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The seismic behaviour of liquid storage tanks has attracted considerable attention due to their critical role in infrastructure systems and their high sensitivity to ground motion. The fundamental theoretical framework for seismic tank analysis was established by Housner (1963) through the decomposition of the liquid mass into impulsive and convective components, thus providing a cornerstone for the analysis of such phenomena. Subsequent studies, including those by Veletsos & Yang (1977), Haroun & Housner (1981), and Malhotra et al. (2000), have demonstrated that fluid-structure interaction (FSI) plays a fundamental role in governing hydrodynamic pressures, forces, and displacement responses during seismic events. However, it is important to note that these early analytical approaches were based on simplified assumptions that often fail to accurately capture the complex dynamic behaviour of elevated tanks supported by slender column systems. It is evident that the comprehension of this phenomenon has been enhanced by the implementation of sophisticated numerical investigations, which have facilitated the incorporation of nonlinear and coupled effects. As Moslemi et al. (2011) demonstrated, consideration of dynamic finite element method (FEM) significantly alters displacement and internal force responses. Furthermore, Dutta et al. (2009) showed that soil-structure interaction (SSI) affects base shear demands and modifies the dynamic characteristics of tank systems. Notwithstanding these advancements, the majority of extant studies have predominantly concentrated on fixed-base configurations, thereby resulting in an inadequate exploration of alternative seismic mitigation strategies. Among these strategies, rocking isolation has emerged as a promising performance-based approach. As demonstrated in previous research, controlled uplift mechanisms have been shown to be effective in reducing inertia-driven force amplification, limiting bending and shear demands, and providing self-centring capability to minimise residual deformations (Housner, 1963; Kelly, 1997; Skinner et al., 1993). The stability of these systems under nonlinear response conditions is contingent on the implementation of appropriate foundation detailing and restraining mechanisms. Recent studies have expanded the application of rocking isolation to elevated liquid storage tanks, emphasising its effectiveness and associated challenges. As demonstrated by Hosseini & Beskhyroun (2025), Mir et al. (2021), and Alemzadeh et al. (2020), a critical trade-off has been reported between force reduction and displacement amplification. Further research by Karimi, Pour & Farsangi (2022), Kumar & Saha (2022) and Agalianos et al. (2018) highlighted the impact of tank filling levels and the combined effects of FSI and SSI on seismic response. The findings from comparative and experimental studies further corroborated the viability of rocking-based systems. In the study conducted by Thomaidis et al. (2020), it was demonstrated that rocking isolation exhibited a superior capacity to mitigate residual displacements in comparison to conventional Lead Rubber Bearings (LRB). However, it was also observed that rocking isolation may, in certain instances, result in an augmentation of displacements and bending moments. As demonstrated by Reyes & Almazán (2020) and Reyes et al. (2022), numerical and experimental investigations have shown that vertical rocking isolation systems have the capacity to significantly reduce seismic demands while maintaining structural stability. In a similar vein, Lu et al. (2023) and Zhao et al. (2023) emphasised pivotal elements of rocking behaviour under diverse loading conditions and soil interaction effects. Despite these advancements, there is a paucity of research that has simultaneously addressed rocking isolation, variable filling levels and multiple earthquake records in elevated tank systems, particularly for high-rise configurations.

The present study addresses this gap by evaluating the seismic response of the Al-Dufail elevated water tank using nonlinear dynamic analysis conducted in ABAQUS. Initially, the behaviour of the non-isolated tank is assessed by considering soil-structure interaction under both rigid and flexible soil conditions. Subsequently, a rocking isolation system is introduced at the interface between the ring beam and the foundation without consideration of SSI effects. The influence of varying water levels is investigated under three operational states: empty, half-full, and fully filled conditions. Furthermore, this study proposes a high-rise tank configuration incorporating a structural system composed of columns and an internal core, an arrangement that has not been sufficiently addressed in previous research. The proposed system demonstrates a reduction in inertia forces and base shear demands, thus highlighting its potential for enhancing seismic performance.

A significant proportion of elevated water tanks in the Syrian Arab Republic were designed in accordance with seismic codes that are no longer considered to be current. This has resulted in these structures being highly vulnerable to earthquake-induced damage, thereby compromising their safety and functionality. Despite the evident efficacy of established seismic isolation techniques, their high cost and limited availability present significant challenges when it comes to their implementation in the retrofitting of existing structures. This underscores the necessity for the development of cost-effective alternatives. Rocking isolation has been identified as a potentially effective solution for enhancing seismic performance. The objective of this study is to enhance the seismic behaviour of a reinforced concrete elevated water tank in Latakia through analytical investigation by: The following three aspects will be evaluated: firstly, the seismic response under fixed-base conditions with soil-structure interaction; secondly, the rocking isolation at the ring beam-foundation interface; and thirdly, the effect of water filling levels on seismic performance.

