不同盐度下深海能源黏土宏微观力学特性离散元分析

李政; 蒋明镜; 王思远

doi:10.11779/CJGE20231117

不同盐度下深海能源黏土宏微观力学特性离散元分析 English Version

李政^1,,
蒋明镜^{2, 3, ,},
王思远¹

1.
天津大学建筑工程学院, 天津 300350
2.
苏州科技大学土木工程学院, 江苏苏州 215009
3.
同济大学土木工程防灾国家重点实验室, 上海 200092

基金项目:

海南省重点研发计划项目 ZDYF2021SHFZ264

国家重大自然灾害防控与公共安全重点专项 2022YFC3003400

国家自然科学基金重大项目 52331010

国家自然科学基金重大项目 51890911

详细信息

作者简介:
李政(1997—)，男，研究生，主要从事深海能源土宏微观数值分析研究。E-mail: lz02181998@163.com

通讯作者:
蒋明镜, E-mail: mingjing.jiang@mail.usts.edu.cn

中图分类号: TU452
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出版历程
- 收稿日期: 2023-11-20
- 网络出版日期: 2024-11-10
- 刊出日期: 2025-04-30

Discrete element analysis of macro- and micro-mechanical properties of methane hydrate-bearing clay under different salinities

1.
School of Civil Engineering, Tianjin University, Tianjin 300350, China
2.
School of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, China
3.
State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 能源土的力学行为与水合物相平衡特性紧密相关，相较于砂土，黏土沉积物具有更小的孔径且孔径对水合物相平衡特性有较大的影响。通过引入孔径对相平衡线的影响，建立了胶结型深海能源黏土温-压-力-化三维微观接触模型，并开展了不同盐度下的深海能源黏土的三轴压缩数值模拟试验，对其应力应变曲线、体变、胶结破坏、团粒破碎率和强度特性等宏微观力学行为进行了分析，并与重塑黏土的力学特性进行了对比，讨论了水合物胶结对深海能源黏土力学特性的增强作用。结果表明：①低围压下，随着盐度的升高，深海能源黏土的峰值抗剪强度逐渐减小，且应变软化特征越不明显，同时体变先剪缩后微弱剪胀再剪缩的特点，高围压下其表现为应变硬化及剪缩特性。②随着围压的增大及环境盐度的升高，深海能源黏土的胶结破坏数和团粒破碎率均逐渐增大。③通过对深海能源黏土的强度特性的分析发现，其强度包线呈现典型的非线性特征。
- 深海能源黏土 /
- 孔径 /
- 离散单元法 /
- 三轴压缩 /
- 盐度
Abstract: The mechanical behavior of methane hydrate bearing soil is closely related to the characteristics of hydrate phase equilibrium. Compared with sand, clay has smaller pore size and the pore size has a great influence on the characteristics of hydrate phase equilibrium. A three-dimensional thermal-hydro-mechanical-chemical bond contact model for grain-cementing type methane hydrate-bearing clay is established by introducing the influences of the pore size on the phase equilibrium line. The numerical simulation of triaxial compression tests on the methane hydrate-bearing clay under different salinities is carried out. The macro- and micro-mechanical behaviors such as stress-strain curve, volume strain, number of bond breakage, aggregate crushing rate and strength characteristics are analyzed and compared with the mechanical properties of remolded clay. The enhancement of bond on the mechanical properties of the methane hydrate-bearing clay is discussed. The results show that (1) Under low confining pressure, with the increase of the salinity, the peak shear strength of the methane hydrate-bearing clay gradually decreases, and the strain softening is less significant. At the same time, the volume strain shows shear contraction first, then weak dilatation and then shear contraction. Under high confining pressure, it shows strain hardening and shear contraction. (2) With the increase of the confining pressure and salinity, the number of bond breakage and the aggregate crushing rate of the methane hydrate-bearing clay gradually increase. (3) Finally, through the analysis of the strength characteristics of the methane hydrate-bearing clay, it is found that its strength envelope presents typical nonlinear characteristics.
- methane hydrate-bearing clay /
- pore size /
- discrete element method /
- triaxial compression /
- salinity

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0. 引言

瑞利波传播过程中主要引起水平方向振动，这种振动与建筑物的自然频率相近时，会引起共振，导致更大的破坏。为进一步明确瑞利波传播特性和衰减规律，大量学者对其进行理论分析^[1]、数值模拟^[2]和试验研究^[3]。瑞利波在介质中的传播受多种因素影响，主要包括介质的弹性参数、密度、重力以及分层结构等^[4]。

桩基在瑞利波作用下的动力响应的研究成为抗震过程中的重要组成部分。Yang等^[5]在考虑桩顶柔性约束的情况下，研究了非饱和土-桩体系在瑞利波作用下的动力响应。此外Cai等^[6]采用刚性排桩作为隔离瑞利波的方法，考虑了软土地质所产生的影响。

