Designing the Engineering Parameters of the Sea Ice Based on a Refined Grid in the Southern Bohai Sea

Abstract

The current standard for sea ice engineering in the Bohai Sea implements a 1/4° grid method, which cannot satisfy the safety of oil and gas activities in the southern Bohai Sea, and therefore more detailed information on ice conditions and a more refined ice zone division are necessary. In the present study, up to 1/12° resolution sea ice characteristic data (period, thickness, concentration, and strength) were obtained based on the NEMO-LIM2 ice–ocean coupling model. On this basis, the design sea ice strength parameters were derived with different return periods from 1 to 100 years. Among the total of 53 grids, the mean ice periods in the southern Bohai Sea from 1951 to 2022 were 2–35 days, the mean ice concentration values were 8.3–64.6%, and the mean ice thicknesses were 2–15 cm. The design uniaxial compressive strengths and shear strengths at almost all grids exceeded 2.00 MPa and 1.00 MPa for return periods over 20 years, respectively. The design flexural strengths for the 100-year return period ranged from 463 to 594 kPa. For the 100-year return period scenario, all grids exhibited design tensile strengths exceeding 200 kPa. Across the southern Bohai Sea, the most severe ice conditions occur in nearshore zones, and the ice conditions display a distinct spatial gradient with Bohai Bay > offshore deep-water areas > Laizhou Bay. The mean ice thickness, concentration, design flexural and tensile strengths derived in this study were lower compared to the ice parameters suggested in the current standard, and design uniaxial compressive and shear strengths derived here were comparable to those suggested in the current standard. The refined grid used here captures more detailed spatial variations in the design strength values of sea ice engineering parameters in the southern Bohai Sea, providing more accurate data support for the anti-ice design of marine structures.

1. Introduction

The Bohai Sea serves as a critical industrial zone in China, supporting dense concentrations of infrastructure for maritime transportation, petroleum operations, and power generation. Located at relatively high latitudes, the region experiences frequent winter incursions of cold air masses, triggering annual ice formation. Recent intensification of extreme climate events, combined with rapid coastal development of ports and oilfields, has significantly altered the sea ice spatiotemporal distribution.

For offshore structures operating in ice-covered waters, understanding the mechanical properties of sea ice is essential for evaluating ice loads and ensuring structural safety [1]. Ice–structure interactions depend strongly on the ice strength and failure behavior, which vary with temperature, salinity, and internal structure of ice [2]. Early research by Li et al. provided a foundational overview of Bohai Sea ice mechanical properties, summarizing long-term observational data to define key design parameters such as strength values and recurrence intervals [3]. Since then, a range of mechanical properties, including uniaxial compressive, flexural, tensile, and shear strength, have been systematically investigated through both laboratory and in situ experiments. Ji et al. conducted flexural and shear experiments across Bohai coastal sites, revealing rate-dependent and brine volume-related strength degradation [4,5]. Uniaxial compressive strength was comprehensively investigated by Wang et al., who conducted over 400 tests across 12 Bohai coastal sites, establishing empirical relationships with temperature, brine volume, and stress rate [6]. In response to climate-induced changes in sea ice formation, particularly increased air content within sea ice, porosity has recently emerged as a critical internal factor in strength modeling [7]. Li et al. proposed a three-dimensional framework linking uniaxial compressive strength with sea ice porosity and strain rate [8]. Chen et al. used Brazilian splitting tests with digital image correlation to assess tensile strength in Bohai Sea ice, finding a clear negative correlation of sea ice tensile strength with porosity [9]. However, these experimental studies were conducted at relatively isolated sites. Although they provided valuable insights into the intrinsic mechanical behavior of sea ice, they have not been systematically linked to large-scale spatial patterns or regional ocean–atmosphere conditions in the Bohai Sea.

With continuous advancements in remote sensing monitoring and numerical modeling, research on the distribution and seasonal evolution of sea ice in the Bohai Sea has become increasingly refined. Sun et al. integrated multi-source datasets, including AVHRR, MODIS, and GOCI, to systematically analyze sea ice area and thickness across major sub-regions in the Bohai Sea over the past 30 years [10]. Their results highlighted the dominant role of Liaodong Bay in regional ice formation and demonstrated strong correlations between ice conditions and cumulative freezing/melting degree days. Yan et al. reported a slight upward trend (~1.38% yr⁻¹) in Bohai Sea ice area from 1988 to 2015, contrary to the general decline observed in polar regions [11]. Ouyang et al. found strong negative correlations between mean ice thickness and mean air temperature, and between median ice extent and negative accumulated temperature in the Bohai Sea [12]. Yan et al. used a multivariate regression approach to extend sea ice area reconstruction to 1958–2015 [13]. Based on long-term sea ice severity data, Zheng et al. revealed a regime shift from heavy to light ice conditions of the Bohai Sea [14]. Most existing studies concentrate on the variations in ice thickness and area, and there remains a lack of distribution of sea ice strength data for engineering applications.

Marine structures in ice-covered waters require information on key ice parameters (e.g., thickness, period, strength) in planning, design, and construction. Current Bohai Sea ice engineering applications derive design ice thickness and strength primarily from the guideline of “Sea Ice Conditions and Application Regulations for China Seas” issued by the China National Offshore Oil Corporation (CNOOC) in 2002 [15]. Over the past two decades, significant alterations in the spatiotemporal distribution of sea ice in the Bohai Sea have probably emerged, driven by extensive coastal development with consequent shoreline modifications and amplified climate change effects. With numerous platforms approaching service-life limits, new constructions and replacements demand urgent attention. This necessitates precise regional assessment of engineering ice parameters across oil and gas development zones, establishing partition-specific design criteria for ice loads. Such refinement ensures winter operational safety and optimizing structural costs in Bohai ice management strategies.