The study examines an elevated water tank located in Latakia, with a storage capacity of 150m³. The tank is composed of a cylindrical shell with a diameter of 9.2m, a height of 4.15m, and a wall thickness of 0.45m. The structure is covered by a roof slab measuring 0.20m in thickness, which is supported by a base slab measuring 0.45m in thickness. The supporting structure has a total height of 15m and comprises six peripheral T-shaped columns arranged around a central core with a diameter of 2.5m. The elements are interconnected by circumferential and radial beams at each level, with cross-sectional dimensions of 0.35×0.80m. The structure is founded on a square raft foundation measuring 11.9×11.9×1.0m, located at an elevation of -2.5m on SC-type soil. The reinforcing bars employed in both the circumferential and radial beams are 12Ø25 bars, while the columns are reinforced with Ø25 bars at 150 mm spacing. The tank wall has been fortified with 10Ø16 bars per metre.

As illustrated in Figure 1, the tank's plan view and vertical section are presented, while Table 1 provides a concise summary of the mechanical properties of the reinforced concrete and steel reinforcement employed. This model forms the basis for the subsequent seismic performance analyses.

Fixed-Base Tank Modeling

The elevated water tank was modelled in three-dimensional (3D) space using wire elements to represent all structural components. The hydrodynamic effects of the contained liquid were simulated based on Housner's equivalent mechanical model. In this model, the fluid is idealised as a system of lumped masses connected to the tank structure either rigidly or through spring elements (Housner, 1959).

As demonstrated in Figure 2, the hydrodynamic response is decomposed into two components:

The term 'impulse mass' (mᵢ) is defined as follows: This component signifies the proportion of the fluid that moves in a rigid manner in conjunction with the tank walls. The mass is connected to the supporting beams beneath the tank through a rigid body constraint, ensuring full compatibility of motion.

The quantity of convective mass (m_c) is defined as follows: This component is responsible for the sloshing motion of the fluid. The structure is connected to the system via a spring element of the type Basic (Cartesian-Rotation) with stiffness K𝑐, thereby allowing relative motion between the fluid and the tank.

Three filling conditions were considered: empty, half-full (h = 1.75m), and full (h = 3.325m).

The parameters of the equivalent fluid system (mᵢ, m𝑐, hᵢ, h𝑐, K𝑐) were calculated using Housner's formulations for cylindrical tanks (Jain & Jaiswal, 2007),  based on the tank diameter (D), liquid height (h), and total liquid mass (m).

The total liquid mass is computed from the product of water density (1000kg/m³) and tank volume, as defined in Equations (1)-(3). The determination of the impulsive and convective masses and their corresponding heights is achieved through the utilisation of Equations (4) through (7), while the convective spring stiffness is derived from Equation (8).

Table 2 summarizes all calculated hydrodynamic parameters used in the dynamic analysis.

Boundary Conditions and Seismic Loading 

A nonlinear time-history analysis was conducted using the software programme ABAQUS to evaluate the seismic response of the tank system. The selected ground motion records are listed in Table 3 and illustrated in Figure 3. In the context of the fixed-base configuration, all degrees of freedom at the base of the supporting columns were constrained, with the exception of horizontal translation in the direction of seismic excitation (X-direction). This boundary condition facilitates the precise implementation of ground motion input while impeding rigid body motion. The comprehensive analytical model, incorporating structural connectivity and boundary conditions, is delineated in Figure 4.

The modelling framework under consideration incorporates both structural response and fluid-structure interaction under realistic seismic loading conditions. This provides a consistent basis for evaluating system behaviour and enables subsequent comparison with alternative configurations.

Soil Modeling (SSI Representation)

In order to account for the flexibility of the soil beneath the foundation, soil-structure interaction (SSI) was represented using equivalent horizontal, vertical, and rotational springs. The implementation of these springs was achieved through the utilisation of Basic (Cartesian-Rotation) connectors, which were assigned beneath each column over an effective length of 2.5m. It was hypothesised that the behaviour of these springs would be linear. The foundation is supported on soft rock (SC-type soil). For surface foundations, the spring stiffness values were calculated using the formulations proposed by Pais and Kausel, as outlined in Table 4. For embedded foundations, stiffness values were modified using correction factors according to Equations (9) – (11) (Pais & Kausel, 1988; Stewart et al., 2012). It is evident that these expressions are capable of accounting for half-length (L) and half-width (B) of the foundation, as well as embedment depth (D), Poisson's ratio (ν), and shear modulus (G). The resulting stiffness values for horizontal, vertical, and rotational springs are presented in Table 5, along with the key properties of the studied system. This SSI modelling approach provides a realistic representation of foundation flexibility and its influence on seismic response. Furthermore, it maintains computational efficiency, making it suitable for nonlinear dynamic analysis (Bapir et al., 2023).

