decrease in the structural response, the frequency of damper must be adjusted based on the frequency of the first mode of structure’s free vibration. Hence, the characteristics of the TLD system such as the dimensions of the tank and the depth of the water inside it should be selected accordingly.

In order to simulate the behavior of a TLD system in FE models, a number of simplified methods have been proposed. The most commonly used one is the lumped mass method based on the linear wave theory. In this method, it is assumed that the wall of the tank is rigid, and the sloshing-induced dynamic pressure has two components that are the impact pressure and oscillatory pressure. The impact pressure is proportional to the acceleration of the fluid-containing tank but in the opposite direction. The oscillatory pressure is the result of generated waves at the water surface and is a function of frequency of the oscillating fluid. As shown in Figure 3, the two above-mentioned hydrodynamic pressures can be represented by two lumped masses attached to the tank wall (Qiao et al., 2007).

Figure 3.

Lumped mass method to simulate the TLD system.

The equations used to calculate the frequency of the fluid oscillating inside the tank can be summarized as follows (Den Hartog, 1956)

M_{1} = m \frac{h_{0}}{\sqrt{3} R} \tanh (\sqrt{3} \frac{R}{h_{0}})

(1)

M_{2} = \frac{0.358 R}{h_{0}} \tanh (\frac{1.837 h_{0}}{R})

(2)

k = 5.4 \frac{M_{2}^{2} g h_{0}}{m R^{2}}

(3)

h_{1} = \frac{3}{8} h_{0} {1 + 2 [\frac{m}{M_{2}} {(\frac{R}{h_{0}})}^{2} - 1]}

(4)

h_{2} = h_{0} [1 - 0.185 (\frac{m}{M_{1}}) {(\frac{R}{h_{0}})}^{2} - 0.56 β \frac{R}{h_{0}} \sqrt{{(\frac{mR}{3 M_{1} h_{0}})}^{2} - 1}]

(5)

where m and h₀ are the mass and the depth of the fluid inside the tank, respectively; R is the radius of the tank; and g is the gravity acceleration. M₁, M₂, h₁, h₂, and k have been defined in Figure 3.

In order to calculate the oscillation frequency of the fluid inside the container, the linear wave theory can be used that includes the implementation of continuity and second-order Navier–Stokes equations. The result is as follows

\begin{matrix} ω_{0} = \sqrt{\frac{π g}{a} \tanh (\frac{π h_{0}}{a})} \\ f_{w} = \frac{1}{2 π} \sqrt{\frac{π g}{a} \tanh (\frac{π h_{0}}{a})} \end{matrix}

(6)

where h₀ is the depth of the fluid inside the tank, g is the acceleration of gravity, ω₀ is the angular frequency (rad/s), f_w is the frequency (Hz), and a is the characteristic dimension of the tank which is equal to tank length and diameter for rectangular and cylindrical tanks, respectively.

FE modeling and analysis

Details of the case study

SPD1 platform which is selected as the case study in this research is one of the platforms installed in the Persian Gulf during the first development phase of the South Pars gas field. The latitude and longitude of the platform’s location are N 43 26 and E 01 52, respectively. SPD1 installed in the water depth of 70.7 m consists of three main parts: superstructure (topside), substructure (jacket), and foundation (piles). The topside of the platform is 16 × 28 m and has three decks: the lower deck, the mezzanine deck, and the upper deck. The height of these decks from the still water level is 13, 17.5, and 21 m, respectively. The substructure is a six-legged jacket that is connected to the sea floor by six piles driven through its legs. The plan dimension of the platform at the sea bed is 23.8 × 38.26 m. The maximum diameter of the jacket legs is 1.534 m and the total mass of the platform is 4334 ton.

Modeling of the jacket

To model the tubular members of the jacket by the FE method, utilized elements should be capable of considering the effects of hydrodynamic forces and the added mass. In this research, ANSYS element–type PIPE59 was used to model the tubular members.

