As the global coastal seismic zone is increasingly active, the pilesupported wharves experience various levels of damage, which may stop the port operations. The Wharves with Seismic Isolation System (SISW), in which the isolation devices are placed on the top of the piles, was proposed to release the constraint of the top of piles and to mitigate damages between the top of piles and the wharf deck. However, current research on SISW was case by case, and a consistent general design method is lacking. This paper presents the PerformanceBased Seismic Design (PBSD) method for SISW. Here, multiple design levels and the corresponding performance objectives are proposed. An example project is introduced to explain the proposed PBSD method and verify the designed performance. The nonlinear time history analysis results demonstrate that the proposed design method effectively achieves the multilevel seismic objectives for SISW. Moreover, implementing SISW with the PBSD method achieves higher seismic performance objectives than NonSeismicIsolated Wharves, which utilize the same type of piles. The seismic resilience of wharves in highintensity seismic regions can be significantly enhanced using the SISW and corresponding design method.
Pilesupported wharves, consisting primarily of decks and piles, are a fundamental structural system in port engineering. They possess advantageous characteristics, such as low sand and gravel consumption, minimal dredging volume, low wave reflection, and favorable mooring conditions. As pivotal maritime transportation hubs, the construction and operation of pilesupported wharves play a crucial role in fostering domestic and global trade growth. However, the escalating seismic activity worldwide has led to varying degrees of damage to wharf pile foundations in previous earthquakes^{[18]}, as exemplified in
Seismic damage to wharf pile foundations. (A) 1989 Loma Prieta earthquake^{[3]}; (B) 2004 Sumatra earthquake^{[4]}; (C) 2010 Maule earthquake^{[7]}.
A pilesupported wharf can be approximately treated as a singledegreeoffreedom system, where the structural mass is primarily concentrated in the deck, which generates seismic forces. At the same time, the piles provide lateral structural stiffness. Current seismic design codes^{[2,911]} typically focus on controlling the horizontal displacement response of the wharf by designing the pile stiffness and relying on pile ductility to withstand intense earthquakes. Nevertheless, such design philosophy tends to underestimate the significance of "short pile failure" [
To mitigate ductile damage and the stiffness concentration effect in pile foundations, the implementation of Wharves with the Seismic Isolation System (SISW) [
Wharves with seismic isolation system (SISW).
Mito
To mitigate stiffness concentration in batter piles, researchers^{[7,18]} and standards^{[11]} have proposed the placement of isolation devices at the top or cap of batter piles [
By adopting the wharves with the SISW, it is possible to control the damage mode of the wharf effectively, reducing pile damage and avoiding stiffness concentration. However, research on SISW has thus far been limited to case studies, and a systematic performancebased seismic design (PBSD) method for SISW has yet to be proposed. Therefore, this study proposes seismic objectives for SISW based on ASCE 6114^{[11]} and presents a twostage PBSD method for SISW. Specifically, the layout and design parameters of the isolation devices are determined based on the Contingency Level Earthquake (CLE) (10% probability of exceedance in 50 years), while the wharf displacement response is examined based on the Maximum Considered Earthquake (MCE) level (2% probability of exceedance in 50 years). Finally, the effectiveness of the proposed design method for SISW is demonstrated and validated through a plumppile wharf design case.
The ASCE code "Seismic Design of Piers and Wharves (ASCE 6114)"^{[11]} establishes the minimum seismic hazard and performance requirements, specifying the performance levels of wharves according to different design classifications and seismic levels. In line with ASCE 6114, this study presents the design objectives for SISW, as outlined in
Design objectives for SISW





