砂土各向异性临界状态模型及砂质海床板锚承载特性评价

王学涛; 王立忠; 洪义; 高智伟

doi:10.11779/CJGE20221010

砂土各向异性临界状态模型及砂质海床板锚承载特性评价 English Version

王学涛^1,,
王立忠¹,
洪义^{1, 2, ,},
高智伟³

1.
浙江大学建筑工程学院, 浙江杭州 310058
2.
浙江大学平衡建筑研究中心, 浙江杭州 310028
3.
格拉斯哥大学, 格拉斯哥 311122

基金项目:

国家重点研发计划项目 2018YFE0109500

国家自然科学基金项目 52122906

国家自然科学基金项目 51939010

浙江省自然科学基金项目 LHZ20E090001

详细信息

作者简介:
王学涛(1996—)，男，博士研究生，主要从事海洋岩土方向的研究工作。E-mail: xuetao_wang@zju.edu.cn

通讯作者:
洪义, E-mail: yi_hong@zju.edu.cn

中图分类号: TU441
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出版历程
- 收稿日期: 2022-08-16
- 网络出版日期: 2023-03-15
- 刊出日期: 2023-10-31

Anisotropic critical state model for sand and evaluation of bearing capacity of plate anchors in sandy seabed

1.
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2.
Center for Balance Architecture, Zhejiang University, Hangzhou 310058, China
3.
James Watt School of Engineering, University of Glasgow, Glasgow 311122, UK

摘要

摘要: 砂土组构各向异性及演化显著影响其力学行为，对砂土海床中板锚等承载特性有重要影响。基于各向异性临界状态理论框架（ACST），引入考虑组构各向异性非共轴流动法则，建立了砂土各向异性非共轴模型，并嵌入有限元ABAQUS；通过引入正则化技术，显著降低了砂土应变局部化导致的网格依赖性。基于不同应力路径砂土单元试验和砂土中板锚上拔离心试验，验证了上述模型；探究了不同组构沉积海床（沉积角α₀为0°，45°，90°）中平板锚的上拔特性。研究表明：①同一应力水平和密实度下，平板锚的上拔峰值承载力随α₀的增大而提高，因为高α₀海床中的砂土组构演化更快、导致峰值摩擦角更高。②如忽略组构各向异性影响，并基于三轴压缩数据标定模型参数，可使砂土中板锚承载力高估达100%；因为各向同性模型在满足三轴压缩预测条件下会高估其他路径下（如三轴伸长、单剪）的砂土强度。③传统极限平衡法不考虑组构各向异性，只能合理预测沉积角α₀=0°时锚板承载力，但低估了α₀为45°，90°时的上拔承载力。
- 各向异性砂土本构 /
- 非共轴各向异性流动法则 /
- 正则化技术 /
- 有限元模拟 /
- 平板锚 /
- 承载力
Abstract: The fabric anisotropy and evolution of sand significantly affect its mechanical behavior, and thus play an important role in altering the bearing capacity of foundations (e.g., plate anchor) in sandy seabed. In this study, an elasto-plastic critical state model for sand considering fabric anisotropy and its evolution along with the non-coaxial plastic flow rule is developed within the framework of anisotropic critical state theory (ACST). The model is then implemented into the three-dimensional finite element program ABAQUS. By introducing the nonlocal plasticity theory, the mesh dependency caused by strain localization of sand is minimized. The predictive capacity of the proposed model is validated through the successful simulation of sand element tests subjected to various stress paths, and the centrifugal model tests on the pull-out behavior of the plate anchor in sand. The effects of fabric anisotropy on the pull-out responses of plate anchors in sandy seabed are investigated via parametric studies, which consider different levels of initial fabric anisotropy (sedimentation angle α₀ =0°, 45°, 90°). It is revealed that: (1) For a given stress level and relative density of the sandy bed, the peak pull-out resistance of the plate anchor increases with α₀. This is because the fabric of the soil along the sliding wedge (above the anchor) evolves faster at a higher α₀ value, leading to a larger peak friction angle. (2) Ignoring the effects of fabric anisotropy leads to significant overestimation (by up to 100%) of the peak pull-out capacity of the plate anchor in sand, because the isotropic model that well predicts the triaxial compression behavior of sand will overestimate the strength of sand under other loading paths (such as triaxial extension and simple shear). (3) The traditional limit equilibrium analysis method does not consider the fabric anisotropy, and can only reasonably predict the pull-out capacity of the anchor plate when the sedimentation angle is α₀=0°, but underestimates the scenarios of α₀=45°, 90°.
- anisotropic sand model /
- non-coaxial plastic flow rule /
- nonlocal theory /
- finite element analysis /
- plate anchor /
- bearing capacity

