Strengthened T-mooring design of self-propelled deck barges under open wharf conditions and its applicable metocean conditions

Abstract

With the rapid expansion of ultra-large industrial modular units (ULIMUs), the demand for maritime transport has grown substantially. These units are typically loaded via roll-on/roll-off (Ro/Ro) operations using ship T-berthing at factory-owned wharves. However, such wharves are often shallow and exposed, subjecting vessels to significant windage and environmental forces. Conventional T-mooring systems (CTS) frequently fail to meet the stringent motion limits required for safe Ro/Ro loading and are prone to mooring line failures. To address this, a strengthened T-mooring system (STS) is proposed. Two supplementary mooring chains are symmetrically added to the bow beyond the CTS. Numerical simulations were first conducted to comparatively analyze the dynamic performance of the CTS and STS. Then, based upon the PIANC criteria for ship motions and the OCIMF guidelines for mooring line strength, the applicable sea conditions for the STS were concluded for both Ro/Ro operations and in-port periods. Finally, the field measurements were utilized to validate the numerical simulation. Results show that the STS significantly reduces surge, sway, and yaw motions and peak mooring-line tensions by up to 70%. These findings demonstrate that the STS provides enhanced stability, improved load distribution, and superior operational safety under exposed open-wharf conditions.

Keywords

ULIMUs Ro/Ro T-mooring system numerical simulations applicable sea conditions

Introduction

Modular construction is a widely adopted engineering approach, prevalent in many industries such as oil and gas, chemical engineering, and offshore engineering.^1–4 The ULIMUs are typically characterized by extreme dimensions, high centers of gravity, and concentrated heavy loads. These cargoes are commonly loaded onto vessels via stern roll-on operations, using self-propelled deck barge in combination with self-propelled modular transporters (SPMT). The loading process, defined as the transfer of large modular cargo from land to a vessel, can be performed through lifting, float-on, sliding, or SPMT roll-on methods.^5,6 Figure 1 illustrates a typical schematic of SPMT roll-on loading. Once loaded, the cargo is transported by sea to the final assembly site for integration.

Figure 1.

Stern roll-on process for ultra-large modular cargos: (a) pre-loading, (b) roll-on, and (c) in-position.

A loading and unloading areas for ULIMUs are often factory-owned open wharf, where the water area offers little shelter and sea conditions are relatively harsh. Correspondingly, ships T-mooring system have a large exposure area and the low stiffness. When encounter to strong lateral loads, excessive ships motion and uneven mooring line tension, prone to mooring line failure and quay damage. Furthermore, the number of mooring lines cannot be increased indefinitely due to limitations in ship mooring resources. Therefore, designing a T-mooring system that satisfies roll-on/roll-off operational requirements while ensuring in-port vessel safety represents a significant engineering challenge.

Extensive research has been conducted on the design and optimization of mooring configurations to improve load distribution and operational safety. Yu et al.,⁷ proposed a hybrid position-keeping system for a floating aquaculture platform, adopting a 2 × 4 steel chain and fiber rope configuration to increase line elasticity and mitigate peak tensions. Huang and Zhang,⁸ proposed a ship outfitting and mooring arrangement and validated its feasibility using the OPTIMOOR software. Theoretical design, numerical simulations, and model tests were carried out to increase mooring capacity and improve cable force uniformity by removing short cables and adopting a fore-and-aft configuration with polymer lines.^9,10 Wang et al.,¹¹ investigated the influence of mooring line diameter and material properties, concluding that increased diameter improves horizontal motion control. Rosa-Santos et al.,¹² Shi et al.,¹³ and Abdelwahab et al.,¹⁴ further examined the effect of pretension on moored ship responses and reported that although higher pretension reduces vessel displacement, its effectiveness diminishes beyond a critical threshold. Wen et al.,¹⁵ and Liu and Liang,¹⁶ demonstrated that the addition of buoy and shore mooring devices significantly improves mooring force distribution and system adaptability to long-period waves.

In parallel with mooring configuration design, another important research direction concerns the dynamic response characteristics of moored ships to the combined effects of wind, waves, and currents. Shi et al.,¹⁷ experimentally investigated motion responses of a large LNG vessel under long-period waves and identified roll amplification near resonance conditions. Shen et al.,¹⁸ and Wang et al.,¹⁹ further analyzed the influence of wave period on ship responses and confirmed that motion amplitude increases as the wave period approaches the natural roll period. Wang et al.,²⁰ conducted physical model tests on moored ship motions under wave excitation, revealing that surge and roll are the critical modes limiting operational safety due to resonance with long-period swells. Sakakibara and Kubo,²¹ demonstrated through field observations that low-frequency harbor oscillations can induce significant ship motions due to resonance and mooring asymmetry. Dong et al.,²² and Zhu et al.,²³ further clarified that horizontal motions are mainly governed by low-frequency wave energy, whereas vertical motions are more sensitive to short-wave components.