Ground motion probability of exceedance  50%/50 years  10%/50 years  2%/50 years  
Design classification  H2  Minimal damage  Minimal damage  Minimal damage 
H1  Minimal damage  Minimal damage  Controlled and repairable damage  
H0*  Minimal damage  Controlled and repairable damage  Life safety protection 
*H0 essentially corresponds to the “High” design classification in ASCE 6114^{[11]}, differing only in the elevation of the “Design Earthquake (DE)” level to the “Maximum Considered Earthquake (MCE)”.
The "Design Earthquake (DE)" level in ASCE 6114 is upgraded to the "MCE" level to enhance the seismic performance of wharves during rare earthquakes.
Two additional design classifications, namely "H1" and "H2", are introduced to achieve highperformance design for SISW.
The definitions and quantification criteria for different performance levels of the pile foundation are referenced from Section 3.9 "STRAIN LIMITS" in ASCE 6114^{[11]}. These performance levels are categorized based on the strain limits along pile plastic hinges. For example, the concrete strain limits for reinforced concrete (RC) pile plastic hinges allowed at the pile top and in the ground are 0.005 within the performance level of "minimal damage" and 0.025 and 0.008, respectively, within "controlled and repairable damage".
In the seismic design of wharves, it is necessary to convert material strains into structural displacements as design demands under different seismic levels. The pushover analysis could be conducted to obtain the displacement demands.
The plumppile wharf is adopted as the example to introduce the PBSD method for SISW. Firstly, the design principles based on uniform pile stiffness are introduced. Secondly, a twostage PBSD method for SISW is proposed.
For pilesupported wharves with sloping embankments [see
When using isolation devices, the lateral stiffness of the pile foundation (referred to as "isolated piles" hereafter) decreases significantly due to the hinged connection at the pile top. This increased seismic deformation in piles reduces the displacement of the isolation devices, which is detrimental to their performance.
To increase the stiffness and integrity of the isolated piles, rigid connecting beams between the pile tops can be installed to limit pile top rotation [see
SISW with rigid coupling beam.
Connecting beams are designed as capacityprotected elements to ensure their elasticity under the MCE levels. Specifically, when the SISW reaches design displacement, the demands for the moment and shear force at coupling beam ends can be calculated by structural mechanics. By multiplying by an overstrength factor (taken as 1.3 in this work), section steel with sufficient capacity can be selected as the main body. Moreover, the connection strength between the connecting beams and the piles needs to be verified through welding or bolted connections.
The design of isolation devices should meet the following conditions:
(1) Isolation devices should possess sufficient initial stiffness to mitigate detrimental vibrations of the wharf caused by wind loads, foundation microvibrations, or ship berthing forces. The isolation devices should maintain optimal vertical load resistance at each seismic level. When isolation devices reach the ultimate horizontal displacement, they should exhibit stability under the most unfavorable axial load.
(2) The mechanical performance of isolation devices should remain stable under aging, creep, temperature variations, and seawater corrosion. The design of isolation devices should account for shortterm and longterm adverse effects caused by uneven structural settlement and deck shrinkage deformation.
This study proposes a twostage PBSD method for SISW, as illustrated in
Performancebased twostage seismic design method for SISW.
For wharf seismic design in China, the common practice is to adopt a transverse singlebay elastic frame for an analysis per response spectrum method. The virtual fixedpoint method, outlined in many countries’ specifications^{[911]} for simplified pilesoil interaction consideration, is adopted to approximate the soil's constraint on the piles by determining the point of fixity on each pile.
To provide a practical SISW design approach, this work adopts the transverse singlebay frame with the virtual fixedpoint method for pilesoil interactions. The process for determining the point of fixity of piles is referenced in^{[10]}. Additionally, in the CLE and MCE design stages, the wharf frame models are elastic and elasticplastic, respectively.
Note: For detailed equations related to the physical quantities in
The design classification and performance objectives for the wharf are determined based on
The CLE level design aims to satisfy the displacement limit,
The specific steps are as follows:
(1)The fundamental period of SISW,
(2)The equivalent lateral stiffness of SISW,
(3)Iteratively calculate
(4)Determine the design parameters of the isolation devices based on
After determining the design parameters of the isolation devices that meet the displacement limit for the CLE level, a nonlinear time history analysis is performed on the SISW model to verify the structural response under the MCE level, considering the material nonlinearity of the piles and isolation devices.
The nonlinear time history analysis should use three or more sets of seismic records^{[10]}. If fewer than seven sets of records are used, the maximum response from each set is taken as the structural response. The average response can be considered if seven or more sets of records are used for analysis.
The deck, isolator connections, and steel connecting beams should be designed as capacityprotected elements by multiplying the calculated peak shear demand from element cross sections by 1.3 at the MCE level.
Additionally, ship berthing forces for the designated ship type should be verified due to the decrease in lateral stiffness after wharf isolation.
This section presents a case study of a marginal wharf with plump piles in China to illustrate the application of the PBSD method for SISW. The target response spectra of CLE and MCE are determined by the seismic exceedance probabilities, the site classification, and the seismic zoning per "Code for Seismic Design of Water Transportation Engineering (JTS 1462012)"^{[10]}. Furthermore, for time history analysis, the input acceleration peak values are modulated to 0.2 g and 0.4 g for CLE and MCE levels, respectively, according to^{[10]}.
Transverse section and plan view of the original wharf. (A) Transverse section (dimensions in mm, elevation in m); (B) Plan view (in mm).
The wharf is constructed using C40 concrete with a deck thickness of 0.4 m. The crane track and transverse beams have a width and height of 1.2 m and 1.5 m, respectively. Circular RC castinplace piles with a diameter of 1m are employed for the wharf. The stacking pressure on the wharf surface is 30 kPa, and the gravity design value of the wharf structure is 8,427 kN. The seismic fortification intensity in the located region is Eight Degrees, according to JTS 1462012^{[10]}. During the gravity design phase, the preliminary selection for the longitudinal reinforcement of the pile is 24Φ24, the stirrup selection is Φ10@200 with HBP300 steel, and the protective layer thickness is 50 mm.
In this case, the H1 design classification is adopted based on
According to Section "Seismic performance objectives for wharf with seismic isolation system", strain limits along pile plastic hinges are employed as quantified indicators for different performance levels per ASCE 6114^{[11]}. However, in SISW seismic design, the deck displacement limits at CLE and MCE levels (
The steps are as follows: (1) Conducting pushover analysis by applying increasing horizontal displacements to the wharf deck; (2) Taking the deck horizontal displacement as the design demand when the plastic hinge strains of piles reach limits stipulated in ASCE 6114^{[11]} under a certain performance level.
The numerical modeling method for pushover analysis can be found in Section "FE model introduction", including element selection, material constitutive, and boundary constraints. The displacement limits for each pile under different performance levels are determined and presented in
Panel displacement (mm) corresponding to pile performance levels (piledeck rigid connection)