Modeling of the piles

During the analysis of jacket-type platforms, provided that the objective of analysis is the study of global behavior of the structure, simplified methods can be used to model the soil–pile interaction. The main objective of this article is the comparison of seismic responses with and without the presence of TLDs. In fact, the responses were studied relative to each other. The absolute values of the responses which are affected by the pile–soil interaction were not of the main interest. Moreover, since practical aspects of the results were of major concern, the equivalent length method usually used in engineering design was implemented.

The equivalent length method is one of the most commonly used simplified techniques in which instead of modeling the full length of the pile along with the surrounding soil, only the pile with an equivalent length is modeled and the individual modeling of the soil is omitted. In this method, the lower end of the pile is assumed to be fixed. The equivalent length should be selected in such a way that the stiffness characteristics of the equivalent pile at the sea bed are identical to the characteristics of the actual pile. The suggested value for the equivalent length of the pile in loose clayey soils is 8D–12D where D is the diameter of the pile. In this research, a value of 12D, approximately equal to 16.5 m, was chosen as the equivalent length of the piles. ANSYS element–type PIPE16 was used to model the steel piles. All the nodes on the part of a pile that is inside the jacket leg were coupled with the corresponding nodes on the leg in the horizontal direction. Hence, the pile and the jacket leg had equal horizontal displacements.

Modeling of the topside

ANSYS element–type PIPE16 and SHELL63 were used to model the topside of the platform. Structural system of the topside was of the portal frame type without bracings. PIPE16 elements were used to model the deck legs. The weights of the equipments were applied as distributed loads on SHELL63 elements utilized to model the decks. Geometrical model and generated mesh are shown in Figures 4 and 5.

Figure 4.

Geometrical model of SPD1 platform generated by ANSYS.

Figure 5.

Topside of SPD1 platform and its connection to the jacket, modeled by ANSYS.

Modeling and the optimum design of TLDs

As mentioned earlier, this research investigates the efficiency of TLD system for reducing the dynamic responses of a jacket-type platform. The proposed TLD system consists of four steel rectangular 3 × 3 × 2.5 m tanks filled with 1.5 m of water which are located on the upper deck of the topside. The reasons behind selecting the above-mentioned dimensions for the tanks are discussed in this section.

ANSYS element–type SHELL63 was used to model the tank. This two-dimensional (2D) element has four nodes and each node has 6 degrees of freedom. To model the water inside the tank, ANSYS element–type FLUID80 was utilized. This three-dimensional (3D) element has eight nodes and each node has 3 transitional degrees of freedom. FLUID80 elements are capable of considering fluid–structure interaction through the calculation of hydrostatic and hydrodynamic pressures. This element models the water as a homogenous, inviscid, incompressible, and irrotational fluid. In defining the material properties of the fluid, the bulk modulus of the water should be introduced instead of the modulus of elasticity.

In FLUID80 elements, the complicated behavior of the free surface of the fluid is modeled based on the nonlinear wave theories. In these elements, in order to retain the continuity of the fluid surface, a gravitational spring is considered on each node located on the free surface of the fluid. In order to take into account the interaction between the fluid and the tank, coincident nodes of fluid and tank were coupled in the orthogonal direction (Figure 6).

Figure 6.

Schematic representation of 2D FE model for the fluid tank.

Generally, the ratio of damper mass to total mass of the structure is 0.75%–3% for tall structures. Since the height of the structure studied in this article is less than 100 m, the value of 1% was selected for this ratio and the configuration of the tanks was assigned based on this value.

As mentioned earlier, in order to enhance the effect of the TLD on the structural vibration, the frequency of the first mode of the fluid oscillation inside the tank should be equal to the fundamental frequency of the structure’s free vibration. In this research, to obtain the optimum values of design parameters for the TLD system, a modal analysis was performed on the SPD1 platform and the fundamental frequency of structure’s free vibration was obtained as 0.488 Hz. To determine the dimensions of the tank, a value of 0.5 was assumed for the ratio of the water depth to the tank length. Then, by the substitution of 0.488 Hz as the frequency of the fluid oscillation in equation (1), the length of the tank was determined as 3.0 m. Afterward, considering the assumed ratio for the water depth to the tank length, a value of 1.5 m was obtained for the depth of the water inside the tank. After the determination of dimensions, a 3 × 3 × 2.5-m tank filled with 1.5 m of water was modeled using ANSYS (Figure 7). After considering the solid–fluid interaction by the coupling of coincident nodes of fluid and tank in the orthogonal direction and selecting the master degrees of freedom, a modal analysis was performed on the fluid-containing tank and the frequency of the first mode of the fluid oscillation inside the tank was obtained as 0.478 Hz that is in good agreement with the result of equation (6).