To support the design of offshore infrastructure in ice-covered waters of the Bohai Sea with high spatial resolution, previous work partitioned the region into a refined 1/12° grid and derived key sea ice parameters, including ice period, thickness, concentration, temperature, and salinity [16]. However, the grid-level sea ice strength data remains unavailable. Indeed, the lack of gridded sea ice strength data extends beyond the Bohai Sea to the Arctic Ocean, obscuring the spatiotemporal evolution of Arctic sea ice strength and complicating engineering design for Arctic offshore structures. Arctic sea ice strength exhibits significant seasonal variability. Sea ice strength is typically obtained by field and experiment measurements. Based on numerous mechanical tests, scholars have proposed influencing factors and empirical relationships for sea ice strength [17,18,19]. In recent years, researchers have attempted to investigate the spatiotemporal distribution of sea ice flexural strength across the Arctic Ocean. Chai et al. utilized freezing degree-days to derive ice thickness and thermohaline properties, subsequently applying empirical formulae to assess the statistical characteristics of level-ice flexural strength at four critical locations along the Northeast Passage during winter [20]. Tarovik et al. integrated meteorological, hydrological, and sea ice thermodynamic data to estimate brine volume fraction and flexural strength, evaluating spatiotemporal distributions across nine Arctic sea areas along the Northeast Passage route [21]. These studies of Arctic ice gridded strength provide valuable scientific references for developing analogous gridded sea ice strength models in the Bohai Sea.

Building on previous work [16], the present study addresses the impacts of climate change on engineering in the Bohai Sea ice zone and provides gridded sea ice mechanical parameters for the region. Focusing specifically on the southern Bohai Sea, where critical infrastructure like the Shengli Oilfield is located, the key engineering parameters of sea ice are derived including flexural strength, uniaxial compressive strength, shear strength, and tensile strength. Crucially, actionable design benchmarks for ice mechanical properties are also established here, advancing the research toward direct engineering implementation.

2. Materials and Methods

2.1. Study Area

The Bohai Sea (37°70^′–41°00^′ N, 117°35^′–121°10^′ E), situated in the mid-latitude monsoon zone of the Northern Hemisphere, represents a semi-enclosed inland sea extending northwestward from the Yellow Sea. Ice formation in the Bohai Sea initiates in late November to early December, progressing southward from shallow coastal zones to deeper offshore areas. The ablation phase commences in mid-to-late February with northward retreat from deep southern basins to shallow northern coasts, culminating in complete ice clearance by mid-March, yielding a 3–4-month ice season.

The southern Bohai Sea (Bohai Bay and Laizhou Bay) hosts numerous offshore oil and gas platforms, notably within the Shengli Oilfield operational waters. To ensure the safety of the platforms during ice season, CNOOC guidelines partition the southern Bohai Sea into sub-grids with assigned design ice parameters [15]. However, the standardized grid system, originally developed for pan-Bohai Sea ice conditions, proves inadequate for the Shengli Oilfield waters due to its insufficient resolution for local operational demands. Our study implements a multi-criteria grid refinement scheme (Figure 1) tailored to the critical area. Deep-water zones (grids 1–6, 47, 51) maintain quarter-degree (1/4° × 1/4°) grids aligned with the current guideline. Nearshore shallow waters (grids 7–14, 43–50, 52–53) adopt 1/12° resolution, with adjacent grids merged based on spatial homogeneity in hydrological and ice regime characteristics. High-priority operation areas implement non-merged 1/12° grids to preserve critical spatial details (grids 15–42). The relevant results of ice condition characteristics in the southern Bohai Sea will be presented based on this new ice zone division hereafter.

2.2. Sea Ice Concentration, Thickness, and Duration

Sea ice concentration, level ice thickness, and sea ice duration were derived based on the NEMO-LIM2 ice–ocean coupling model. The model was generated here to provide detailed information on the ice characteristics in the Bohai Sea from 1951 to 2022 with a refined ice zone division [16]. The model domain is located in a spatial range of 35–41° N, 117–127° E, covering the entire Bohai Sea with a spatial resolution of 1/12°. The topographic data in the NEMO model uses the ETOPO1 public data set, with a spatial resolution of 1 km, which is interpolated into the NEMO model grid through bilinear interpolation. The ice–ocean coupling model can finely simulate the ocean and sea ice environments near complex islands and shorelines.

It should be stated that compared to LIM2 model, LIM3 model employs a five-category ice thickness scheme, which aims to improve performance in high-latitude ice-covered regions by better representing ice thickness heterogeneity [22]. However, the Bohai Sea represents the lowest-latitude ice-covered region in the Northern Hemisphere. All sea ice here is first-year ice, and ice thickness rarely exceeds 0.5 m. Consequently, the complex ice thickness categorization scheme of LIM3 cannot be fully utilized in the Bohai Sea.

2.3. Sea Ice Strength

Currently, there are no theoretical formulae for calculating sea ice strength; existing formulae are empirical. These empirical equations are in simple forms but exhibit direct physical meaning, clearly indicating that sea ice strength is directly related to specific ice parameters. To guide oil and gas production operations in ice-covered regions of the Bohai Sea, the CNOOC guideline provides recommended methodologies for calculating sea ice load parameters in the Bohai Sea [15]. The sea ice uniaxial compressive strength, flexural strength, shear strength, and tensile strength were calculated here based on the regulation.

The sea ice uniaxial compressive strength was determined using Equation (1).

$${\sigma }_{\mathrm{c}}=1.77-0.13T_{\mathrm{i}}$$

(1)

where T_i is sea ice temperature (°C), and σ_c is maximum uniaxial compressive strength of level ice loaded horizontally to ice surface (MPa).

The sea ice shear strength was determined using Equation (2).

$$\tau ={\displaystyle \raisebox{1ex}{${\sigma }_{\mathrm{c}}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

(2)

where τ is sea ice shear strength (MPa).

The sea ice flexural strength was determined using Equation (3).

$${\sigma }_{\mathrm{f}}=340-64T_{\mathrm{i}}$$

(3)

where σ_f is sea ice flexural strength (kPa).

The sea ice tensile strength was determined using Equation (4).

$${\sigma }_{\mathrm{t}}=95+50\left|T_{\mathrm{i}}\right|$$

(4)

where σ_t is sea ice tensile strength (kPa).