Minimal damage  205  151  110  74  46 
Controlled and repairable damage  484  392  307  206  124 
Life safety protection  756  616  484  315  190 
According to
In this case, isolating inboard piles C, D, and E is preliminarily determined. Among the nonseismicisolated piles, pile B, with a shorter free length than pile A, becomes the most critical pile for SISW. Therefore, the displacement limits of pile B under different performance levels are utilized as the design demands of SISW, namely
The fundamental period of the reference wharf (NSIW),
Distribution of pile stiffness for SISW (kN/m)







Before distribution  2,289.5  3,501.6  5,745.3  10,399.6  21,806.2  43,742.1 
Isolator stiffness 
    2,872.7  2,872.7  2,872.7   
After distribution  2,289.5  3,501.6  1,915.1  2,250.9  2,538.3  12,495.3 
Since the period of SISW,
Where
The calculation yields
Where
The primary objective of SISW design is to mitigate the stiffness concentration effect on the inboard piles. To achieve this, the structural stiffness (
As noticed in
The structural stiffness of the SISW after isolation denoted as
Considering the factors of isolated piles’ quantity and relative stiffness between isolators and piles on the structural damping ratio, Equation (4) is used to calculate the equivalent structural damping ratio of SISW
Where
Using Equation (4), the equivalent damping ratio of the wharf is
Friction pendulum isolators are employed here, considering the inherent selfcentering capacity. Moreover, friction pendulum isolators can adjust stiffness and damping by modifying friction materials and curvature radius to adapt to the required seismic objectives. The hysteresis model for the friction pendulum isolator is depicted in
Friction pendulum isolator hysteresis model.
Design parameters for friction pendulum isolation devices