通过以上讨论发现：考虑竖向荷载影响的瑞利波作用下桩水平动力响应分析比较复杂。且对于软土地基中桩在瑞利波作用下的动力响应的研究也相对较少。因此，本文建立考虑竖向荷载对瑞利波作用下饱和软土地基中桩的水平动力响应影响的计算模型。研究结果为瑞利波作用下桩基动力分析和设计提供理论指导。

1. 计算模型

1.1 问题描述

在瑞利波的作用下饱和土-桩体系的数学模型如图 1所示，其中桩长为L，半径为r_a，截面积为A_p，密度为ρ_p，杨氏模量为E_p，剪切模量为G_p。桩体模型简化为桩端为固定边界条件的Timoshenko梁，桩顶视为质量为M₀的刚性块体。桩周饱和土视为线弹性材料，泊松比、阻尼比和剪切模量分别取为 ${\nu _0}$ ， ${\varepsilon _0}$ ，s和G_s。其中瑞利波的作用方式是以波的形式穿过土体传播到桩体上。

图 1 瑞利波作用下桩在饱和土中的计算模型

Figure 1. Computational model for pile in saturated soils under Rayleigh waves

下载: 全尺寸图片幻灯片

1.2 基本方程

根据Biot’s理论，运动方程可以表示为

${\sigma _{ij, j}} = {\rho _{\text{s}}}{\ddot u_i} + {\rho _{\text{f}}}{\ddot w_i} \text{, }\;$

(1)

$- {p_{{\text{f}}, i}} = {\rho _{\text{f}}}{\ddot u_i} + {m_1}{\ddot w_i} + {r_1}{\dot w_i} 。$

(2)

式中： ${u_i}$ 为土体位移； ${w_i}$ 为流体位移； $\lambda$ ，μ为拉梅常数；m₁= ${\rho _{\text{f}}}$ /n为孔隙中流体密度与孔隙率的比值；r₁= ${\rho _{\text{f}}}$ g/k_d，k_d为土壤达西渗透系数， ${p_{\text{f}}}$ 为孔隙中流体压力；α和M分别为两相材料的Biot’s参数。

基于Timoshenko理论，建立桩段控制微分方程^[7]：

$\begin{array}{l} {A_{\text{p}}}{G_{\text{p}}}{k_{\text{0}}}\left( {\frac{{{\partial ^2}{u_{\text{p}}}}}{{\partial {z^2}}} - \frac{{\partial {\theta _{\text{p}}}}}{{\partial z}}} \right) + {\rho _{\text{p}}}{A_{\text{p}}}\frac{{{\partial ^2}{u_{\text{p}}}}}{{\partial {t^2}}} +\\ \;\;\;\;\;\;\;\;\;\;\;\;({k_{\text{h}}} + {\text{i}}{c_{\text{h}}})({u_{\text{p}}} - {u_{\text{r}}}\cos \theta ) = 0 \text{, }\; \end{array}$

(3)

$\begin{array}{l} {A_{\text{p}}}{G_{\text{p}}}{k_{\text{0}}}\left( {\frac{{\partial {u_{\text{p}}}}}{{\partial z}} - {\theta _{\text{p}}}} \right) - {\rho _{\text{p}}}{I_{\text{p}}}\frac{{{\partial ^2}{u_{\text{p}}}}}{{\partial {t^2}}} - \\ \;\;\;\;\;\;\;\;\;\;\;\;{E_{\text{p}}}{I_{\text{p}}}\frac{{{\partial ^2}{\theta _{\text{p}}}}}{{\partial {{\text{z}}^2}}} + {A_{\text{p}}}P\frac{{\partial {u_{\text{p}}}}}{{\partial z}} = 0 。 \end{array}$

(4)

式中： ${u_{\text{p}}}(z, t) = {\bar u_{\text{p}}}(z){{\text{e}}^{{\text{i}}\omega t}}$ ， ${\theta _{\text{p}}}(z, t) = {\bar \theta _{\text{p}}}(z){{\text{e}}^{{\text{i}}\omega t}}$ 分别为桩的水平位移和转角；k₀为Timoshenko梁理论中的修正剪切因子；P为由上部结构质量引起的竖向荷载。

2. 方程的求解

由式（2）得：

${w_{\text{r}}} = \frac{{{\omega ^2}{\rho _{\text{f}}}{u_{\text{r}}}}}{\vartheta } - \frac{1}{\vartheta }\frac{{\partial {p_{\text{f}}}}}{{\partial r}} \text{, }\; {w_\theta } = \frac{{{\omega ^2}{\rho _{\text{f}}}{u_\theta }}}{\vartheta } - \frac{1}{\vartheta }\frac{{\partial {p_{\text{f}}}}}{{r\partial \theta }} 。$

(5)