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图 1 丰浦砂试验与模拟结果对比

Figure 1. Comparison between model simulations and test data on Toyoura sand

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图 2 典型锚板上拔离心机试验的有限元模型网格

Figure 2. Mesh details along with boundary conditions used in simulation of plate anchor

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图 3 网格尺寸对平板锚承载力的影响

Figure 3. Effects of mesh size on bearing capacity of plate anchor predicted by anisotropic model

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图 4 UWA硅砂20g下平板锚上拔试验

Figure 4. Comparison of simulated and measured mobilised N_p for circular anchors in UWA silica sand at H/D = 3, 6, 9 and 12

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图 5 不同组构沉积角下的承载力位移曲线（D_r0=0.85）

Figure 5. Bearing capacity-displacement relationship for a plate anchor in sand with different bedding plane orientations

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图 6 H/D=3各向异性平板锚承载力峰值时刻摩擦角云图

Figure 6. Contours of peak friction angle by different models

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图 7 不同组构海床中承载力峰值时刻板锚两侧发挥摩擦角云图

Figure 7. Contours of peak friction angle with different bedding plane orientations

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图 8 不同组构海床中峰值时刻板锚两侧各向异性变量云图

Figure 8. Contours of anisotropy variable with different bedding plane orientations

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表 1 本文的公式

Table 1 Proposed equations

描述	控制方程	模型参数
弹性模量	$G = {G_0}\frac{{{{(2.97 - e)}^2}}}{{1 + e}}\sqrt {p{\text{'}}{p_{\text{a}}}}$	弹性模量 ${G_0}$
弹性模量	$K = G\frac{{2(1 + \nu )}}{{3(1 - 2\nu )}}$	泊松比 $\nu$
组构张量	${\boldsymbol{F}_{ij}} = \left( {\begin{array}{{20}{c}} {{F_z}}&0&0 \\ 0&{{F_x}}&0 \\ 0&0&{{F_y}} \end{array}} \right) = \sqrt {\frac{2}{3}} \left( {\begin{array}{{20}{c}} {{F_{\text{0}}}}&0&0 \\ 0&{ - \frac{{{F_{\text{0}}}}}{2}}&0 \\ 0&0&{ - \frac{{{F_{\text{0}}}}}{2}} \end{array}} \right)$	初始组构各向异性参数 ${F_{\text{0}}}$
各向异性变量	$A = {\boldsymbol{F}_{ij}}{\boldsymbol{n}_{ij}} = \boldsymbol{Fn}_{ij}^F{\boldsymbol{n}_{ij}} = FN$
组构演化	${\text{d}}{\boldsymbol{F}_{ij}} = L{k_{\text{f}}}({\boldsymbol{n}_{ij}} - {\boldsymbol{F}_{ij}}){e^A}$	组构演化参数 ${k_{\text{f}}}$
屈服面方程	$f = \frac{R}{{g(\theta )}} - H{e^{ - {k_{\text{h}}}{{\left( {A - 1} \right)}^2}}} = 0$	硬化参数 ${k_{\text{h}}}$