Pile C  1,922  0.04  1.26  9,877.7  1,519 
Pile D  1,922  0.04  1.26  9,877.7  1,519 
Pile E  1,660  0.05  1.27  8,491.4  1,306 
The initial stiffness
Where:
To verify whether the deck displacement
A transverse singlebay frame of SISW based on the virtual fixedpoint method is established using ABAQUS/Standard^{[23]}, as depicted in
Schematic diagram of the numerical model of the SISW. The calculation Equation for "LSP" (pile strain penetration length at the piledeck connection) is provided in^{[11]}.
Timoshenko beam elements (B21) are chosen for both the pile foundations and the deck, allowing for the consideration of shear and bending deformations. Through mesh sensitivity analysis during preliminary modeling, it was found that using 1,000 mm and 500 mm mesh sizes for the deck and piles ensured both accurate results and higher computational efficiency.
The mechanical behavior of the friction pendulum system is simulated using the "Connector" featured in ABAQUS, which defines the forcedisplacement relationship between the top pile node and the deck node at all degrees of freedom [
The connecting beams on the isolated piles are constrained through the "MPC Beam constraint" in ABAQUS, binding the degrees of freedom of adjacent pile nodes. Additionally, rigid connections between nodes are established using "Tie" in ABAQUS to connect the nonseismicisolated piles and the deck.
For the boundary constraints, the bottom nodes of each pile are coupled to a reference point ("Coupling" in ABAQUS), and displacement constraints are defined at the reference point. During time history analysis, the reference point is subjected to horizontal seismic acceleration while other degrees of freedom are restricted.
The loading protocol consists of two steps. First, a static analysis step is conducted to apply gravity loads to the wharf. Then, an implicit dynamic analysis step is performed to simulate horizontal unidirectional seismic acceleration.
The deck and pile foundation are constructed using C40 concrete, which has an elastic modulus of
Parameters of the CDP model





30°  0.1  1.16  0.667  0.005 
The reinforcement used in the pile foundation is HBP300 steel with an elastic modulus of 2 × 10^{5} MPa. It has a yield strength of 300 MPa, an ultimate strength of 632 MPa, and an ultimate tensile strain of 0.14. The constitutive model employs a bilinear isotropic hardening model.
Three sets of natural seismic waves are selected from the PEER ground motion database^{[25]} [
Selected seismic waves and response spectra (MCE level). (A) Seismic waves (PGA = 0.4 g); (B) Acceleration spectra
Selected ground motion records








1  Hollister  America  1961  5.6  0.11  335.5  40 
2  Kobe  Japan  1995  6.9  0.32  312  41 
3  Friuli  Italy  1976  6.5  0.36  505.23  36 
In the subsequent time history analysis, the seismic motion is scaled to the MCE level to verify the displacement response of the SISW during large earthquakes. Additionally, a fivesecond free vibration period is added after applying the seismic motion to determine the residual displacement of the structure following the earthquake.
The maximum displacement of the wharf deck under the three seismic waves is 0.154 m [
Maximum deck displacement for NSIW and SISW (mm)


















NSIW  046  46124  124190  74.2  119.8  52.1  137.6  25.6  56.0 
SISW  0151  151392  392616  70.7  154.1  72.9  147.8  34.7  61.1 
The seismic demands on the protective components of the wharf deck, connecting beams, and isolated piles were verified, and the results indicate that the demands are smaller than the design loadbearing capacity of these components.
In the wharf example, a 5,000ton class bulk carrier with a full load displacement of 6,700 t is considered. The design mooring speed is 0.2 m/s. Based on the Chinese Code for Harbor Engineering Loads
In conclusion, the twostage seismic design confirms that the reference wharf can meet the seismic objectives of CLE and MCE levels for design classification H1. This demonstrates the effectiveness of the PBSD method for the SISW.
This section establishes a numerical model for an NSIW (with the same model size, pile foundation material, and modeling method as the SISW) to conduct time history analysis at CLE and MCE levels. The dynamic response results of the SISW in Section "Application of the PBSD method for wharf with seismic isolation system" are compared to discuss the differences between them in deck displacement, acceleration, pile bending moment, and structural energy dissipation.
Comparison of deck displacement.
The peak displacements of the SISW are generally higher than those of the NSIW. This is primarily due to the longer fundamental periods of the former. However, since the SISW decouples the motion between the deck and the inboard piles, the structural ductility and displacement limits are significantly increased. Combining
Furthermore, as shown in
Comparison of displacement of seismic piles and deck in SISW.
Maximum horizontal displacement for deck and isolated piles in SISW (mm)












Deck  70.7  154.1  72.9  147.8  34.7  61.1 
Isolated piles  12.4  28.2  11.3  34.5  6.8  8.0 
It is evident that through pile head isolation, the displacements of isolated piles and the deck are decoupled. The maximum displacements of isolated piles at the CLE and MCE levels are 12.4 mm and 34.5 mm, respectively, falling within the "Minimal damage" limit [
Deck acceleration time histories for two types of wharves.
Maximum deck acceleration for two types of wharves (g)












