﻿ 改进的Winkler弹性地基模型在触地段动力分析中的应用
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (9): 1451-1457  DOI: 10.11990/jheu.201702050 0

### 引用本文

DAI Yunyun, ZHOU Jing. Application of an improved Winkler elastic foundation-based model to the dynamic analysis of damaged pipelines in the touchdown zone[J]. Journal of Harbin Engineering University, 2018, 39(9), 1451-1457. DOI: 10.11990/jheu.201702050.

### 文章历史

Application of an improved Winkler elastic foundation-based model to the dynamic analysis of damaged pipelines in the touchdown zone
DAI Yunyun, ZHOU Jing
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China
Abstract: To detect the dynamic response of a damaged pipeline in a riser located in a touchdown zone under complicated loads, an improved Winkler elastic foundation-based model is proposed to determine soil resistance and its distribution, taking into account the geological condition of the South China Sea. The finite element method was used to scatter the soil resistance into soil springs, and the correctness of the proposed model was verified by a large-scale indoor model test. The model was applied to the dynamic analysis of a full-sized damaged seabed pipeline, and the dynamic responses of the damaged pipeline in the touchdown zone were determined at different nodes. The results obtained were consistent with actual observations, and excellent application effects were achieved. The proposed model shows promising value for dealing with the practical problems associated with pipelines in touchdown zones.
Keywords: touchdown zone of riser    Winkler elastic foundation-based model    model test    volume damage    dynamic response    submarine pipeline

1 改进的Winkler弹性地基模型

 Download: 图 1 管道压入Winkler弹性地基模型 Fig. 1 The model of pipeline on Winkler elastic foundation
1.1 理论推导

 $a = \sqrt {\frac{{4P{R^ * }}}{{{\rm{ \mathsf{ π} }}{E^ * }}}}$ (1)

 $\left\{ \begin{array}{l} {E^ * } = \left( {\frac{{1 - v_1^2}}{{{E_1}}} + \frac{{1 - v_2^2}}{{{E_2}}}} \right) - 1\\ {R^ * } = {\left( {\frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}} \right)^{ - 1}} \end{array} \right.$ (2)

 $\left\{ \begin{array}{l} {E^ * } = {E_2}/\left( {1 - \nu _2^2} \right) = 1.10{E_2}\\ {R^ * } = {R_1} = R \end{array} \right.$ (3)

 $P = \frac{2}{3}\left( {\frac{{ka}}{h}} \right)\frac{{{a^2}}}{R}$ (4)
 $\delta = {a^2}/2R$ (5)

 ${\sigma _y}\left( x \right) = {\sigma _0}{\left[ {1 - {{\left( {\frac{x}{a}} \right)}^2}} \right]^{1/2}}$ (6)

 $k/h = 1.18{E^ * }/a$ (7)

 $P = \frac{2}{3}\left( {1.18{E^ * }} \right)\frac{{{a^2}}}{R}$ (8)

 ${a_{\max }} = D/3/2 = R/3$ (9)

a取最大值的时候，土体抗力达到最大。将式(9)代入式(8)，可得最大土体抗力PmaxR的关系为

 ${P_{\max }} = \frac{2}{3}\left( {1.18{E^ * }} \right)\frac{R}{9}$ (10)

 Download: 图 3 等效海床竖向土弹簧的P-y曲线 Fig. 3 Equivalent P-y curves of seabed soil spring

 ${P_{\max ,n}} = \int_{{x_n} - 1}^{{x_n}} {{\sigma _y}\left( x \right){\rm{d}}x}$ (11)

1.2 建立改进的Winkler弹性地基模型

 ${k_n} = \frac{{{P_{\max ,n}}}}{{{y_s}}}$ (12)

 Download: 图 4 改进的Winkler弹性地基模型改进的Winkler弹性地基模型 Fig. 4 Sketch of improved Winkler elastic foundation model

2 改进模型的试验验证 2.1 试验装置

2.1.1 固结海床

2.1.2 管道模型

2.1.3 传感器的布置

2.2 模型验证

 Download: 图 6 模型的验证过程 Fig. 6 Validation procedure of the improved model
2.2.1 建立有限元模型

 Download: 图 7 PVC管道的有限元模型 Fig. 7 View of finite element model of PVC pipeline
2.2.2 验证结果分析

 Download: 图 8 基于模型试验与数值模拟的振型对比图 Fig. 8 Comparison of mode shapes vertically based on test and numerical simulation
3 改进模型的应用

3.1 建立损伤管道与海床相互作用的模型

 Download: 图 9 海底管道体积损伤部位的完整模型 Fig. 9 Finite element model of pipeline in damaged zone

3.2 结果分析 3.2.1 位移响应

 Download: 图 10 节点12105和15250的位移响应 Fig. 10 Displacement response of node 12105 and node 15250
3.2.2 应力响应

 Download: 图 11 节点12105和15250的有效应力响应 Fig. 11 Stress response of node 12105 and node 15250

4 结论

1) 改进模型在数值计算过程中考虑管材和海床在相互作用过程中的材料非线性、几何非线性以及接触非线性，使计算结果更加符合工程实际。

2) 改进模型充分考虑了触地段管道较大的位移载荷和弯曲变形，更加符合立管质量和海床约束力的连续分布的特点。

3) 改进模型不仅可以模拟体积缺陷等损伤管道，还可以模拟管道所受的内压、外压等载荷，进而对管道进行深度分析。

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