剪胀方程	$D = \frac{{{\text{d}}\varepsilon _{{\text{ii}}}^{\text{p}}}}{{\sqrt {\frac{2}{3}{\text{d}}e_{ij}^{\text{p}}{\text{d}}e_{ij}^{\text{p}}} }} = \frac{{{d_1}}}{{{M_{\text{c}}}g(\theta )}}\left[ {1 + \frac{R}{{{M_{\text{c}}}g(\theta )}}} \right]\left[ {{M_{\text{c}}}g(\theta ){e^{m\zeta }} - R} \right]$	三轴压缩临界状态应力比 ${M_{\text{c}}}$ 剪胀参数 ${d}_{1}，m$
流动法则	${\text{d}}e_{ij}^{\text{p}} = L{m_{ij}}$ , ${m_{ij}} = \frac{{m_{ij}^{{\text{co}}} + m_{ij}^{{\text{nc}}}}}{{m_{ij}^{{\text{co}}} + m_{ij}^{{\text{nc}}}}}$
	$m_{ij}^{{\text{co}}} = \frac{{\frac{{\partial g}}{{\partial {r_{ij}}}} - \frac{{\partial g}}{{\partial {r_{mn}}}}{\delta _{mn}}\frac{{{\delta _{ij}}}}{3}}}{{\frac{{\partial g}}{{\partial {r_{ij}}}} - \frac{{\partial g}}{{\partial {r_{mn}}}}{\delta _{mn}}\frac{{{\delta _{ij}}}}{3}}}$ (共轴部分)
	$m_{ij}^{{\text{nc}}} = k(1 - A){F_{ij}}$ （非共轴部分）	非共轴参数 $k$
硬化法则	${\text{d}}H = L{r_{\text{h}}} = L\frac{{G({c_{\text{h}}} - e)}}{{p'}}\left[ {\frac{{{M_{\text{c}}}g(\theta ){e^{ - n\zeta }}}}{R} - 1} \right]$
塑性模量	${K_{\text{p}}} = \frac{R}{{g(\theta )}}\left\{ {\frac{{G(1 - {c_{\text{h}}}e)}}{{p'H}}\left[ {\frac{{{M_{\text{c}}}g(\theta ){e^{ - n\zeta }}}}{R} - 1} \right] + 2{k_{\text{h}}}{k_{\text{f}}}{{(1 - A)}^2}} \right\}$	硬化参数 ${c_{\text{h}}}$ ， $n$
$e - {\left( {\frac{{p{\text{'}}}}{{{p_{\text{a}}}}}} \right)^\xi }$ 空间的临界状态线	${e_{\text{c}}} = {e_{{\Gamma }}} - {\lambda _{\text{c}}}{\left( {\frac{{p{\text{'}}}}{{{p_{\text{a}}}}}} \right)^\xi }$	临界状态线在 $e - {\left( {\frac{{p{\text{'}}}}{{{p_{\text{a}}}}}} \right)^\xi }$ 空间的截距、斜率、参数 $\text{ }{e}_{\text{Γ}}，{\lambda }_{\text{c}}，\xi$
	$\zeta = e - {e_{\text{c}}} - {e_{\text{A}}}(A - 1)$	状态相关参数 ${e_{\text{A}}}$

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表 2 本构模型参数

Table 2 Parameters of constitutive model

参数		丰浦砂基于各向异性性模型	丰浦砂基于各向同性模型	UWA石英砂基于各向异性模型
弹性参数	G₀	125	125	135
弹性参数	$\nu$	0.1	0.1	0.05
临界状态参数	${M_{\text{c}}}$	1.25	1.25	1.296
	${e}_ \mathit{\Gamma }$	0.934	0.934	0.812
	${\lambda _{\text{c}}}$	0.02	0.02	0.0189
	$\xi$	0.7	0.7	0.7
剪胀参数	${d_1}$	0.2	0.2	1
剪胀参数	m	5	5	3.5
组构参数	${e_{\text{A}}}$	0.095	—	0.045
	${k_{\text{f}}}$	4.8	—	3
	${F_{\text{0}}}$	0.45	—	0.35
非共轴参数	k	0.5	—	0.4
硬化参数	${c_{\text{h}}}$	1.4	1.4	0.45
	${k_{\text{h}}}$	0.03	0.03	0.03
	n	3	3	2

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