NSIW  0.15  0.17  0.13  0.16  0.1  0.14 
SISW  0.09  0.13  0.09  0.14  0.07  0.09 
Reduction rate (%)  40.9  24.1  28.0  16.4  31.2  32.0 
The reduction rate refers to the ratio between the difference in peak accelerations of the two types of wharves and the peak acceleration of the NSIW.
Comparison of pile bending moments (piles A and B) at the moment of maximum displacement for the two types of wharves.
Comparison of pile bending moments (piles C, D, E) at the moment of maximum displacement for the two types of wharves.
Maximum pile bending moments for the two types of wharves



















Hollister  CLE  503.5  1,137  604.5  1,409  847.9  336.4  1,131  452.6  1,440  507.9 
MCE  1,089  1,450  1,254  1,820  1,512  390  1,860  707  2,280  1,210  
Kobe  CLE  831.9  1,115  954.5  1,201  1,189  501.5  1,608  729.6  2,236  1,004 
MCE  1,134  1,508  1,323  1,741  9,783  438.6  14,100  561.3  2,273  880.8  
Friuli  CLE  406.3  574.1  530.5  686.3  650.3  230.9  781.9  365.9  1,037  578.5 
MCE  734.6  1,323  1,013  1,585  1,302  257.5  1,566  410.6  2,066  635 
According to the Abaqus manual^{[23]}, The total energy balance of the wharf FE models can be written as:
Where: ALLWK  External work (available only for the whole model), ALLKE  Kinetic energy, ALLIE  Total strain energy, ALLVD  Energy dissipated by structural damping, ALLFD  Total energy dissipated through frictional effects (available only for the whole model).
In Equation (7), the kinetic energy (ALLKE) approaches zero after the earthquake. The frictional energy dissipated in the model contacts (ALLKE) is also zero, as the model does not consider contact interactions. Therefore, the input energy to the structure is primarily consumed in the form of internal energy (including total strain energy, ALLIE, and energy dissipated by structural damping, ALLVD)^{[2830]}. The total strain energy ALLIE consumed by wharf models consists of energy dissipated through structural plastic deformation, including pile hysteresis deformation and isolators' nonlinear sliding.
Comparison of energy dissipation between the two types of wharves.
In the seismic design of marginal pilesupported wharves, the ductile damage to pile foundations hampers postearthquake operation, and the concentration of stiffness in inboard piles or batter piles results in severe local damage. To mitigate wharf pile damage and stiffness concentration under various seismic levels, this paper introduces a PBSD method for wharves with the SISW, wherein structural inelasticity is confined to the isolation layer. Subsequently, a wharf case is designed using the proposed method, and its seismic performance is numerically investigated. The major conclusions are summarized as follows:
(1) Performancebased seismic objectives for SISW are suggested. Classifications H_{1} and H_{2} with "minimal damage" objectives under CLE and MCE levels, respectively, are introduced to achieve highperformance seismic design for SISW.
(2) A twostage PBSD method for SISW is proposed. During the elastic design stage under the CLE level, the isolators are designed based on the elastic response spectrum method. During the displacement verification stage under the MCE level, the deck displacement is verified based on the nonlinear time history analysis.
(3) A design case is presented to show the application for the proposed twostage PBSD method. The nonlinear time history analysis results indicate that the SISW showed higher seismic performance than the NSIW. The SISW avoids "short pile failure" caused by increased stiffness in inboard piles compared to NSIW. By confining inelastic deformation to the isolation layer, SISW exhibits a higher energy dissipation capacity than NSIW, effectively controlling ductile damage in pile foundations.
This study proposed a practical PBSD method for SISW. The feasibility of the design method is verified with the designbased 2D model, providing the potential for standardized design for SISW. In the future, the design method's applicability will be validated by 3D numerical models with multidirectional seismic inputs^{[31,32]}. Refined pilesoil interaction and the pilewave interaction will also be considered.
Methodology, software, investigation, formal analysis, writing  original draft: Wang Z
Conceptualization, data curation, supervision, writing  review & editing: Cao M
Validation, investigation: Li J
Conceptualization, funding acquisition, data curation, supervision, writing  review & editing: Cui Y
The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.
This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFB2600703).
All authors declared that there are no conflicts of interest.
Written informed consent for publication of this paper was obtained from the Dalian University of Technology and all authors.
Not applicable.
© The Author(s) 2023.
Appendix