Beyond mooring configuration design and response analyses, several studies have examined optimization strategies and the establishment of safety evaluation criteria for moored vessels. Yan et al.,²⁴ numerically evaluated the hydrodynamic response of moored ships under harbor oscillations and showed that optimized stiffness distribution can mitigate motion amplification. Wen et al.,¹⁵ experimentally investigated multi-buoy-assisted mooring systems and demonstrated that auxiliary buoy devices improve load redistribution and adaptability to long-period swell conditions.

In parallel with these strategy-oriented efforts, substantial work has also focused on establishing safety evaluation methods and operational limits. Ziylan and Nas,²⁵ proposed a quasi-static mooring analysis approach to simplify safety assessments for berthed ships. De Carvalho et al.,²⁶ proposed a dynamic amplification factor method, which is effective for evaluating mooring safety under long-period waves. Gu and Tang,²⁷ established environmental limits for ship mooring and loading/unloading operations, including specific conditions for container ships at open wharves. Figuero et al.,²⁸ determined operational movement limits by comparing measured ship motions with international cargo handling standards. Yuan et al.,²⁹ further established mooring limit conditions for open quays based on environmental load analyses.

Despite these advances, existing studies mainly focus on conventional lateral mooring systems. The unique characteristics of T-berthing configurations operating at exposed factory-owned open wharves, where shallow water depth, limited sheltering, and high windage ultra-large modular cargo coexist have not been systematically examined. In particular, the applicability of stiffness-enhanced T-mooring systems under defined met ocean conditions for both Ro/Ro operations and in-port periods remains insufficiently clarified.

To address these gaps, the present study proposes a strengthened T-mooring system, in which additional mooring chains are appended to the bow to enhance stiffness and improve load distribution. Numerical modeling and safety-based assessments are employed to evaluate the dynamic performance of the STS and define its applicable sea conditions for Ro/Ro operations at exposed factory-owned wharves.

Design of the ship T-mooring system

Ship and mooring facilities conditions

This study adopted the T-berthing of a 20,000 DWT self-propelled deck barge at a factory-owned wharf as typical case, whose principal specifications are summarized in Table 1. The barge is used for roll-on loading and sea transportation of an oversized FPSO module (3305.75 tons, 40 m × 32 m × 35 m, center of gravity 25 m above deck).

Table 1.

Characteristics of the self-propelled deck barge.

Parameter	Unit	Value
Length overall	m	155.8
Beam	m	40.0
Depth	m	9.0
Draft	m	5.0
Displacement	ton	21,920.0
Metacentric height	m	19.5
Height of center of gravity	m	7.10

Sea condition

During the ships T-berthing period, subjected to two critical sea conditions: the critical sea condition for roll-on/roll-off operation (CSC-RoRo), representing the most adverse sea state experienced during cargo loading, and the critical sea condition in port (CSC-InPort), representing extreme conditions potentially encountered between berthing and departure. These conditions are typically derived from historical meteorological data and port design specifications. The representative combined sea state conditions for CSC-RoRo and CSC-InPort are summarized in Table 2. Given the symmetry of the ship T-berthing and mooring system, the most adverse combinations of environmental forces were considered, with the current direction fixed at −180° and the wind and wave directions set to 180°, 210°, 240°, and 270°.

Table 2.

Sea state parameters for ships T-mooring system.

Operation stage	Load case	Wind speed/(m·s⁻¹)	Surface current/(m·s⁻¹)	Wave height/(m)	Spectral peak wave period/(s)	Wind direction/(°)
CSC-RoRo	LC1	10.8	0.514	0.5	6.0	180
	LC2	10.8	0.514	0.5	6.0	210
	LC3	10.8	0.514	0.5	6.0	240
	LC4	10.8	0.514	0.5	6.0	270
CSC-InPort	LC5	13.8	0.514	0.8	6.0	180
	LC6	13.8	0.514	0.8	6.0	210
	LC7	13.8	0.514	0.8	6.0	240
	LC8	13.8	0.514	0.8	6.0	270

Mooring pattern and configuration

The strengthened T-mooring system was developed on the basis of the conventional T-mooring system. In the STS configuration, one additional mooring chain is installed on each bow side, consisting of 110 m chains arranged at an angle of 45°, together with four high-strength fiber ropes per side connected to the wharf dolphins. The mooring layouts of the CTS and STS are compared in Figure 2.