As shown in Equations (1)–(4), sea ice temperature is a key parameter to determine sea ice strength. In the CNOOC regulation [15], according to the characteristics of sea ice in the Bohai Sea, the ice temperature was determined using Equation (5).

$$T_{\mathrm{i}}=(T_{\mathrm{ia}}+T_{\mathrm{iw}})/2-273.15$$

(5)

where T_ia and T_iw are sea ice temperatures (K) at the top and bottom surfaces of the ice cover determined by Equations (6) and (7).

$$T_{\mathrm{ia}}={\displaystyle \frac{\lambda (-1.4-T_{\mathrm{a}})}{4.7}}+T_{\mathrm{a}}$$

(6)

$$T_{\mathrm{iw}}=-1.4-{\displaystyle \frac{\lambda (-1.4-T_{\mathrm{a}})}{125}}$$

(7)

where λ is thermal conductivity coefficient of sea ice (kJm⁻²·h⁻¹·K⁻¹) determined using Equation (8), T_a is air temperature (K). T_a was adopted from Climate Forecast System Reanalysis data issued from the National Centers for Environmental Prediction (NCEP).

$$\lambda ={\left(0.221+{\displaystyle \frac{H}{2}}\right)}^{-1}$$

(8)

where H is ice thickness (m).

2.4. Sensitivity Analysis

The primary inputs of NEMO-LIM2 model include shortwave/longwave radiation, 2 m air temperature, 2 m humidity, 10 m wind fields, and precipitation. Comprehensive sensitivity tests have been performed in the previous work of [23]. Through observational comparisons, sea ice thermodynamic and dynamic parameters were calibrated to ensure model stability and applicability in the Bohai Sea. Sea ice strength values were calculated using standardized formulae recommended by established specifications. As these represent fundamental principles rather than adjustable parameters, sensitivity analysis would not yield meaningful insights.

2.5. Model Verification

The details on the configuration of the model were reported in the previous work [16]. Comparisons between observed and simulated sea ice thickness and duration showed high accuracy of the model. The correlation coefficient between the hindcasting sea ice thickness and observations was above 0.60, with an absolute error of less than 4.0 cm. The hindcasting data could better reflect the distribution of ice periods in mild and severe ice years. Sea ice strength values were not directly validated, as they were derived from ice thickness and air temperature. Therefore, we focused our verification efforts on ice thickness, which plays a key role in the estimation of sea ice strength. Sea ice concentration validation was also omitted due to methodological differences between conventional coastal station observations and model-derived estimates. It was found that there is a good consistency between ice thickness and concentration, so the validation effect of ice thickness can also represent the accuracy of other sea ice parameters to a certain extent [16].

2.6. Return Period Design

The sea ice strength was designed using the Pearson-III (P-III) distribution with different return periods (100, 50, 25, 20, 10, 5, 2, 1 years). When determining the design ice engineering parameters, an excessively small estimate may lead to damage to marine structures, while an excessively large estimate can result in increased costs. The biggest advantage of the P-III distribution is its large elasticity. In most cases, it can be fitted well with the theoretical curve and empirical frequency points by repeatedly fitting the line or adjusting the coefficient of variation and mean appropriately. The probability density function of P-III distribution is Equation (9).

$$f(x)={\displaystyle \frac{{\beta }^{\alpha }}{\mathsf{\Gamma }(\alpha )}}{(x-x_0)}^{\alpha -1}\exp [-\beta (x-x_0)]$$

(9)

where Γ(·) is the Gamma function, and α, β as well as x₀ are the shape, scale, and position coefficients, respectively, related to the statistical parameters of the random variables:

$$\alpha ={\displaystyle \frac{4}{C_s^2}}$$

(10)

$$\beta ={\displaystyle \frac{2}{\overline{x}{C}_v{\mathrm{C}}_s}}$$

(11)

$$x_0=\overline{x}(1-{\displaystyle \frac{2C_v}{{\mathrm{C}}_s}})$$

(12)

where C_s is skewness coefficient, C_v is variation coefficient, and $\overline{x}$ is the average.

Therefore, the determination of the probability density function of P-III distribution is transformed into the determination of the statistical parameters. In general, the observations of ice parameters are not long enough, the empirical distribution based on observations must be extended to determine the design ice parameters. The preliminary values of the statistical parameters were obtained first using the observation data, and an empirical distribution curve was then depicted. Afterwards, the statistical parameters were adjusted until the corresponding empirical distribution curve fitted well with the observations. The statistical parameters after adjustment were selected to determine the final P-III distribution, and the design ice parameters were determined from corresponding cumulative frequency density curve according to the return period.

3. Results

3.1. Ice Duration

Accurate assessment of ice duration is important for engineering design and operational safety in ice-covered waters. The ice duration is defined as the temporal span between initial ice formation and final ice clearance (measured in days). Figure 2 presents the spatial distributions of average ice duration across study regions. The ice duration exhibited a decreasing gradient across the study area, with the longest persistence at the coastal Bohai Bay, intermediate duration at the coastal Laizhou Bay, and the shortest in central deep basins.

Table 1. The maximum, minimum, and average ice periods from 1951 to 2022 in each grid division.

Grid No.	Maximum/d	Minimum/d	Average/d	Grid No.	Maximum/d	Minimum/d	Average/d
1	80	0	35	28	64	0	5
2	80	0	33	29	64	0	5
3	74	0	25	30	64	0	5
4	71	0	15	31	61	0	3
5	69	0	9	32	61	0	3
6	63	0	4	33	63	0	4
7	81	0	33	34	59	0	6
8	82	0	32	35	59	0	6
9	82	0	31	36	59	0	7
10	81	0	31	37	52	0	2
11	81	0	30	38	52	0	3
12	79	0	30	39	62	0	3
13	80	0	31	40	63	0	4
14	78	0	29	41	59	0	4
15	73	0	22	42	59	0	6
16	73	0	22	43	51	0	2
17	73	0	22	44	47	0	3
18	73	0	19	45	59	0	10
19	73	0	19	46	58	0	10
20	73	0	19	47	60	0	10
21	73	0	22	48	62	0	14
22	73	0	22	49	67	0	16
23	73	0	22	50	67	0	18
24	66	0	7	51	67	0	18
25	65	0	6	52	66	0	19
26	60	0	5	53	68	0	18
27	64	0	5

provides the maximum, minimum, and average ice duration of each grid division. The Diaokou nearshore area demonstrated prolonged severe ice periods compared to adjacent waters, attributable to shallow bathymetry facilitating ice grounding and obstruction effects from the eastern No.168 artificial island limiting ice drift. The western sectors showed longer ice durations than eastern counterparts. The maximum ice period days and the average ice period days near Dongying Port were short.