式中： $\eta _{\text{a}}^2 = 2/(1 - \nu )$ ， $\vartheta = {\text{i}}\omega {\rho _{\text{f}}}g/{k_{\text{d}}} - {m_1}{\omega ^2}$ 。

将式（5）代入式（1），（2）结合本构方程得

$\begin{array}{c} \eta _{\text{b}}^{\text{2}}\frac{\partial }{{\partial r}}\left[ {\frac{1}{r}\left( {\frac{{\partial (r{u_r})}}{{\partial r}} + \frac{{\partial {u_\theta }}}{{\partial \theta }}} \right)} \right] - \frac{1}{{{r^2}}}\frac{\partial }{{\partial \theta }}\left[ {\frac{{\partial (r{u_\theta })}}{{\partial r}} - \frac{{\partial {u_r}}}{{\partial \theta }}} \right] +\\ \frac{{{\partial ^2}{u_r}}}{{\partial {z^2}}} + {c_{\text{1}}}\frac{{{\rho _{\text{s}}}{\omega ^2}}}{{{G_s}}}{u_r} - {c_{\text{2}}}\frac{{\partial {p_{\text{f}}}}}{{\partial r}} = 0 \text{, }\; \end{array}$

(6)

$\begin{array}{c} \frac{\partial }{{\partial r}}\left[ {\frac{1}{r}\left( {\frac{{\partial (r{u_\theta })}}{{\partial r}} - \frac{{\partial {u_{\text{r}}}}}{{\partial \theta }}} \right)} \right] + \eta _{\text{b}}^{\text{2}}\frac{1}{{{r^2}}}\frac{\partial }{{\partial \theta }}\left[ {\frac{{\partial (r{u_r})}}{{\partial r}} + \frac{{\partial {u_\theta }}}{{\partial \theta }}} \right] +\\ \frac{{{\partial ^2}{u_\theta }}}{{\partial {z^2}}} + {c_{\text{1}}}\frac{{{\rho _{\text{s}}}{\omega ^2}}}{{{G_{\text{s}}}}}{u_\theta } - {c_{\text{2}}}\frac{{\partial {p_{\text{f}}}}}{{r\partial \theta }} = 0 。 \end{array}$

(7)

式中： ${c_{\text{1}}} = 1 + \frac{{{\omega ^2}\rho _{\text{f}}^2}}{{{\rho _{\text{s}}}\vartheta }};{c_{\text{2}}} = \frac{\alpha }{{2\mu }}\frac{{1 - 2\nu }}{{1 - \nu }} + \frac{{{\omega ^2}{\rho _{\text{f}}}}}{{{\mu _{\text{s}}}\vartheta }};$ $\eta _{\text{b}}^{\text{2}} = \frac{{2 - \nu }}{{1 - \nu }}$

忽略流体的垂直位移：

$\begin{array}{l} \left( {\frac{{{\omega ^{\text{2}}}{\rho _{\text{f}}}}}{\vartheta } - \alpha \frac{{1 - 2{\nu _{\text{0}}}}}{{1 - {\nu _{\text{0}}}}}} \right)\left( {\frac{{\partial {u_r}}}{{\partial r}} + \frac{{{u_r}}}{r} + \frac{1}{r}\frac{{\partial {u_\theta }}}{{\partial \theta }}} \right) \\ \;\;\;\;\;\;\;\;\;\;\;\; = \frac{1}{\vartheta }{\nabla ^2}{p_{\text{f}}} + \left( {\frac{{{\alpha ^2}}}{\lambda }\frac{{{\nu _{\text{0}}}}}{{1 - {\nu _{\text{0}}}}} + \frac{1}{M}} \right){p_{\text{f}}} 。 \end{array}$

(8)

水平位移和切向位移用两个势函数Φ和Ψ表示为

${u_r} = \frac{{\partial \phi }}{{\partial r}} + \frac{1}{r}\frac{{\partial \psi }}{{\partial \theta }} \text{, }\; {u_\theta } = \frac{1}{r}\frac{{\partial \phi }}{{\partial \theta }} - \frac{{\partial \psi }}{{\partial {\text{r}}}} 。$

(9)

将式（9）代入式（6）~（8），联立得

$\eta _{\text{b}}^2{\nabla ^2}\phi + \frac{{{\partial ^2}\phi }}{{\partial {z^2}}} + {c_{\text{1}}}\frac{{{\rho _{\text{s}}}}}{{{G_{\text{s}}}}}{\omega ^2}\phi = {c_{\text{2}}}{p_{\text{f}}} \text{, }\;$

(10)

${\nabla ^2}\psi + \frac{{{\partial ^2}\psi }}{{\partial {z^2}}} + {c_{\text{1}}}\frac{{{\rho _{\text{s}}}}}{{{G_{\text{s}}}}}{\omega ^2}\psi = 0 \text{, }\;$