Figure 2.

Mooring arrangements of the 20,000 DWT self-propelled deck barge: (a) strengthen T-mooring pattern and (b) conventional T-mooring pattern.

The barge is equipped with Ф80 mm Polypropylene Filament (PF) ropes and Ф73 mm anchor chains, considered as the primary mooring lines. Based on conducted experimental measurements, the minimum breaking loads of the Ф80 mm PF cables and Ф73 mm anchor chain are 720.0 kN and 3988.0 kN, respectively. 50% of the MBL for the PF cables (360 kN) is considered as the Safe Working Load (SWL).

Simulation model sets

An advanced and widely adopted approach for evaluating the safety of T-mooring systems is the use of a three-dimensional potential flow theory-based hydrodynamic numerical model, which enables the simulation of system responses under complex environmental loads, including waves, currents, and wind. The overall analysis procedure is illustrated in Figure 3.

Figure 3.

Overall analysis procedure for ships T-mooring system.

Numerical modeling approach

Using the 3D potential flow theory, the motion equation of the ship mooring system in the time domain can be expressed as:

\begin{matrix} (M + m) \overset{\cdot\cdot}{x} + \int_{- \infty}^{t} K (t - τ) \overset{\cdot}{x} (t) d τ + C_{x} (t) \\ = F_{wa} (t) + F_{c} (t) + F_{wi} (t) + F_{m} (t) + F_{f} (t) \end{matrix}

(1)

where $M$ and $m$ respectively represent the generalized mass and additional mass matrices of the floating body, $K (t - τ)$ is the delay function matrix of the system, $F_{wa} (t), F_{c} (t), F_{wi} (t), F_{m} (t), and F_{f} (t)$ are respectively wave, the flow, wind, mooring, and fender forces, … is the restoring force coefficient matrix of the floating body in still water, x, $\overset{\cdot}{x}$ , and $\overset{\cdot\cdot}{x}$ are the displacement vector, velocity, and acceleration of the system, respectively.

(1) Wind loads

According to the relevant provisions of the American Petroleum Institute and DNV GL, the longitudinal wind force ( $F_{xw}$ ), lateral wind force ( $F_{yw}$ ), and yawing moment acting on the hull ( $M_{Xyw}$ ) are defined as.^30,31

{\begin{matrix} F_{xwi} = \frac{1}{2} C_{xw} ρ_{w} V_{w}^{2} A_{T} \\ F_{ywi} = \frac{1}{2} C_{yw} ρ_{w} V_{w}^{2} A_{L} \\ M_{xywi} = \frac{1}{2} C_{xyw} ρ_{w} V_{w}^{2} A_{L} L_{BP} \end{matrix}

(2)

Where $ρ_{w}$ is the air density, $V_{W}$ is the wind speed, $A_{T}$ is the transverse wind area of the mooring system, $A_{L}$ and $L_{BP}$ are the length of the longitudinal wind area and the distance from the vertical line of the ship, respectively.

(2) Current loads

A ship under steady flow undergoes a planar force along the velocity direction and a yawing moment around the Z-axis. The hydrodynamic force in the longitudinal direction ( $F_{xc})$ , hydrodynamic force in the transverse direction ( $F_{yc}$ ), and yawing moment $(M_{Xyc})$ are defined as:

{\begin{matrix} F_{xc} = \frac{1}{2} C_{xc} ρ_{c} V_{c}^{2} L_{BP} T \\ F_{yc} = \frac{1}{2} C_{yc} ρ_{c} V_{c}^{2} L_{BP}^{2} T \\ M_{xyc} = \frac{1}{2} C_{xyc} ρ_{c} V_{c}^{2} A_{L} L_{BP}^{2} T \end{matrix}

(3)

Where $ρ_{C}$ is the seawater density, $V_{c}$ is the current velocity, $L_{BP}$ is the length between perpendiculars, and T is the draft.

Numerical model setup

The coordinate system of the model and the mooring points is illustrated in Figure 4 and 5(a). Note that the X-axis is positioned at stern perpendicular pointing towards the bow, the Y-axis points from the starboard side to the port side, the Z-axis is perpendicular to the horizontal plane and directed upward along the depth of the ship. The coordinate system for the sea state environment and the motion of the ship is defined with counterclockwise rotation for the Z-axis (positive direction), and the longitudinal axis from stern to bow is set at 0°.