Modeling Strategy and Assumptions 

The adopted modelling approach integrates structural behaviour, hydrodynamic effects, and soil flexibility within a unified numerical framework. The fundamental assumptions underpinning this approach are as follows:

• The soil springs demonstrate linear elastic behaviour.
• The lumped-mass representation of fluid behaviour is based on Housner's theory.
• It is evident that there is a rigid connection between impulsive mass and structure.
• The representation of convective (sloshing) effects is based on the spring model.
• The application of unidirectional seismic excitation in the X-direction is a subject of particular interest.

These assumptions facilitate the capture of the dominant dynamic characteristics of the system, while maintaining a balance between modelling accuracy and computational efficiency.

The developed numerical model serves as the reference configuration for evaluating seismic performance and forms the basis for subsequent comparison with rocking-isolated systems.

Modeling and Implementation of the Rocking Isolation System 

The implementation of the rocking isolation system entailed the integration of connector elements between the ring beams, which were connected to the column bases, and the foundation along the entire perimeter of the tank. This configuration facilitates regulated interaction at the column-foundation interface, a prerequisite for activating the rocking mechanism.

In the numerical model, the contact region between the ring beams and the foundation was represented using Basic (Cartesian-Rotation) connector elements with a nominal length of 1mm, as illustrated in Figure 5. This approach circumvents the necessity for intricate geometric modelling of the contact interface, while concurrently enabling precise delineation of its mechanical behaviour.

Connector elements function as mechanical links between two nodes, thereby enabling the assignment of stiffness properties and nonlinear response in selected degrees of freedom. This enables precise simulation of force and displacement transfer while preserving computational efficiency. In the present study, these elements were utilised to illustrate the interface behaviour between the foundation and the structural system under seismic loading.

Depending on the direction of motion, different behavioural definitions were assigned to the connector.

Horizontal direction (X): A rigid response was assumed to ensure full transfer of seismic forces from the superstructure to the foundation without relative sliding. This assumption reflects the high in-plane stiffness of the connection and prevents unrealistic horizontal deformation.

The vertical direction (Y) is defined as follows: A nonlinear force-displacement (F-U) relationship was defined in order to facilitate the controlled uplift of the structure. This facilitates the modelling of partial separation between the ring beams and the foundation under overturning moments induced by seismic excitation.

The vertical nonlinear behaviour was calibrated using the force–displacement relationship presented in Table 6. This formulation enables the system to remain fully engaged under compressive forces while limiting tensile resistance to a predefined threshold corresponding to the initiation of uplift.

Once this threshold is exceeded, separation occurs, and the structure rotates about the compressed edge of the foundation, thereby activating the rocking mechanism. This behaviour can be regarded as the fundamental physical principle that underpins the concept of rocking isolation, wherein seismic energy is dissipated through the process of controlled uplift and re-contact, as opposed to the complete transfer of energy to the structural elements.

The connector parameters were calibrated to achieve the following performance objectives:

The primary objective is to ensure stability in uplift, whilst avoiding numerical instability. Additionally, there is a need to reduce overturning moment transfer to the supporting columns. Finally, sufficient re-centering capability after seismic excitation is required.

This modelling strategy has been developed to concentrate nonlinear behaviour at the column-foundation interface. The strategy is intended to protect the primary structural elements while promoting energy dissipation through rocking motion. Consequently, the system undergoes a transition from a force-based response to a displacement-controlled mechanism, a fundamental aspect of the efficacy of rocking isolation systems.

Fixed-Base Tank Response 

A comparative evaluation between the fixed-base model and the soil-structure interaction (SSI) model for the half-full condition (h = 1.75 m) under the El-Centro earthquake is indicated in Figure 6. This figure demonstrates that foundation flexibility exerts a secondary yet systematic influence on global seismic response. As demonstrated in Table 7, the effects of SSI are twofold. Firstly, it has been shown to reduce base shear by 9.40%. Secondly, however, it has also been demonstrated to increase top column displacement by 15.5%. This asymmetric response is attributed to the period elongation induced by soil compliance, which reduces spectral acceleration demand but simultaneously increases displacement sensitivity. The observed behaviour confirms that SSI acts primarily as a displacement-amplifying mechanism rather than a force-reduction mechanism for systems founded on relatively stiff soil (SC classification). Consequently, the fixed-base assumption remains acceptable for global force estimation, although it may slightly underestimate deformation demand.