3.2. Level Ice Thickness

Precise quantification of ice thickness is critical for structural integrity assessments, as it directly governs ice load on offshore infrastructure. Figure 3 presents the spatial distributions of maximum ice thickness and mean ice thickness in the southern Bohai Sea from 1951 to 2022. The maximum ice thickness across the study area was 13–36 cm, and the mean ice thickness was 2–15 cm. The southwestern Bohai Bay and western Laizhou Bay exhibited significantly greater maximum ice thickness. Diaokou coastal waters also showed a high maximum ice thickness. The southern Bohai Bay consistently maintained a mean ice thickness > 10 cm, exceeding the mean ice thickness in the western Laizhou Bay.

The refined grid division in this study corresponds to grids No. 9 and No. 10 in the original regulation. Under the original zoning, both grids No. 9 and No. 10 had a maximum ice thickness of 35 cm, with average thicknesses of 18 cm and 15 cm, respectively. Figure 4 shows the changes in ice thickness between the new zoning and original regulations, revealing that both maximum and average ice thicknesses decreased under the refined zoning, with relatively more significant reductions along the western coastal areas of Laizhou Bay.

3.3. Sea Ice Concentration

As a primary driver of ice dynamics, accurate spatial mapping of sea ice concentration is critical for quantifying ice–structure interaction on platforms, wind turbines, and subsea pipelines. Figure 5 presents the spatial distributions of maximum and mean sea ice concentration in the southern Bohai Sea from 1951 to 2022. Bohai Bay exhibited higher sea ice concentrations, followed by Laizhou Bay. In the southern Bohai Bay and southwestern Laizhou Bay, the maximum sea ice concentration exceeded 90% across most areas, with sea ice concentrations reaching up to 99.8% in the Feiyantan offshore area. Regarding average sea ice concentration, the Bohai Bay region generally showed higher values than the Laizhou Bay region.

According to the original regulation, the maximum sea ice concentrations for grids No. 9 and No. 10 are 94.4% and 85.7%, respectively, with average concentrations of 63.4% and 43.8%. As shown in Figure 6, in this study, the maximum sea ice concentration in the southern Bohai Bay showed values essentially consistent with the original standard; the maximum sea ice concentration in the eastern sections of the study area were slightly below the original standards; and the maximum sea ice concentration in the southwestern Laizhou Bay exceeded the standard values. For average sea ice concentration, all zones in the southern Bohai Sea demonstrated lower values than the original standard, and the most significant reduction occurred near the Dongying Port area.

The decrease in sea ice concentration near the Dongying Port area compared to the values in the original standard is primarily caused by two reasons. First, the CNOOC standard was implemented and published in 2002. Over the past 15 years, sea ice severity in the China Seas has exhibited an overall declining trend. This regional trend is a key factor contributing to the generally lower average sea ice concentrations found in our results for the southern Bohai Sea compared to the baseline values established in the original standard. Second, the CNOOC standard utilized shore-based observation data from the Diaokou location. Diaokou is situated within a shallow river channel. Sea ice concentration within such confined, shallow riverine environments is typically higher than in the adjacent open sea. Consequently, the sea ice concentration values adopted in the original standard for the Dongying Port area, based on Diaokou data, were inherently biased upwards due to this localized effect. In contrast, the data used in our analysis was derived entirely from NEMO numerical model results. Therefore, our results for Dongying Port reflected the open-water sea ice conditions more accurately, thus avoiding the overestimation presented in the original standard data source for this specific area.

3.4. Sea Ice Uniaxial Compressive Strength

Sea ice uniaxial compressive strength governs the ice loads against vertical structures in ice-covered waters. Figure 7 presents the spatial distributions of design sea ice maximum uniaxial compressive strength in the southern Bohai Sea. The design values of maximum sea ice uniaxial compressive strength exhibited a distinct spatial gradient, decreasing sequentially from the Bohai Bay (highest values) through deep-water area (medium values) to the Laizhou Bay (lowest values), with the Bohai Bay bottom and Dongying Port areas showing the most severe strength values.

Table A1. The design uniaxial compressive strength (in MPa) of sea ice for different return periods.