Figure 4.

Definition of coordinate system.

Figure 5.

(a) Coordinate of mooring point and (b) hydrodynamic model of T-mooring system.

A hydrodynamic model for the self-propelled deck barge and wharf was developed using AQWA hydrodynamic analysis software. Hydrodynamic model of the T-mooring system is shown in Figure 5(b). Catenary models are adopted to simulate the cables and chains in the hydrodynamic model, while the parameters of the rope and fenders are derived from tensile testing. The corresponding load-deformation curves are shown in Figure 6. The pretension of each mooring line is set to 10% of the Maximum Breaking Load (MBL) by adjusting its length, while the fender damping and friction coefficients are equal to 0.06 and 0.02, respectively.

Figure 6.

(a) Fender and (b) mooring line tension-deformation curves.

Safety evaluation criteria

The safe operation criteria for different operational stages of a ship’s T-type mooring system are defined as follows:

(1) In the stage of Ro/Ro operation, the procedure is typically constrained to wind conditions not exceeding Beaufort Scale 6. then the safe operation criteria focus on the maximum resistance of the T-mooring system to environmental forces within the permissible ship motion range.

(2) In the berthing period, the movement of the vessel has minimal impact on subsequent operations, such as sea fastening. The safe operation criteria are determined by evaluating the maximum resistance of the T-mooring system to environmental loads within the safe load limits of the mooring lines.

Criteria for movements of moored ships

As Ro/Ro operation imposes rigid requirements on moored ship movements, this work adopts “Criteria for Movements of Moored Ships in Harbors” of PIANCwith permissible movement limits under loading conditions detailed in Table 3.^32,33

Table 3.

Criteria for movements of moored ships in Ro/Ro operation.

Surge/(m)	Sway/(m)	Heave/(m)	Roll/(deg)	Pitch/(deg)	Yaw/(deg)
0.8	0.6	0.8	4.0	1.0	1.0

Criteria for strength of mooring line

The mooring equipment guidelines issued by the International Maritime Forum of Petroleum Companies mention that the allowable load for marine mooring cables should not exceed 55% of the Minimum Breaking Load (MBL) for wire ropes. For chemical fiber ropes, other than nylon, this load should not exceed 50% of the MBL, while that of nylon ropes should not exceed 45% of the MBL for ensuring sufficient safety redundancy under dynamic loads.³⁴

Result analyses

The dynamic performance of the mooring system is evaluated under the CSC-RoRo and CSC-InPort conditions. Two key indicators are adopted: ship movements, which assess compliance with Ro/Ro operational requirements, and maximum mooring line tension, which evaluates system safety and reliability under extreme in-port conditions. Together, these metrics provide a comprehensive basis for assessing the overall performance of the ship’s T-mooring system.

Ship movements

Tables 4 and 5 shows that STS consistently outperforms CTS in controlling ship motions. Under the CSC-Ro/Ro condition (LC4), CTS exhibited a sway of 2.591 m and a yaw of 0.420°, while STS reduced these to 0.658 m and 0.100°, representing reductions of about 75%. In the extreme CSC-InPort case (LC8), CTS reached 4.265 m in sway and 2.9° in yaw, whereas STS limited them to 1.732 m and 1.2°, with reductions of approximately 60%. Surge motion also decreased by 30% to 70% across both scenarios.

Table 4.

Berthed ship’s movements under the CSC-RoRo.

Systems	Load case	Encounter direction (deg)	Surge (m)	Sway (m)	Heave (m)	Roll (deg)	Pitch (deg)	Yaw (deg)
CTS	LC1	180	0.150	0.000	0.011	0.000	0.030	0.000
	LC2	210	0.108	0.754	0.011	0.010	0.010	0.010
	LC3	240	0.085	1.700	0.010	0.020	0.010	0.250
	LC4	270	0.162	2.591	0.038	0.050	0.000	0.420
STS	LC1	180	0.071	0.000	0.012	0.000	0.020	0.000
	LC2	210	0.079	0.118	0.010	0.010	0.010	0.020
	LC3	240	0.084	0.290	0.008	0.020	0.010	0.030
	LC4	270	0.113	0.658	0.037	0.050	0.000	0.100

Table 5.

Berthed ship’s movements under the CSC-InPort.