Figure 7.

FE model of tuned liquid damper.

Since the lumped mass matrix is the only available option for the ANSYS element–type FLUID80, only the reduced method can be used for the modal analysis of the models generated using this type of element. The selection of master degrees of freedom is essential for the application of reduced method. These degrees of freedom should be selected from the free surface of the fluid and the walls of the tank. The implementation of master degrees of freedom leads to an exact stiffness matrix but an approximate mass matrix. On the free surface of the fluid, degrees of freedom perpendicular to the free surface should be introduced as the master ones; and on the tank wall, degrees of freedom parallel to the direction of structural vibration must be selected as master degrees of freedom. The number of selected master degrees of freedom should be at least twice the number of extracted modes in the modal analysis.

Material properties

The properties of the steel used for the modeling of the jacket and the physical and mechanical characteristics of the water introduced during the modeling of the TLD system are presented in Table 1.

Table 1.

Steel and water properties for the FE modeling.

Steel
Density	7850 kg/m³
Young’s modulus	210 GPa
Poisson’s ratio	0.3
Water
Density	1000 kg/m³
Bulk modulus	2.068 GPa

In order to consider the material nonlinearity, bilinear stress–strain curve was used. The slope of the curve in the plastic region was 2% of its slope in the elastic region.

Selected accelerograms and their coordination (scaling)

In a time-history analysis, the appropriate selection of applied earthquake records based on the location of the structure under consideration is essential. These records that should be applied at the base of the structure as lateral loadings can be the ground displacement, ground velocity, or ground acceleration due to the earthquake. In this research, earthquake acceleration records provided by the University of Berkley database were used. These records were selected in such a way that their frequency content, the earthquake duration, and the soil characteristics were in accordance with the environmental traits of the SPD1 platform’s location. Unfortunately, records from offshore sites were not available to be used in this research. It is recommended that at least three accelerograms should be used for the time-history analysis in order to obtain accurate results. Accelerograms used in this research are the ones obtained from El Centro/US/1940, Tabas/Iran/1978, and Kobe/Japan/1995 earthquakes (Table 2).

Table 2.

Characteristics of considered accelerograms.

Earthquake	Magnitude (M)	Peak groundacceleration (g)	Time step (s)	Duration (s)
El Centro	6.95	0.215	0.01	40
Tabas	6.9	0.503	0.01	40.95
Kobe	7.4	0.852	0.02	32.8

If the accelerograms are not coordinated (scaled), very different responses may be obtained for various accelerograms, and consequently it can be difficult to draw a conclusion from the analysis results. In fact, the scaling of the accelerograms leads to less scattered yet more compatible results. Since in this research the objective was the relative comparison of platform responses, all the selected accelerograms were scaled based on their maximum values. In other words, they were scaled according to the maximum acceleration at the ductility level of the platform which was equal to 0.35 g.

Modal analysis

In order to extract the mode shapes of structural free vibration and the corresponding frequencies, a modal analysis was performed on the platform using ANSYS. The first three mode shapes are shown in Figure 8. The obtained frequencies were used for the verification of the FE model generated for the jacket-type platform and the TLDs, the optimum design of the TLD system, and the definition of parameters for Rayleigh damping in the time-history analysis. By the comparison of the first 10 frequencies of the generated model with the corresponding frequencies of the SPD1 platform extracted by Bargi et al. (2011), it can be concluded that the generated FE model for the jacket-type platform has adequate accuracy to produce valid results (Table 3). More than 50 models were generated before obtaining a model which was accurate enough to be verified by the results of Bargi et al. (2011).