Tank with Rocking Isolation

The rocking-isolated system introduces nonlinear uplift, stiffness degradation, and dynamic decoupling at the foundation interface, thereby fundamentally altering seismic demand distribution compared to the fixed-base case. A series of analyses were conducted to ascertain the effects of earthquake-induced damage to tanks containing varying levels of liquid. The tanks were subjected to the El-Centro, Kushiro and Tabas earthquakes, as illustrated in Figures 7 to 16.

Base Shear Response

As demonstrated in Figure 7 of the El-Centro earthquake, the base shear reaches 11,059.2kN in the full tank and 8,429.51kN in the empty tank (fixed-base). With rocking isolation, values are reduced to 6587.68kN (full) and 4284.25kN (empty), confirming a consistent reduction mechanism governed by increased flexibility and partial uplift at the base. However, the interaction observed under the Kushiro earthquake Figure 8 is more complex. The maximum base shear increases to 35,341.2kN (full tank), while the empty tank records 27,634.5kN (fixed-base). In the context of rocking isolation, the half-full condition assumes critical importance, attaining a maximum of 18604.9kN as a consequence of augmented fluid-structure interaction and resonance-like coupling between sloshing and rocking motion. The minimum value is 14293.3kN (empty tank). As illustrated in Figure 9 of the Tabas earthquake study, the maximum base shear is recorded as 12,110 kN (full tank), while the minimum is 8,765.24 kN (empty tank). Utilising rocking isolation, the maximum response is observed at 4905.58kN in the empty tank, while the half-full condition exhibits a decrease to 4302.45kN. This finding suggests that moderate-intensity ground motion does not significantly induce fluid resonance, leading to more uniform force reduction behaviour. Rocking isolation has been shown to achieve an average base shear reduction of approximately 50%, although its efficiency is clearly dependent on excitation characteristics and fluid participation level.

Top Column Displacement

As demonstrated in Figure 10 of the El-Centro earthquake, displacement varies from 3.37cm (empty tank) to 2.89cm (half-full) in the fixed-base case. It is evident that with the implementation of rocking isolation, there is an augmentation in displacement to 4.34 cm (full tank) and a concomitant reduction to 2.28 cm (half-full). This observation serves to substantiate the phenomenon of displacement amplification, a consequence of base flexibility. As demonstrated in Figure 11 of the Kushiro earthquake study, the fixed-base displacement reaches a maximum of 100.38cm in an empty tank and reduces to 40.01cm in a tank that is half full. It is evident that with the implementation of rocking isolation, the maximum capacity is further augmented to 111.74 cm (corresponding to a half-full state), while the minimum is recorded at 67.77 cm (representing a full tank). This pronounced amplification is attributed to long-duration excitation, which promotes cumulative rocking cycles and strengthens fluid-structure coupling. As illustrated in Figure 12 of the Tabas earthquake, displacement remains comparatively lower, ranging from 3.56cm (empty tank) to 2.21cm (half-full) in the fixed-base case. With the implementation of rocking isolation, values increased to 4.08cm and 1.75cm, respectively. The findings of this study suggest that rocking isolation has the effect of shifting the governing design criterion from force demand to displacement capacity. The impulsive water mass demonstrates a response pattern that is consistent with the structural displacement, which is a consequence of strong dynamic synchronization with tank motion.

Code-Based Drift Interpretation

The limits on seismic drift set out in design codes are based on assumptions of fixed bases and distributed deformation mechanisms. In the American Society of Civil Engineers (ASCE) 7/International Building Code (IBC), inelastic drift is defined as follows: The formula for the design load is given by (Cd·δxe)/Ie, with allowable limits ranging from 0.010h to 0.025h depending on the structural importance (2018 International Building Code (IBC), n.d.; Minimum Design Loads and Associated Criteria for Buildings and Other Structures, 2017). It is evident that analogous provisions are extant in Eurocode 8, NZS 1170.5, IS 1893 and ASCE 41 (Eurocode 8: Design of Structures for Earthquake Resistance | Eurocodes: The construction of the future, undated; IS 1893: Part 1: 2016. The following criteria are to be considered when undertaking earthquake-resistant design of structures: firstly, general provisions; secondly, buildings; and thirdly, the Bureau of Indian Standards. The Internet Archive (n.d.) offers a variety of options for accessing, borrowing, and streaming materials, including the New Zealand Standard 1170.5:2004 (excluding A1) Structural Design Actions - Part 5: Earthquake Design Actions. The Building Code Hub (n.d.) published a document in 2017 entitled 'Seismic Evaluation and Retrofit of Existing Buildings'. However, rocking systems introduce concentrated rotation at the base, which contradicts the underlying assumptions of conventional drift-based design. Consequently, the established drift limits may underestimate the true deformation demands in rocking-isolated tanks.