Systems	Load case	Surge (m)	Sway (m)	Heave (m)	Roll (deg)	Pitch (deg)	Yaw (deg)
CTS	LC5	0.170	0.000	0.035	0.000	0.151	0.000
	LC6	0.230	1.996	0.066	0.100	0.100	1.400
	LC7	0.450	3.897	0.036	0.100	0.100	2.700
	LC8	0.860	4.265	0.155	0.700	0.000	2.900
STS	LC5	0.140	0.000	0.026	0.000	0.150	0.000
	LC6	0.170	0.343	0.032	0.100	0.100	0.300
	LC7	0.270	1.159	0.025	0.200	0.100	1.000
	LC8	0.240	1.732	0.110	0.800	0.000	1.200

These results indicate that the addition of anchor chains in STS significantly enhances system stiffness, effectively suppressing low-frequency surge, sway, and yaw motions. Consequently, STS not only ensures a more stable berthing posture but also expands the operational safety margin for Ro/Ro loading and in-port mooring under exposed wharf conditions.

Mooring force

Comparative analysis of mooring line tensions for the STS and CTS under the CSC-Ro/Ro and CSC-InPort (Figures 7 and 8) indicates that, as the wave incidence angle shifts from 180° (head sea) to 270° (beam seas), Encounter-side lines of the CTS experience sharply increased and uneven tensions. In contrast, the STS maintains more moderate tension variations with a uniform load distribution.

Figure 7.

Mooring line forces under the CSC-Ro/Ro.

Figure 8.

Mooring line forces under the CSC-InPort.

Quantitatively, under CSC-Ro/Ro, the maximum tension reductions for encounter-side P1, P2, and P3 lines in the STS relative to the CTS are 61.1%, 63.8%, and 64.4%, respectively; under CSC-InPort, the reductions are 71.7%, 72.3%, and 63.3%. These results demonstrate that the STS effectively mitigates peak tensions on the wave-exposed side while enhancing load uniformity.

Mechanistically, the addition of bow anchor chains in the STS increases overall system stiffness, suppresses mooring-induced motions, and shares environmental loads. Consequently, line tensions are reduced, and their distribution is more even, demonstrating the superior mechanical performance and environmental adaptability of the STS across operational scenarios.

Verification of the effectiveness of the STS

To further verify the effectiveness of the STS and validate the accuracy of the numerical models, a field test was conducted under practical operational conditions.

Berthing wharf

The self-propelled deck barges for the field test are berthed at Dock No. 3 of a factory-owned wharf of China North, which is a typical reclaimed, open-sea berth. The quay has a water depth of 6.5 m and is equipped with evenly distributed cylindrical rubber fenders (CY1200 × 600 × 2000 mm) with an energy absorption capacity of 102 kJ and a reaction force of 314 kN at 52.5% deflection. The bollards have a Safe Working Load (SWL) of 100 tons. The ship berthing location and on-site photograph as shown in Figure 9.

Figure 9.

Ship berthing location and on-site photograph.

Field test data acquisition

According to the ship logs, the proposed self-propelled deck barge is moored to the quay at noon on December 12, 2024. An actual view of the ship mooring is presented in Figure 10. Ro/Ro operations are conducted on December 13 from 08:00 to 12:00 h. Afterwards, the cargo is secured until the ship departs the port on the morning of December 17. In this period, a sea state environment acquisition system is installed to collect real-time data on environmental parameters, such as wind, waves, and currents, while ship motion and mooring force monitors record safety evaluation indices for the mooring system. CSC-RoRo and CSC-InPort are statistically analyzed. The obtained results are shown in Table 6.

Figure 10.

Ship T-mooring system at open wharf.

Table 6.

Sea state parameters during T-berthing period.

Condition	Time	Wind speed/(m·s⁻¹/°)	Current speed/(m·s⁻¹/°)	Wave/(m/°)	Wave period/(s)
CSC-RoRo(LC9)	December 13, 2024 08:00–10:00	8.1/225	0.5/180	0.5/225	3.1
CSC-InPort (LC10)	December 13, 2024 12:00–14:00	9.2/225	0.5/180	0.8/225	4.0

Comparison analysis of results

The ship motion responses were continuously monitored during the field measurements at a sampling frequency of 10 Hz using a ship motion monitoring system based on an integrated ship attitude measurement unit. The system integrates RTK positioning, MEMS gyroscopes, tri-axial accelerometers, and geomagnetic sensors to obtain real-time vessel motion data. To improve measurement reliability and data redundancy, additional INEM301 motion sensors were installed at the bow, midship, and stern of the vessel, as illustrated in Figure 11. The measurement accuracy of the system is approximately 0.008 m + 1 ppm (RMS)for surge and sway motion, 0.015 m + 1 ppm (RMS) for heave motion, and 0.01° (RMS) for roll, pitch, and yaw, with an output resolution of 0.001 m and 0.001°.