Grid No.	Return Period/Year
	100	50	25	20	10	5	2	1
1	2.14	2.12	2.09	2.08	2.05	2.01	1.93	1.88
2	2.13	2.11	2.08	2.07	2.05	2.01	1.95	1.89
3	2.14	2.12	2.09	2.08	2.05	2.02	1.95	1.89
4	2.14	2.12	2.09	2.08	2.06	2.02	1.95	1.89
5	2.14	2.11	2.09	2.08	2.05	2.02	1.95	1.89
6	2.06	2.04	2.02	2.02	1.99	1.96	1.90	1.85
7	2.27	2.24	2.21	2.20	2.16	2.12	2.04	1.96
8	2.28	2.25	2.22	2.21	2.17	2.13	2.05	1.97
9	2.28	2.25	2.22	2.21	2.18	2.13	2.05	1.97
10	2.28	2.26	2.23	2.21	2.18	2.13	2.05	1.98
11	2.28	2.25	2.22	2.21	2.18	2.13	2.05	1.98
12	2.28	2.26	2.23	2.22	2.18	2.13	2.05	1.98
13	2.29	2.26	2.23	2.22	2.18	2.14	2.06	1.98
14	2.22	2.19	2.16	2.15	2.12	2.08	2.01	1.94
15	2.22	2.19	2.17	2.16	2.12	2.09	2.01	1.95
16	2.21	2.19	2.16	2.15	2.12	2.08	2.01	1.94
17	2.21	2.19	2.16	2.15	2.12	2.08	2.01	1.94
18	2.22	2.19	2.17	2.16	2.13	2.09	2.01	1.95
19	2.22	2.19	2.17	2.16	2.13	2.09	2.01	1.95
20	2.10	2.08	2.05	2.05	2.02	1.99	1.92	1.87
21	2.10	2.08	2.06	2.05	2.02	1.99	1.93	1.87
22	2.10	2.08	2.05	2.05	2.02	1.99	1.92	1.87
23	2.10	2.08	2.06	2.05	2.02	1.99	1.93	1.87
24	2.10	2.08	2.06	2.05	2.03	1.99	1.93	1.88
25	2.10	2.08	2.06	2.05	2.02	1.99	1.93	1.87
26	2.10	2.08	2.06	2.05	2.02	1.99	1.93	1.87
27	2.11	2.09	2.06	2.06	2.03	2.00	1.93	1.88
28	2.10	2.08	2.06	2.05	2.02	1.99	1.93	1.87
29	2.17	2.15	2.12	2.11	2.08	2.04	1.97	1.91
30	2.17	2.15	2.12	2.11	2.08	2.04	1.97	1.91
31	2.04	2.02	2.00	2.00	1.97	1.94	1.88	1.83
32	2.04	2.02	2.00	1.99	1.97	1.94	1.88	1.83
33	2.04	2.02	2.00	1.99	1.96	1.93	1.88	1.83
34	2.05	2.03	2.01	2.00	1.97	1.94	1.88	1.83
35	2.05	2.03	2.01	2.00	1.97	1.94	1.88	1.83
36	2.04	2.03	2.01	2.00	1.97	1.94	1.88	1.83
37	2.04	2.03	2.01	2.00	1.97	1.94	1.89	1.83
38	2.04	2.02	2.00	1.99	1.97	1.94	1.88	1.83
39	2.04	2.02	2.00	1.99	1.97	1.94	1.88	1.83
40	2.05	2.03	2.01	2.00	1.98	1.95	1.89	1.84
41	2.05	2.03	2.01	2.00	1.98	1.95	1.89	1.84
42	2.05	2.03	2.01	2.00	1.97	1.94	1.89	1.83
43	2.05	2.03	2.01	2.00	1.98	1.95	1.89	1.84
44	2.05	2.03	2.01	2.01	1.98	1.95	1.89	1.84
45	2.05	2.03	2.01	2.00	1.97	1.94	1.89	1.84
46	2.05	2.03	2.01	2.00	1.98	1.94	1.89	1.84
47	2.02	2.00	1.98	1.97	1.95	1.92	1.87	1.82
48	2.04	2.02	2.00	1.99	1.97	1.94	1.88	1.83
49	2.04	2.02	2.00	1.99	1.97	1.94	1.88	1.83
50	2.04	2.02	2.00	1.99	1.97	1.94	1.88	1.83
51	2.02	2.00	1.98	1.98	1.95	1.92	1.87	1.82
52	2.02	2.00	1.98	1.97	1.95	1.92	1.86	1.81
53	2.02	2.00	1.98	1.97	1.95	1.92	1.86	1.82

in Appendix A specifies the design strength values for different return periods. The design strength values at almost all grids exceeded 2.00 MPa for return periods over 20 years. The design strength values in the Bohai Bay and Dongying Port areas maintained >2.00 MPa for 10-year and 5-year return periods while the design strength values at other regions fell below 2.00 MPa. For 2-year and 1-year return periods, the design strength values at almost all grids were <2.00 MPa.

3.5. Sea Ice Shear Strength

Sea ice shear strength is another important parameter determining the ice load during ice–structure interaction. Figure 8 presents the spatial distributions of design sea ice shear strength in the southern Bohai Sea. Since the shear strength was determined based on the uniaxial compressive strength, the spatial variation pattern of design sea ice shear strength in the southern Bohai Sea was consistent with the distribution characteristics of the design uniaxial compressive strength.

Table A2. The design shear strength (in kPa) of sea ice for different return periods.

Grid No.	Return Period/Year
	100	50	25	20	10	5	2	1
1	1071	1059	1045	1040	1024	1004	965	938
2	1063	1053	1041	1037	1023	1006	973	945
3	1069	1058	1046	1042	1027	1009	976	947
4	1070	1059	1047	1042	1028	1010	977	947
5	1068	1057	1045	1040	1026	1008	974	944
6	1032	1022	1012	1008	996	980	951	926
7	1133	1119	1104	1099	1081	1059	1018	981
8	1140	1126	1111	1105	1087	1065	1023	986
9	1141	1127	1112	1106	1088	1066	1024	987
10	1142	1128	1113	1107	1089	1067	1025	988
11	1141	1127	1112	1107	1088	1067	1025	988
12	1142	1128	1113	1108	1089	1067	1026	989
13	1143	1130	1115	1109	1091	1069	1028	991
14	1108	1096	1082	1077	1061	1042	1004	972
15	1109	1096	1083	1078	1062	1043	1005	973
16	1107	1094	1081	1076	1060	1041	1003	971
17	1107	1094	1081	1076	1060	1041	1003	971
18	1109	1097	1084	1079	1063	1043	1006	973
19	1109	1097	1084	1079	1063	1043	1006	973
20	1049	1039	1027	1023	1010	993	962	934
21	1051	1041	1029	1025	1012	995	964	936
22	1049	1039	1027	1023	1010	993	962	934
23	1051	1041	1029	1025	1012	995	964	936
24	1052	1042	1031	1027	1013	997	965	938
25	1050	1040	1028	1025	1011	994	963	935
26	1050	1039	1028	1024	1010	994	963	935
27	1053	1043	1032	1028	1014	998	966	939
28	1051	1041	1030	1026	1012	996	964	937
29	1085	1073	1060	1056	1040	1022	986	955
30	1085	1073	1060	1056	1040	1022	986	955
31	1021	1012	1001	998	985	970	941	916
32	1019	1010	999	996	983	968	940	914
33	1018	1009	999	995	982	967	939	913
34	1023	1014	1003	999	987	972	942	917
35	1023	1013	1003	999	986	971	942	917
36	1022	1013	1003	999	986	971	942	917
37	1022	1013	1003	999	986	971	943	917
38	1021	1011	1001	997	985	970	941	916
39	1020	1011	1000	997	984	969	940	915
40	1025	1015	1005	1001	989	973	944	919
41	1024	1015	1004	1000	988	973	943	918
42	1023	1014	1003	1000	987	972	943	917
43	1024	1014	1004	1000	988	973	944	919
44	1027	1017	1007	1003	990	975	946	921
45	1024	1014	1004	1000	987	972	943	918
46	1024	1014	1004	1000	988	972	943	918
47	1010	1001	991	987	975	961	933	909
48	1019	1010	999	996	983	968	939	914
49	1019	1010	999	996	983	968	939	914
50	1019	1010	1000	996	984	969	940	914
51	1010	1001	991	988	976	961	934	910
52	1008	999	989	986	974	959	932	907
53	1009	1000	990	986	974	960	932	908

