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Discussion of penetration depth of ship anchoring based on finite element method
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摘要: 船舶抛锚贯入深度的准确计算，对穿越锚地与航道河床以下管线工程的安全性至关重要。依据投锚试验结果，对比分析了现有的计算抛锚贯入深度的经验法、标准法、理论公式法的计算精度。以霍尔锚为例，基于有限元软件，提出了一种能够考虑复杂土层、触底水平速度及触底姿态等多因素的抛锚贯入深度数值模拟方法，并通过几何形态分析，研究了拖锚对贯入深度的影响。计算结果表明，触底水平速度、触底夹角和拖锚均影响贯入深度，其中拖锚的影响程度最大，触底夹角次之，触底水平速度的影响程度最小。考虑触底水平速度、触底夹角及拖锚影响的贯入深度更有利于保障工程安全。Abstract: The accurate calculation of the penetration depth of ship anchoring is of vital importance to the safety of pipeline projects passing through anchorage areas and navigation channels below the riverbed. Based on the results of the ship anchoring experiment, we first study the calculation accuracy of various existing anchor penetration depth calculation methods including empirical method, standard method and theoretical formula method. Then, we take Hall anchor as an example, and use the finite element software ANSYS-DYNA to propose a numerical simulation method of anchor penetration depth that can consider multiple factors such as complex layered soils, bottoming horizontal velocity and bottoming angle. The influence of anchor dragging on penetration depth is also studied in this paper through the method of geometric analysis. The calculation results show that the bottoming horizontal velocity, bottoming angle and anchor dragging have influences on penetration depth, and among them, anchor dragging has the most significant effect, the influence of bottoming angle comes the second place, and bottoming horizontal velocity has the least influence. It can be obviously seen that after considering the impacts of the bottoming horizontal velocity, the bottoming angle and the anchor dragging, the calculation results will be more conducive to ensuring the safety of engineering projects.
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Key words:
- ship anchoring /
- penetration depth /
- pipeline burial depth /
- bottoming velocity
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图 5 触底水平速度对贯入深度的影响
Figure 5. Relation diagram of the impact of bottoming horizontal velocity on penetration depth
图 6 触底夹角对贯入深度的影响
Figure 6. Relation diagram of the impact of bottoming angle on penetration depth
表 1 各方法计算得到的贯入深度对比
Table 1. Comparison of penetration depths calculated by various methods
锚质量/t 土质 贯入深度/m 经验法 GB 50217—2018标准法 DNV理论公式法 投锚试验 4.89 砂土 1.50 2.63 1.17~1.92 0.25~1.13 淤泥土 4.50 2.63 1.92~2.59 1.13~4.34 8.30 砂土 1.79 3.27 1.39~2.28 0.30~1.41 淤泥土 5.37 3.27 2.28~3.07 1.41~4.72 12.30 砂土 2.04 3.77 1.58~2.60 0.34~1.61 淤泥土 6.12 3.77 2.60~3.50 1.61~5.00 18.80 砂土 2.35 4.34 1.82~2.99 0.38~1.83 淤泥土 7.05 4.34 2.99~4.03 1.83~5.30 23.00 砂土 2.51 4.61 1.95~3.20 0.40~1.93 淤泥土 7.53 4.61 3.20~4.31 1.93~5.45 注：计算时，DNV理论公式中，$ {N_\gamma } $取值范围参照文献[14]，附加质量系数取1~2。投锚试验结果由图1中拟合得到的上、下边界及分界线方程计算。 
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表 2 土层物理力学参数
Table 2. Physical and mechanical parameters of soil layer
地层号 天然密度/（kg·m−3) 含水率/
%黏聚力/kPa 摩擦角/
°体积模量/
MPa剪切模量/
MPa土层高程范围/
m1淤泥质 1 780 38.90 13.01 8.38 5.12 1.09 −20.46~ −26.35 1-1粉砂 1 950 25.20 8.00 36.00 2.99 1.79 −26.35~ −33.33 6-1粉土 1 790 33.60 15.09 24.87 4.10 1.89 −33.33~ −38.69 6粉质黏土 1 790 33.80 17.34 9.85 4.63 1.54 −38.69~ −47.31 7粉砂 1 930 25.20 4.00 28.00 4.67 2.15 −47.31~ −70.46
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表 3 计算工况
Table 3. Calculation scenarios
模型
编号锚质量/t 触底垂直速度/
(m·s−1)触底水平速度/
(m·s−1)触底夹角/° 模型
编号锚质量/t 触底垂直速度/
(m·s−1)触底水平速度/
(m·s−1)触底夹角/° 1 4.89 6.44 0 90 8 29.00 8.57 2.00 90 2 8.30 6.96 0 90 9 29.00 8.57 3.50 90 3 12.30 7.43 0 90 10 29.00 8.57 5.00 90 4 18.80 7.97 0 90 11 29.00 8.57 3.50 75 5 23.00 8.25 0 90 12 29.00 8.57 3.50 60 6 29.00 8.57 0 90 13 29.00 8.57 3.50 45 7 29.00 8.57 1.00 90 14 29.00 8.57 3.50 30
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表 4 不同质量锚的啮土深度
Table 4. Depth of engagement in soil of anchors with different weights
锚质量/t 对应工况 锚爪长度/m 锚冠厚度/m H1/m H2/m 比无拖锚时的增幅/% 4.89 1 1.50 0.33 1.00 1.50 170.5 8.30 2 1.79 0.39 1.20 1.78 172.8 12.30 3 2.04 0.45 1.37 2.04 167.2 18.80 4 2.35 0.52 1.57 2.35 169.1 23.00 5 2.51 0.55 1.68 2.50 147.9 29.00 6 2.72 0.60 1.82 2.72 136.7 注：H1为锚爪没入土时的啮土深度；H2为锚冠没入土体时的啮土深度。
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