Figure 11.

Arrangement of the ship motion monitoring system.

Maximum ship motions and mooring line forces were statistically analyzed under CSC-RoRo and CSC-InPor. A comparison between measured and simulated results is presented in Table 7. Under CSC-RoRo conditions, the surge, sway, and heave motions were 0.071, 0.142, and 0.041 m, respectively, while roll, pitch, and yaw remained below 1°. Under CSC-InPort, the maximum surge, roll, and heave motions increased to 0.095, 0.182, and 0.055 m, respectively. The maximum relative errors between measured and simulated motions were 7.04% for surge, sway, and heave, and 7.27% for roll, pitch, and yaw. These discrepancies are within acceptable limits for engineering applications, confirming the reliability of the numerical models.

Table 7.

Comparison between the measured and numerical results for ship movements.

Condition	Data type	Surge/m	Sway/m	Heave/m	Roll/deg	Pitch/deg	Yaw/deg
CSC-RoRo	Measured	0.071	0.142	0.041	0.055	0.025	0.052
	Numerical	0.069	0.132	0.040	0.053	0.024	0.051
	Relative error	2.82%	7.04%	2.44%	3.64%	4.00%	1.92%
CSC-InPort	Measured	0.095	0.182	0.055	0.146	0.128	0.055
	Numerical	0.091	0.179	0.051	0.138	0.122	0.051
	Relative error	4.21%	1.65%	7.27%	5.48%	4.69%	7.27%

The measured and simulated forces of the mooring lines are summarized in Figure 12. The absolute errors between measured and numerical results range from 2.2% to 8.0%, this error falls within the acceptable range. The mooring rope on the windward side bears most of the environmental load acting on the ship, while the mooring force on the leeward side remains low. In addition, the short mooring rope at the stern undergoes higher tension than that at the mid rope, which is due to its greater stiffness and higher nonlinear response.

Figure 12.

Measured and numerical results of the mooring force.

By comparing the numerical simulation results with the measured data from the field test, it is deduced that the simulation model accurately replicates the motion of the moored ship and accurately calculates the distribution of the mooring forces. Thus, the effectiveness of the proposed STS and the reliability of the simulation model are validated.

Discussion

Based on the safety evaluation criteria established in Chapter 2.5 and the motion response analyses presented in Chapter 3, this chapter derives the applicable metocean conditions for STS operations under both Ro/Ro loading and in-port periods. These conditions are obtained by systematically varying sea state parameters in the validated numerical model and evaluating the simulated ship motions and mooring line forces against the pre-defined thresholds.

Applicable metocean conditions for Ro/Ro operations

In compliance with local port regulations under CSC-RoRo, the wind speed for CSC-RoRo is limited to a maximum of 10.8 m/s, and the current velocity is set to a peak of 0.514 m/s at low tide. Under CSC-RoRo conditions, wave heights are varied from 0.4 m to 1.0 m, while the spectral peak period is incrementally increased from 4s until the mooring system fails to satisfy the defined safety criteria. Wave directions are set to the most adverse scenarios of 180° and 270°, as these orientations generate the highest longitudinal and lateral loads on the mooring system.

Figures 13 and 14 show that, for a constant wave height, when the peak period increases, the movement of the ship in the six degrees of freedom (e.g. sway, heave, and roll) exhibits different degrees of increase. At a wave height (H_s) of 0.6 m, the impacts of the period on the sway and roll are the most significant, while at H_s of 0.4 m, it has a more significant impact on heave and roll. This phenomenon can be explained by the dominant impact of the wave height in conditions exhibiting high waves and short period wave, where the impact of the period is minimal. On the contrary, under conditions of low wave height and long period wave, the extended duration of wave energy results in a more significant impact on heave and roll.

Figure 13.

Ship horizontal motion magnitudes under different sea states.

Figure 14.

Ship’s rotational motion under different sea states.

Safe operation criteria for the Ro/Ro operations are established based on the movements control thresholds for the six degrees of freedom of the berthed ship (cf. Table 8), as shown in Table 8.

Table 8.

Safe operation criteria for Ro/Ro operations.