in the Appendix A specifies the design shear strength values for different return periods. The design shear strength values at almost all grids exceeded 1.00 MPa for return periods over 20 years. The design strength values in the Bohai Bay and Dongying Port areas maintained >1.00 MPa for 10-year and 5-year return periods while the design strength values at other regions fell below 1.00 MPa. For design values with 2-year and 1-year return periods, the strength values at almost all grids were <1.00 MPa.

3.6. Sea Ice Flexural Strength

As the critical parameter controlling ice failure on sloped structures, quantification of sea ice flexural strength is essential for the design of ice-breaking cones. Figure 9 presents the spatial distributions of design sea ice flexural strength in the southern Bohai Sea. The design values of sea ice flexural strength exhibited a distinct spatial gradient, decreasing sequentially from the Bohai Bay (highest values) through deep-water area (medium values) to the Laizhou Bay (lowest values), with the Bohai Bay bottom and Dongying Port areas showing the most severe strength values.

Table A3. The design flexural strength (in kPa) of sea ice for different return periods.

Grid No.	Return Period/Year
	100	50	25	20	10	5	2	1
1	520	508	495	490	474	455	419	389
2	517	506	494	490	476	459	427	399
3	522	511	499	495	480	463	430	400
4	523	512	500	496	481	464	430	401
5	515	504	492	488	474	458	428	401
6	487	477	467	463	450	435	405	380
7	584	571	556	551	533	512	471	435
8	591	577	562	557	539	517	475	439
9	592	578	563	558	540	518	476	440
10	593	579	564	559	541	519	477	441
11	592	578	563	558	540	519	478	442
12	593	579	564	559	541	520	478	442
13	594	581	566	561	543	522	480	444
14	559	547	534	529	513	494	458	425
15	560	548	535	530	514	495	458	426
16	558	546	533	528	512	493	456	424
17	558	546	533	528	512	493	456	424
18	561	549	536	531	515	496	459	427
19	561	549	536	531	515	496	459	427
20	504	494	482	478	464	448	416	388
21	507	497	485	481	467	450	418	389
22	504	494	482	478	464	448	416	388
23	507	497	485	481	467	450	418	389
24	499	490	479	476	463	448	419	394
25	506	495	484	480	466	449	417	389
26	505	495	483	479	465	448	416	388
27	501	491	481	477	465	449	420	395
28	508	497	486	482	468	451	418	390
29	537	525	513	508	493	475	440	409
30	537	525	513	508	493	475	440	409
31	474	464	454	451	438	424	395	371
32	471	462	452	448	436	422	394	369
33	470	461	451	447	435	421	393	368
34	474	465	455	452	439	425	397	372
35	474	465	455	451	439	424	396	372
36	474	465	454	451	439	424	396	372
37	475	466	456	452	440	425	397	372
38	473	464	454	450	438	423	395	371
39	472	463	453	449	437	422	394	370
40	477	468	457	454	442	427	398	373
41	476	467	456	453	441	426	398	373
42	475	466	456	452	440	425	397	372
43	477	468	457	454	442	427	398	373
44	479	470	460	456	444	429	400	375
45	475	466	456	452	440	425	397	373
46	475	466	456	452	440	426	397	373
47	466	457	446	443	431	416	388	363
48	471	462	452	448	436	421	393	369
49	471	462	452	448	436	421	393	369
50	471	462	452	449	436	422	394	369
51	467	458	447	444	431	416	388	363
52	463	454	444	441	429	414	386	361
53	464	455	445	441	429	414	386	362

in the Appendix A specifies the design flexural strength values for different return periods. The design flexural strength for the 100-year return period ranged from 463 to 594 kPa. The design values decreased with shorter return periods. For return periods of 5 years and above, the minimum and maximum design flexural strengths remained greater than 400 kPa and 500 kPa, respectively. At the 2-year return period, the design flexural strength decreased to 386 kPa and 480 kPa.

3.7. Sea Ice Tensile Strength

Despite its low magnitude compared to uniaxial compressive strength, sea ice tensile strength influences the crack formation of large ice cover. Figure 10 presents the spatial distributions of sea ice tensile strength in the southern Bohai Sea. The design values of sea ice tensile strength exhibited a distinct spatial gradient, decreasing sequentially from the Bohai Bay (highest values) through deep-water area (medium values) to the Laizhou Bay (lowest values), with the Bohai Bay bottom and Dongying Port areas showing the most severe strength values.

Table A4. The design tensile strength (in kPa) of sea ice for different return periods.