Figure 8.

First three mode shapes of free vibration.

Table 3.

Results of modal analysis for the platform without the TLD system.

Mode number	Frequency of FE model (Hz)	Frequency of SPD1 platform (Hz) (Bargi et al., 2011)	Difference (%)
1	0.488	0.488	0
2	0.525	0.526	0.2
3	0.795	0.658	17
4	1.46	1.22	16
5	1.49	1.33	10
6	1.79	1.89	5
7	2.39	2.00	16
8	2.69	2.04	24
9	2.89	2.13	26
10	3.05	2.17	29

FE: finite element.

In order to verify the FE model developed for the TLD system, after obtaining the tank dimensions and the water depth inside the tanks (section “Modeling and the optimum design of TLDs”), a modal analysis was performed with the reduced method on the fluid-containing tank. The frequency of the first mode of fluid oscillation was obtained as 0.478 Hz which was in a good agreement with the result of theoretical relation (equation (6)).

Time-history analysis

To apply the selected accelerograms for the time-history analyses, these records were adjusted as one-column matrices using MATLAB. The first mode of oscillation for the TLD system used in this research, just like the first mode of the platform oscillation, is along the Y-axis. Hence, the Y components of three selected accelerograms were used for the excitation of the structure. Each record was applied, using a macro, at the fixity level of the equivalent piles as a horizontal component along the Y-axis of the FE model’s coordinate system. The lateral component of the El Centro earthquake accelerogram is shown in Figure 9.

Figure 9.

Lateral component of El Centro earthquake’s accelerogram.

For the structural damping, Rayleigh method was used and damping matrix was assumed to be a linear combination of mass and stiffness matrices. Rayleigh coefficients were computed based on a 3% value for critical damping ratio of SPD1 platform. The added mass was also considered by activating the added mass options in ANSYS software.

To investigate the effect of a TLD system on the dynamic responses of SPD1 platform, a nonlinear time-history analysis is more suitable compared to the other methods of analysis. In this research, the considered platform was analyzed in two conditions: with and without TLDs. The proposed TLD system consisted of four steel rectangular 3 × 3 × 2.5 m tanks filled with 1.5 m of water which were located on the upper deck of the topside (Figure 10). As can be seen in Figure 10, the first mode of the fluid oscillation inside the tanks is the displacement along the Y-axis. This figure shows that when the structure moves to the left, the fluid inside the tanks moves to the right. This perpetual movement in the opposite direction leads to the reduction in the dynamic responses of the platform.

Figure 10.

Oscillation of SPD1 platform incorporated with the proposed TLD system.

Results and discussion

The effect of the TLD system on the displacement of the upper deck

The time histories of the displacement for the upper deck of the platform due to the excitation applied by the accelerograms of El Centro, Kobe, and Tabas earthquakes have been presented in Figure 11 for the platforms with and without the TLD system. The maximum values of the upper deck displacement in the platforms with and without the TLDs have been compared in Table 4. According to Figure 11 and Table 4, it can be concluded that the proposed optimally designed TLD system can lead to a considerable decrease in the upper deck displacement. As mentioned in Table 4, the amount of decrement in the case of SPD1 platform is 21%–22%.

Figure 11.

The time history of displacement for the upper deck of the platform with and without the TLD system under the earthquake records of (a) El Centro, (b) Kobe, and (c) Tabas.

Table 4.

The effect of TLD system on the displacement of platform’s upper deck.

Earthquake record	Upper deck’s maximum displacement (m)		Difference (%)
Earthquake record	Without TLD	With TLD	Difference (%)
El Centro	0.530	0.412	22
Kobe	0.164	0.127	21
Tabas	0.276	0.217	21

TLD: tuned liquid damper.

The effect of the TLD system on the base shear

The base shear at the sea bed elevation is one of the effective parameters in the assessment of integrity and safety of the platform. Large base shear can cause damages such as the lateral failure of the piles due to the formation of plastic hinges and the yielding of the soil surrounding the piles.