Condition	Surface current (m/s)	Wind speed (m/s)	Wave height (m)	Wave period (s)
CSC-RoRo	0.514	10.8	0.6	4.0
			0.5	6.0
			0.4	8.0

Applicable metocean conditions for In-Port period

Figure 15 shows that when the wave height (H_s) and period (T_p) increase, the forces on the mooring lines and anchor chains significantly increase, and they are unevenly distributed. The forces on the stern mooring rope and bow mooring chain are much higher than those on the other mooring lines, which indicates a high risk of overloading. Under conditions of high wave height or long-period waves, particular attention should be paid to the forces on these overload-prone mooring lines to ensure that their loads remain within the SWL limits.

Figure 15.

Mooring line force under different sea states.

Based on the T-mooring safety evaluation criteria presented in Section 4.1, 50% of the MBL is considered as the control threshold for mooring line force. The safe mooring criteria for the T-mooring system under In-Port conditions are then determined and presented in Table 9.

Table 9.

Safety criteria for In-Port.

Condition	Surface current (m/s)	Wind speed (m/s)	Wave height (m)	Wave period (s)
CSC-InPort	0.514 m/s	10.8	1.0	4.0
			0.8	6.0
			0.6	12.0

Based on the ships T–mooring safety evaluation criteria in Section 4.1, 50% of the MBL is set as the control threshold for mooring line force. The safe mooring criteria for the T-mooring system under CSC-InPort are determined and presented in Table 9.

Conclusion

Under exposed factory-owned open wharf conditions, conventional T-mooring systems frequently fail to satisfy the stringent motion limits required for Ro/Ro cargo loading and are susceptible to mooring line overload. In this study, the performance and applicability of a strengthened T-mooring system designed for self-propelled deck barges were systematically investigated. Numerical simulations and field measurements were employed to comparatively analyze ship motions, mooring line forces, and to verify the effectiveness of the STS. Based on safety evaluation criteria for T-mooring systems, the applicable metocean conditions for the STS were further defined for both Ro/Ro operations and in-port periods.

The main findings are summarized as follows:

(1) Compared with CTS, the STS markedly suppresses surge, sway, and yaw motions under critical Ro/Ro and in-port conditions. Especially, sway motion during beam sea conditions of CSC-RoRo was reduced by up to 74.6%. Moreover, the addition of bow anchor chains improved load distribution, reducing peak tensions of encounter-side mooring lines by more than 72.3%.

(2) Statistical analyses of the ship movements indicate that vessel motions are primarily governed by wave height during short-period seas, whereas wave period becomes dominant under low wave heights and long-period seas.

(3) Statistical analysis of the mooring force shows that increasing the encounter angle intensifies rolling, pitch, and yaw motions, amplifying the non-uniform distribution of mooring line forces. The stern mooring rope and bow mooring chain experience significantly higher forces than other positions, highlighting the need for careful monitoring of ship sway and mooring line tensions during operations.

The study only considered typical metocean conditions and did not examine extreme events or long-term fatigue on mooring lines. Future works could explore a wider range of environmental scenarios, optimize mooring configurations, and integrate real-time monitoring systems to further enhance operational safety and reliability.

Footnotes

Handling Editor: Mingyang Zhang

ORCID iD

Rongjie Yu

Author contributions

Hailiang Cheng: Software, filed test, data curation, writing original draft, visualization. Jian Chen: Supervision, writing review and editing. Rongjie Yu: Conceptualization, methodology, writing review and editing, validation.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the financial supports provided by the Sponsored by China COSCO Shipping Group (24PRRD06).

Declaration of conflicting interests

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

References

Tanabe

Miyake

. Safety design approach for onshore modularized LNG liquefaction plant. J Loss Prev Process Ind 2010; 23(4): 507–514.

Yang

. Analysis on site selection of plant modularization construction basement. Nonferr Met Eng Res 2013; (1): 37–39. (in Chinese)

Tak

Taghaddos

Mousaei

, et al. Evaluating industrial modularization strategies: local vs. overseas fabrication. Automat Constr 2020; 114: 103175.

Wrigley

Wood

O’Neill

, et al. Off-site modular construction and design in nuclear power: a systematic literature review. Progr Nucl Ener 2021; 134: 103664.

Ham

Roh

. Dynamic analysis of block offloading using self-propelled modular transporters. Automat Constr 2018; 96: 411–432.

Zhu

, et al. Optimization solutions for self-propelled modular transporter (SPMT) load-outs based on ballast simulation. Ocean Eng 2020; 206: 107355.

Cheng

Fan

, et al. Mooring design of offshore aquaculture platform and its dynamic performance. Ocean Eng 2023; 275: 114146.