Grid No.	Return Period/Year
	100	50	25	20	10	5	2	1
1	233	224	214	210	198	184	157	136
2	232	224	215	212	201	188	163	142
3	233	225	216	213	202	189	165	144
4	233	225	217	213	203	190	166	144
5	230	223	214	211	200	188	164	143
6	208	201	193	190	181	169	147	127
7	290	279	267	263	248	231	197	168
8	296	284	272	268	253	235	201	171
9	296	285	273	269	254	236	202	172
10	297	286	274	269	255	237	202	172
11	292	281	270	265	252	235	202	174
12	292	282	270	266	252	235	203	175
13	294	283	272	268	254	237	205	177
14	266	257	247	243	231	216	187	162
15	267	258	247	244	231	216	188	162
16	265	256	246	242	230	215	186	161
17	265	256	246	242	230	215	186	161
18	267	258	248	244	232	217	188	163
19	267	258	248	244	232	217	188	163
20	219	212	203	200	190	178	155	134
21	221	213	205	202	192	180	156	135
22	219	212	203	200	190	178	155	134
23	221	213	205	202	192	180	156	135
24	222	215	206	203	193	181	157	136
25	220	213	204	201	191	179	155	135
26	220	212	204	201	191	179	155	135
27	223	216	207	204	194	182	158	137
28	222	214	205	202	192	180	156	136
29	249	240	230	226	215	200	173	149
30	249	240	230	226	215	200	173	149
31	202	194	186	183	173	161	139	121
32	201	193	184	181	171	159	138	120
33	199	191	183	180	170	158	137	119
34	203	195	187	184	174	162	140	122
35	203	195	186	183	173	162	140	121
36	202	195	186	183	173	161	140	121
37	203	195	187	184	174	162	140	122
38	202	194	185	182	172	160	139	121
39	201	193	184	181	172	160	138	120
40	204	196	188	185	175	163	141	123
41	203	196	187	184	174	163	141	122
42	203	195	187	184	174	162	140	122
43	203	195	187	184	174	163	141	123
44	205	197	189	186	176	165	143	124
45	203	196	187	184	174	162	140	122
46	203	196	187	184	174	162	141	122
47	195	187	179	176	166	155	133	116
48	201	193	184	181	171	159	137	120
49	201	193	184	181	171	159	137	120
50	202	193	185	182	171	159	138	120
51	194	186	178	175	165	154	133	116
52	192	184	176	173	164	152	132	115
53	193	185	176	174	164	153	132	115

in the Appendix A specifies the design tensile strength values for different return periods. For the 100-year return period scenario, all grids exhibited design tensile strengths exceeding 200 kPa. For return periods between 50 and 20 years, the Laizhou Bay area showed design tensile strengths below 200 kPa, and other locations maintained values above 200 kPa. Below the 20-year return period, only several severe grids demonstrated tensile strengths surpassing 200 kPa. Under 1-year return period conditions, all grids displayed design tensile strengths less than 200 kPa.

4. Discussion

4.1. The Selection of Sea Ice Strength Formulae

Numerous uniaxial compressive strength tests have been conducted on Bohai Sea ice. However, these tests have predominantly focused on the Liaodong Bay, where ice conditions are relatively severe, whereas data availability for the Laizhou Bay has been limited. Both of the Chinese ice-region engineering design codes [15,24] recommend that, in the absence of measured data, the peak value of sea ice uniaxial compressive strength be calculated using Equation (1).

The National Marine Environmental Monitoring Center (NMEMC) historically conducted uniaxial compressive strength tests on sea ice in the Yellow River Estuary area near the Laizhou Bay [25]. These tests served as design references for offshore oil production structures of the Shengli Oilfield, providing the relationship between the design value of uniaxial compressive strength of level ice in the Yellow River Estuary and ice temperature, as expressed by Equation (13).

$${\sigma }_{\mathrm{c}}=1.84-0.161T_{\mathrm{i}}$$

(13)

Recently, during the 2020/2021 winter, ice blocks were collected at different sites in the southern Bohai Sea (Feiyantan, No. 168 artificial island, and Zhuangxi 106). Ice samples were then machined to carry out uniaxial compressive strength tests of sea ice at different ice temperatures in the laboratory. Test results showed that as the temperature of the ice samples decreased, the uniaxial compressive strength of the sea ice increased. Previous studies have typically employed a linear relationship to fit the variation in the peak uniaxial compressive strength of ice with temperature. Although the linear fitting yielded good results, it fails to account for the fact that the ice strength approaches zero as the ice temperature nears the freezing point. Therefore, a nonlinear relationship was adopted for fitting, as shown in Equations (14)–(16).

For sea ice in the Zhuangxi 106 site,

$${\sigma }_{\mathrm{c}}=1.11\ln (\left|T_{\mathrm{i}}\right|)+0.45$$

(14)

For sea ice in the No. 168 artificial island,

$${\sigma }_{\mathrm{c}}=0.7\ln (\left|T_{\mathrm{i}}\right|)+0.52$$

(15)

For sea ice in the Feiyantan site,

$${\sigma }_{\mathrm{c}}=0.61\ln (\left|T_{\mathrm{i}}\right|)+1.21$$

(16)

The relationship curves between the peak compressive strength of the sea ice and ice temperature, as derived from the aforementioned formulae, were compared in Figure 11. It can be observed that the formula for the sea ice in the Yellow River Estuary area (Equation (13)) and the code-specified formula (Equation (1)) all yield higher values than the recent laboratory-derived relationships between peak strength and ice temperature (Equations (14)–(16)). The discrepancy can be attributed to the impact of climate warming on ice conditions in China. Climate warming has made extremely low air temperatures less frequent, resulting in higher air temperatures during sea ice growth periods. The warmer environment increases the brine and gas content within the ice, leading to reduced strength. Compared to Equation (13), Equation (1) shows closer agreement with the field measurement data obtained in the 2020/2021 winter. The ice sampling sites for deriving Equation (13) were closer to the Yellow River Estuary, where sea ice has lower salinity and consequently higher strength. Therefore, Equation (1) was selected as the calculation formula for uniaxial compressive strength in this paper.