Convective Water Mass Displacement

As illustrated in Figure 13 of the El-Centro earthquake, the magnitude of sloshing displacement increases marginally from 36.19cm (full tank) and 31.57cm (half-full) in the fixed-base scenario to 36.71cm and 32.01cm under rocking isolation. As illustrated in Figure 14, which details the effects of the Kushiro earthquake, the maximum sloshing displacement is recorded as 122.43cm in a full tank, while the minimum is 71.22cm in a half-full tank. It is evident that, with the implementation of rocking isolation, the half-full case attains a critical point at 122.24cm, while the full tank experiences a reduction to 73.93cm. This phenomenon is indicative of resonance-type amplification, a consequence of the interplay between sloshing and rocking motions. As illustrated in Figure 15 of the Tabas earthquake, the amplitude of sloshing varies marginally between 32.06cm (full tank) and 17.19cm (half-full), exhibiting a slight increase under conditions of rocking isolation, reaching 32.56cm and 17.74cm, respectively. Overall, changes in convective response range from approximately 2% to 70%, demonstrating strong sensitivity to both excitation frequency content and filling ratio.

Rocking Response

As demonstrated in Figure 16, the rocking rotation reaches 0.077 rad for both full and empty tanks during the El-Centro earthquake. In the context of the Kushiro earthquake, the half-full condition governs the maximum response at 2.633rad. In the aftermath of the Tabas earthquake, the level of the empty tank is recorded as 0.077rad.

This behaviour is indicative of a dual mechanism: in moderate excitation, sloshing introduces phase lag, which partially mitigates overturning moments; however, under strong excitation, sloshing becomes dynamically amplified, increasing rotational demand. Full tanks primarily exhibit behaviour as impulsive systems, with negligible energy dissipation, while empty tanks demonstrate a lack of hydrodynamic damping. Consequently, both conditions exhibit elevated rocking demand in comparison to partially filled tanks under moderate loading.

Overall Performance Interpretation

Rocking isolation has been demonstrated to reduce base shear by approximately 50-60%, thereby confirming its effectiveness in force mitigation. However, displacement demand increases significantly and becomes the governing design parameter. The system response is characterised by significant non-linearity with respect to both filling ratio and earthquake intensity, manifesting as force-controlled behaviour under low-to-moderate excitation, displacement-controlled behaviour under strong excitation, and resonance-sensitive behaviour in partially filled tanks. This demonstrates that rocking isolation must be evaluated within a multi-performance framework incorporating force demand, displacement capacity, and fluid-structure interaction effects.

Rocking isolation has been demonstrated to enhance the seismic performance of elevated tanks, with a documented reduction in base shear of 40-60%. However, this reduction is accompanied by an increased demand for displacement, indicating a fundamental shift towards displacement-governed design. The half-full condition is of particular significance due to the pronounced fluid–structure interaction, particularly in the context of the Kushiro earthquake, where dynamic amplification is most evident. It has been demonstrated that fully filled tanks exhibit more stable behaviour, with 16-30% displacement reduction under the Kushiro and Tabas earthquakes. However, the El-Centro record may induce slight increases. It has been demonstrated that empty tanks exhibit an increase in displacement of 8-15%, attributable to enhanced flexibility and a reduction in damping. Convective effects become significant under strong ground motion, especially in partially filled conditions, where rocking motion may amplify sloshing through dynamic coupling. From a design perspective, rocking isolation is only effective when sufficient displacement and rotational capacity are ensured. The implementation of supplemental damping systems and the optimisation of interface properties are recommended in order to control excessive response.

It is recommended that future research endeavours encompass experimental validation, refined nonlinear fluid-structure interaction modelling, and the development of vertical restraining systems to limit uplift and enhance stability.

Authors’ Contributions

D.B.: Conceptualization.

R.A.: Supervision.

A.A.: Software.

Conflict Of Interest

The authors declare that there are no conflicts of interest.

Funding

The authors declare that this research received no external funding.

Declaration On The Use Of Generative AI And AI-Assisted Technologies

Not applicable

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgement

Not applicable

Ethics

This study did not involve human participants or animals; hence, no ethical approval was required.