Model tests on penetration depth of hall anchor in silty sand
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摘要: 航船应急抛锚时锚板贯入土体可能会影响河床或海床中的结构物甚者造成破坏，因此在通航频繁的航道，结构物埋深的设计需要充分考虑应急抛锚时锚板的贯入深度。本文通过缩尺模型试验模拟了霍尔锚在中等密实度粉细砂中的抛锚贯入过程，研究了不同抛锚速度(1.15～4.4 m/s)及粉细砂相对密实度(0.45～0.65)对抛锚贯入深度的影响；基于太沙基极限承载力理论和能量守恒定律，推导出霍尔锚在粉细砂土中贯入深度的表达式，与模型试验结果对比显示理论计算结果偏于保守。基于试验结果提出修正系数，修正后的理论公式能够较好地快速预测霍尔锚在中等密实度粉细砂中的贯入深度。研究结果为粉细砂土河床或海床中的结构物埋深设计提供了一定的技术参考。Abstract: The structures in the riverbed or seabed may be affected or damaged by emergency anchoring. In the channel with frequent navigation, the emergency anchoring penetration depth need to be fully considered during the design of the buried depth of structures in riverbed. In this paper, small scale model tests are carried out to simulate the process of anchoring penetration of hall anchor in silty sand, and the influences of different impact velocities (1.15−4.4 m/s) and relative density of silty sand (0.45−0.65) on anchoring penetration depth are investigated. Based on the Terzaghi ultimate bearing capacity theory and the energy conservation law, the expression of penetration depth of the hall anchor in silty sand is deduced, and the theoretical calculation results are conservative compared with experimental results, the revised results of the theoretical calculation results are in good agreement with experimental data. The research results can provide a reference for the design of buried depth of structures in silty sand riverbed or seabed.
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Key words:
- Hall anchor /
- silty sand /
- penetration depth /
- impact velocity
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图 4 铺设排水层、土工布和滤纸示意图
Fig. 4 Schematic diagram of laying the draining layer, geotextile and filter paper
图 7 锚入土前的下落速度随距离土面高度变化曲线（工况H13，v0=2.78 m/s）
Fig. 7 Curves of anchor’s velocity vs. position before penetrating into sand (case H13, v0=2.78 m/s)
图 8 高速相机采集的霍尔锚抛锚下落过程照片(工况H4，v0=2.13 m/s)
Fig. 8 Photos of the Hall anchor anchoring process captured by a high-speed camera (case H4, v0=2.13 m/s)
图 9 抛锚试验结果(工况H4，v0=2.13 m/s)
Fig. 9 Dynamic penetration test results (case H4, v0=2.13 m/s)
图 10 霍尔锚底部贯入面积随贯入深度变化
Fig. 10 The variety of the bottom penetration area with penetration depth
图 11 采用不同的承载力系数计算得到的贯入深度曲线
Fig. 11 Curves of penetration depth vs. Ek calculated with different bearing capacity coefficients
表 1 砂土中船锚动力贯入模型试验相似关系
Tab. 1 Similarity relationships of dynamic penetration model tests in sand
物理量 长度L 面积A 速度v 抛锚深度z 重力W 阻力Fs 内摩擦角φ 动能Ek 势能Ep 比尺 λL λA λv λz λW λF λφ λE λp 相似关系 λL $ {\lambda_L^2}$ $ {\lambda_L^{1/2}}$ λL $ {\lambda_L^3}$ $ {\lambda_L^3}$ 1 $ {\lambda_L^4}$ $ {\lambda_L^4}$ 模型试验 1/λL 1/$ {\lambda_L^2}$ 1/$ {\lambda_L^{1/2}}$ 1/λL 1/$ {\lambda_L^3}$ 1/$ {\lambda_L^3}$ 1 1/$ {\lambda_L^4}$ 1/$ {\lambda_L^4}$ 
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表 2 霍尔锚模型尺寸