4.2. Comparions with Original CNOOC Guideline

The CNOOC Guideline was issued in 2002, reflecting sea ice conditions under prevailing climatic-hydrological regimes of the previous era. Comparing the sea ice parameters derived here with the values proposed in the CNOOC guideline provides climate-driven modifications in Bohai Sea ice conditions to some degree. As shown in Figure 4b and Figure 5b, the southern Bohai Sea exhibits marked declines in both average ice thickness and concentration.

Compared with the sea ice uniaxial compressive strength in the original standards, our refined grid division shows generally comparable design sea ice strength values across the southern Bohai Sea. The most notable differences occurred for 100-year, 50-year and 1-year return periods, where the original design values are slightly higher, but only by 0.05 MPa. For sea ice shear strength, there is no obvious difference either. The maximum difference was 43 kPa occurring under the 10-year return period design condition, while the minimum difference was 11 kPa which was observed for the 1-year return period scenario.

The flexural strength and tensile strength of sea ice show significant differences. Compared with the design sea ice flexural strength in the corresponding grids of the original standards, our refined grid yielded lower values. The original guideline provided design flexural strengths of 642.5–23.5 kPa for return periods varying from 100 to 1 years. The maximum differences reached 132 kPa for the 100-year return period, and the minimum difference was 85 kPa for the 5-year return period.

Compared with the design sea ice tensile strength in the corresponding grids of the original standards, our refined grid yielded lower values. The original guideline provided design flexural strengths of 331.5–237.5 kPa for return periods varying from 100 to 1 years. The maximum differences reached 103 kPa for the 100-year return period, and the minimum difference was 66 kPa for the 5-year return period.

Moreover, the original guideline characterizes southern Bohai Sea ice conditions using only two grid cells, which is not enough to resolve critical differences between nearshore and offshore ice regimes. The refined grid here successfully captures more detailed spatial variations in the design strength values of sea ice engineering parameters throughout the study waters. The most severe ice conditions occur in nearshore zones, exhibiting maximum values in thickness, concentration, and design ice strength. Across the southern Bohai Sea, the ice conditions display a distinct spatial gradient with Bohai Bay > offshore deep-water areas > Laizhou Bay.

4.3. Potential Impacts of Climate Change on Bohai Sea Ice Engineering

The Bohai Sea ice management authority in China classifies ice severity into five levels (Level 1–5) based on floating ice extent, where Level 1 represents the mildest conditions and Level 5 the most severe. With global warming, according to the China Marine Disaster Bulletin, from 1951 to 2023, the ice severity in the Bohai Bay has decreased from Level 4 towards Level 2 in general, and Laizhou Bay has declined from Level 3 towards Level 2 typically.

This changing ice regime is further evidenced by comparing our results with the original CNOOC guideline. Compared to the previous standards, our analysis yields lower values for key sea ice parameters, including ice thickness, concentration, and flexural and tensile strength. These changed ice parameters may carry significant practical implications for engineering in the Bohai Sea. The reduced ice thickness and ice strength will reduce ice loads on structure. The reduced ice loads translate directly into lighter and more economical structures, lowering material requirements and construction costs. It is also necessary to update design sea ice parameters to reflect the climate-driven reduction in ice severity, avoiding unnecessary over-engineering while maintaining safety margins appropriate for the actual, diminished ice hazard.

4.4. Limitations of the Study

There are several limitations in this study. First, the high-resolution sea ice strength model was specifically developed for the southern Bohai Sea and may be less applicable to other ice-covered regions due to unique local characteristics. Bohai Sea is the lowest-latitude freezing sea in the Northern Hemisphere, exhibiting significant interannual ice variability with maximum annual ice thickness not exceeding 0.5 m. Its shallow bathymetry, high water temperatures, substantial river discharge, and high brine/gas porosity in sea ice have led to the development of region-specific parameterization methods for ice strength (the approach adopted in this study). While regionally constrained, the core framework of nesting mechanical parameterization within climatic/oceanographic models provides transferable methodology for gridded ice strength assessment in other regions, including the Arctic.

Second, gridded sea ice strength values were calculated using standardized formulae recommended by established specifications, and were not validated by field measurements. Validating gridded strength data presents critical technical challenges. Sea ice strength measurements rely on in situ tests and exhibit diurnal variations due to changing ice temperatures. Achieving spatiotemporal resolution matching between field measurements and model outputs in the future may be an effective method.

5. Conclusions

Based on our previous high-resolution study of sea ice parameters in the Bohai Sea [16], this study extends the focus to the southern Bohai Sea where intensive oil and gas operations are located and sea ice strength properties are critical for engineering design.

As the most intensive offshore oil-gas development area in China, the southern Bohai Sea undergoes annual sea ice encroachment, creating unique operational challenges. Current design standards characterize this region with only two coarse-resolution grids for ice thickness, concentration, and strength parameters. Our study employed high-resolution meshing (minimum 1/12° grids) to partition the southern Bohai Sea into 51 zones. Utilizing the NEMO-LIM2 sea ice–ocean coupled model, the grid-specific outputs for ice thickness, concentration, and period were obtained, and through return-period analysis, design values of sea ice strength parameters were further derived for each grid. The analysis reveals pronounced spatial variations in ice conditions across the southern Bohai Sea. Nearshore zones exhibit the most severe ice conditions, demonstrating maximum values in thickness, concentration, and design ice strength. A clear spatial gradient of ice conditions is displayed in the southern Bohai Sea with Bohai Bay > offshore deep-water areas > Laizhou Bay.

Compared to the current standards of CNOOC, the mean ice thickness and concentration derived here were reduced. For design sea ice strength values, the flexural and tensile strength derived here were lower than those in the current standards. The reductions in sea ice thickness, concentration, and flexural strength compared to current standards yield significant engineering benefits. First, the lower ice loads enable substantial cost savings through optimized structural designs. Second, the mitigated ice–structure interactions directly reduce operational risks. Third, these findings support design enhancements such as revising ice load zoning maps for Bohai Sea offshore blocks.