The time histories of the base shear of the platform due to the excitation applied by the accelerograms of El Centro, Kobe, and Tabas earthquakes for the platforms with and without the TLD system were extracted and compared (Figure 12). According to Figure 12, it can be concluded that the proposed TLD system results in a substantial decrease in the base shear. The amount of decrement in the case of SPD1 platform is 10%–21%.

Figure 12.

The time history of the platform’s base shear with and without the TLD system under the earthquake records of (a) El Centro, (b) Kobe, and (c) Tabas.

The effect of the TLD system on the acceleration of the upper deck

High accelerations of the topside chiefly lead to the damage in nonstructural parts of the decks such as equipments and installations. Such damages may result in personnel injuries, the leakage of hazardous materials, and environmental pollutions.

The time histories of the acceleration of the upper deck of the platform due to the excitation applied by the accelerograms of El Centro, Kobe, and Tabas earthquakes for the platforms with and without the TLD system were extracted and compared. The obtained charts are not presented here for the sake of brevity. The maximum values of the upper deck acceleration in the platforms with and without the TLDs have been compared in Table 5. According to this table, it can be concluded that the proposed TLD system is capable of decreasing the upper deck acceleration considerably. As can be observed in Table 5, the amount of decrement in the case of SPD1 platform is 18%–27%.

Table 5.

The effect of TLD system on the acceleration of platform’s upper deck.

Earthquake record	Upper deck’s maximum acceleration (m/s²)		Difference (%)
Earthquake record	Without TLD	With TLD	Difference (%)
El Centro	6.19	4.51	27
Kobe	4.35	3.57	18
Tabas	3.83	3.07	20

TLD: tuned liquid damper.

Conclusion

In this article, the efficiency of TLDs for the reduction of dynamic responses of offshore jacket-type platforms was investigated. As a case study, SPD1 platform installed in the Persian Gulf was modeled by FE software ANSYS. A modal analysis was performed on the model and the results were used for the verification of the FE model, the optimum design of the proposed TLD system, and the determination of Rayleigh damping parameters for the time-history analysis. After the design of the TLD system, a new FE model of SPD1 platform was generated which was incorporated with TLDs. Then, a set of time-history analyses were performed on the FE models subjected to seismic excitations applied by El Centro, Kobe, and Tabas accelerograms; and the dynamic responses of the platforms with and without the TLD system were compared. The results of this research can be useful for the design of new jacket-type platforms as well as the seismic retrofit of the existing platforms.

In order to enhance the effect of the TLD system on the structural vibration, the frequency of the first mode of the fluid oscillation inside the tank should be equal to the fundamental frequency of structure’s free vibration. The TLD system proposed in this research for the SPD1 platform, which meets the above-mentioned criterion, consists of four steel rectangular 3 × 3 × 2.5 m tanks filled with 1.5 m of water located on the upper deck of the topside.

The results showed that the effectiveness of the TLD system in reducing the seismic responses of the platform under the excitations applied by the accelerograms of El Centro, Kobe, and Tabas earthquakes is different. In fact, the efficiency of the TLD system in reducing the dynamic response depends on the frequency content of the earthquake.

The proposed TLD system results in a substantial decrease in the seismic responses of the offshore jacket-type platform. The amounts of decrement in the case of SPD1 platform are 21%–22%, 10%–21%, and 18%–27% for the maximum displacement of the upper deck, platform’s maximum base shear, and the maximum acceleration of the upper deck, respectively.

Suggestions for future research works

Instead of using equivalent length method, the pile–soil interaction may be considered more rigorously in the FE model leading to more reliable results.

This research may be extended to cover more cases of tank shapes and configurations.

Footnotes

Acknowledgements

Three anonymous reviewers are acknowledged for their useful comments on the draft version of this article.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the University of Tabriz for supporting this work under the Research Grant Contract No. 27/3570-7.

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Abbasi

Samali

. (2012) Experimental investigation of utilizing TLD with baffles in a scaled down 5-story benchmark building. Journal of Fluids and Structures 28: 194–210.