Tab. 2 Hall anchor model size
锚重/kg H/mm h/mm h1/mm L/mm L1/mm B/mm B1/mm 模型 1.74 193.27 104.6 23 148.93 104.6 57.93 68.73 原型 5610 2899 1569 345 2234 1569 869 1031 注：表中各符号代表的含义标注在图2中。
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表 3 模型试验土样颗粒筛分结果
Tab. 3 Partical screening test result of soil sample
颗粒直径/mm 0.25～0.5 0.075～0.25 <0.075 试验土颗粒组成百分数 17.5% 50% 32.5% 现场土颗粒组成百分数 8.3% 58.4% 33.2%
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表 4 不同相对密实度下土体干密度与内摩擦角
Tab. 4 Dry density and internal friction angle of soil sample under different relative density
相对密实度 0.45 0.55 0.65 干密度/g·cm−3 1.457 1.515 1.577 内摩擦角/(°) 36.9 38.9 39.5
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表 5 抛锚试验工况及结果
Tab. 5 Tests conditions and results
工况 抛锚高度/m Dr 抛锚速度/m·s−1 贯入深度/m 模型 原型 模型 原型 H1 0.09 0.45 1.15 4.45 0.055 0.825 H2 0.15 0.45 1.64 6.35 0.083 1.245 H3 0.21 0.45 2.01 7.78 0.108 1.620 H4 0.25 0.45 2.13 8.25 0.110 1.650 H5 0.35 0.45 2.56 9.91 0.140 2.100 H6 0.70 0.45 3.66 14.18 0.187 3.405 H7 0.84 0.45 4.02 15.57 0.196 3.890 H8 0.15 0.55 1.66 6.42 0.050 0.750 H9 0.22 0.55 2.03 7.86 0.059 0.891 H10 0.25 0.55 2.12 8.22 0.065 0.975 H11 0.30 0.55 2.42 9.39 0.073 1.089 H12 0.40 0.55 2.76 10.71 0.077 1.155 H13 0.41 0.55 2.78 10.78 0.082 1.230 H14 0.52 0.55 3.19 12.36 0.090 1.350 H15 0.62 0.55 3.49 13.50 0.092 1.386 H16 0.80 0.55 3.96 15.34 0.121 1.815 H17 1.00 0.55 4.40 17.06 0.132 1.980 H18 0.15 0.65 1.60 6.20 0.038 0.567 H19 0.28 0.65 2.31 8.95 0.040 0.600 H20 0.42 0.65 2.86 11.08 0.045 0.675 H21 0.59 0.65 3.35 12.97 0.075 1.125 H22 0.70 0.65 3.66 14.18 0.071 1.071 H23 0.82 0.65 4.00 15.49 0.090 1.354
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表 6 各学者建议的承载力系数计算公式
Tab. 6 Formulas for calculating the bearing capacity coefficient recommended by various scholars
参考文献 Nc Nq Nγ 文献[19] ${\left( { {N_{{q} } } - 1} \right)\cot \varphi }$ ${\dfrac{ { {\rm{e}^{\left( {\dfrac{ {3{\text π} } }{2} - \varphi } \right)\tan \varphi } } } }{ {2{ {\cos }^2}\left( {\dfrac{ {\text π} }{4} + \dfrac{\varphi }{2} } \right)} } }$ ${1.8\left( { {N_{{q} } } - 1} \right)\tan \varphi }$ 文献[18] ${\left( { {N_{{q} } } - 1} \right)\cot \varphi }$ ${ {\rm{e}^{ {\text π} \tan \varphi } }{ {\tan }^2}\left( {\dfrac{ {\text π} }{4} + \dfrac{\varphi }{2} } \right)}$ ${\left( { {N_{{q} } } - 1} \right)\tan (1.4\varphi )}$ 文献[20] ${\left( { {N_{{q} } } - 1} \right)\cot \varphi }$ ${ {\rm{e}^{ {\text π} \tan \varphi } }{ {\tan }^2}\left( {\dfrac{ {\text π} }{4} + \dfrac{\varphi }{2} } \right)}$ ${2\left( { {N_{{q} } } - 1} \right)\tan \varphi }$ 文献[17] ${\left( { {N_{{q} } } - 1} \right)\cot \varphi }$ ${ {\rm{e}^{ {\text π} \tan \varphi } }{ {\tan }^2}\left( {\dfrac{ {\text π} }{4} + \dfrac{\varphi }{2} } \right)}$ ${1.8\left( { {N_{{q} } } - 1} \right)\tan \varphi }$
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