Huang

Zhang

. Concept design of side-by-side mooring of ships for large outfitting wharves. Port Waterw Coast Eng 2024; 61(3): 8–12. (in Chinese)

Wang

, et al. Research on design and optimization of mooring mode for large ships. Ships 2020; 31(2): 11. (in Chinese)

10.

Gao

, et al. Time domain analysis of ship dock mooring under the combined action of wind and wave. Ship Sci Technol 2023; 45(6): 78–83. (in Chinese)

11.

Wang

Liu

, et al. Numerical simulation of influence of cable material and diameter on mooring ship motion. Water Transp Eng 2022; (11): 43–49. (in Chinese)

12.

Rosa-Santos

Taveira-Pinto

Veloso-Gomes

. Experimental evaluation of the tension mooring effect on the response of moored ships. Coast Eng 2014; 85: 60–71.

13.

Shi

Zhang

Chen

, et al. Analysis of influence of pretension on maximum tension of mooring cable and ship displacement. Marine Eng 2023; 52(5): 58–63. (in Chinese)

14.

Abdelwahab

Pinheiro

Santos

, et al. Experimental investigation of wave severity and mooring pretension on the operability of a moored tanker in a port terminal. Ocean Eng 2024; 291: 116243.

15.

Wen

Zhu

Ren

, et al. Experimental study of multi-buoy-assisted moored ship motion at open berth. Marine Struct 2023; 92: 103496.

16.

Liu

Liang

. Study on ship mooring conditions in terms of unshieled terminal under action of long periodic waves. Port Waterw Offsh Eng 2025; 62(1): 18–23.

17.

Shi

Zhang

Yang

. Experimental study of the motion responses of a large mooring (LNG) ship in the waves with grand period. J Ship Mech 2012; 16(9): 980–989.

18.

Shen

Zhao

Liu

, et al. Research of wave period effect on the dynamic response characteristics of a small ship. J Ship Mech 2022; 3: e026. (in Chinese)

19.

Wang

Yang

Sun

, et al. Experimental study on dynamic response characteristics of moored ships. Ship Eng 2024; 46(1): 58–64. (in Chinese)

20.

Wang

Zhu

Shen

, et al. Dock mooring model test of 30000 DWT bulk carrier. Ship Eng 2020; 42(8): 55–58+121. (in Chinese)

21.

Sakakibara

Kubo

. Characteristics of low-frequency motions of ships moored inside ports and harbors on the basis of field observations. Marine Struct 2008; 21(2–3): 196–223.

22.

Dong

Yan

Zheng

, et al. Experimental investigation on the hydrodynamic response of a moored ship to low-frequency harbor oscillations. Ocean Eng 2022; 262: 112261.

23.

Zhu

, et al. Experimental and numerical investigation of dynamic characteristics and safe mooring criteria of moored outfitting ships under swell conditions. Ocean Eng 2024; 314: 119771.

24.

Yan

Zheng

Sun

, et al. Numerical evaluation of the tension mooring effects on the hydrodynamic response of moored ships under harbor oscillations. Ocean Eng 2023; 288: 116127.

25.

Ziylan

Nas

. A quasi-static mooring analysis approach for berthed ships. Ocean Eng 2024; 309: 118488.

26.

De Carvalho

AVL

Campello

Franzini

, et al. An assessment of mooring systems’ forces of ships berthed at dolphins. Ocean Eng 2022; 253: 111090.

27.

Tang

. Physical model test method for mooring of heavy cargo Ro/Ro docks. Chin Harb Constr 2021; 41(7): 5.

28.

Figuero

Sande

Peña

, et al. Operational thresholds of moored ships at the oil terminal of inner port of A Coruña (Spain). Ocean Eng 2019; 172: 599–613.

29.

Yuan

Wang

Zhang

, et al. Mooring limit conditions for open quays in coastal ports. Voyag Chin 2024; 47(S1): 74–81.

30.

American Petroleum Institute. Design and analysis of station Kee systems for floating structures. American Petroleum Institute, 2005.

31.

DNV

. DNVGL-NT-001: marine operations and marine warranty (NT-001). DNV GL AS, 2021.

32.

Ministry of Transport of China. Code for design of general layout of sea ports (JTS 165-2013). China Communications Press, 2013.

33.

PIANC. Criteria for acceptable movement of ships at berths. Report of WorkingGroup MarCom WG212. PIANC General Secretariat, 2023.

34.

OCIMF. Mooring equipment guidelines: (MEG4). Witherby SeamanshipInternational Ltd, 2018.