(11)

${\nabla }^{2}{p}_{\text{f}}+\left(\frac{\vartheta {\alpha }^{2}}{\lambda }\frac{{\nu }_{\text{0}}}{1-{\nu }_{\text{0}}}+\frac{\vartheta }{M}\right){p}_{\text{f}}=\left({\omega }^{\text{2}}{\rho }_{\text{f}}-\alpha \vartheta \frac{1-2{\nu }_{\text{0}}}{1-{\nu }_{\text{0}}}\right){\nabla }^{2}\phi 。$

(12)

采用分离变量法，设 $\phi (r, \theta , z) = {\phi _1}(r, \theta )Z(z),$ 假设 $\varphi (r, \theta , z) = {\varphi _1}(r, \theta )Z(z)$ ， $\frac{{{{\text{d}}^2}Z}}{{{\text{d}}{z^2}}} + {a^2}Z = 0$ ，将Z(z)表示为

$Z(z)=B_0 \cos (a z)+B_1 \sin (a z)。$

(13)

联立式（10）~（12）并将式（13）代入得

${\nabla ^2}{\psi _{\text{1}}} - \left[ {{a^2} - {c_{\text{1}}}\frac{{{\rho _{\text{s}}}}}{{{G_{\text{s}}}}}{\omega ^2}} \right]{\psi _{\text{1}}} = 0 。$

(14)

$({\nabla ^{\text{2}}} - \zeta _{{\text{11}}}^{\text{2}})({\nabla ^{\text{2}}} - \zeta _{{\text{12}}}^{\text{2}}){\phi _{\text{1}}} = {\text{0}}$

(15)

这里设： ${d_{11}} = \frac{{{c_1}}}{{\eta _{\text{b}}^{\text{2}}}}\frac{{{\rho _{\text{s}}}}}{{{G_{\text{s}}}}}{\omega ^2} + \frac{\vartheta }{M} - \frac{{{a^2}}}{{\eta _{\text{b}}^{\text{2}}}} + \frac{{{c_2}\alpha \vartheta }}{{\eta _{\text{b}}^{\text{2}}}}\frac{{1 - 2{\nu _{\text{0}}}}}{{1 - {\nu _{\text{0}}}}} - \frac{{{c_2}{\omega ^{\text{2}}}{\rho _{\text{f}}}}}{{\eta _{\text{b}}^{\text{2}}}}$ + $\frac{\vartheta {\alpha }^{2}}{\lambda }\frac{{\nu }_{\text{0}}}{1-{\nu }_{\text{0}}}$ ， ${d_{{\text{12}}}} = \frac{\vartheta }{{\eta _{\text{b}}^{\text{2}}}}\left[ {{c_1}\frac{{{\rho _{\text{s}}}}}{{{G_{\text{s}}}}}{\omega ^2}\left( {\frac{{{\alpha ^2}}}{\lambda }\frac{{{\nu _{\text{0}}}}}{{1 - {\nu _{\text{0}}}}} + \frac{{\text{1}}}{M}} \right) - } \right.$ $\left. {\frac{{{a^2}{\alpha ^2}}}{\lambda }\frac{{{\nu _{\text{0}}}}}{{1 - {\nu _{\text{0}}}}} - \frac{{{a^2}}}{M}} \right] \text{, }\; \zeta _{{\text{11}}}^{\text{2}} = \frac{{ - {d_{11}} + \sqrt {d_{11}^2 - 4{d_{12}}} }}{2}$ , $\zeta _{{\text{12}}}^{\text{2}} =\frac{{ - {d_{11}} - \sqrt {d_{11}^2 - 4{d_{12}}} }}{2}$ ， ${v_{\text{s}}} = \sqrt {\frac{{{G_{\text{s}}}}}{{{\rho _{\text{s}}}}}}$ ，从而得到

$({\nabla ^{\text{2}}} + k_{{\text{a1}}}^2)({\nabla ^{\text{2}}} + k_{{\text{a2}}}^2){\phi _{\text{1}}} = {\text{0}} \text{, }\;$

(16)

$({\nabla ^2} + k_{{\text{b1}}}^2){\psi _{\text{1}}} = 0 。$

(17)

通过算子分解理论和分离变量法得：

$\begin{array}{l} {\phi _{\text{1}}} = {A_{{\text{s1}}}}\exp ( - {s_1}r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta ) +\\ \;\;\;\;{A_{{\text{s2}}}}\exp ( - {s_2}r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta ) \text{, }\; \end{array}$

(18)

${\psi _{\text{1}}} = {B_{\text{s}}}\exp ( - \gamma r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta ) 。$

(19)

式中：A_s1，A_s2，B_s分别为与边界条件有关的待定常数；k_R，V_R=ω/k_R分别为瑞利波的复波速和相速度； ${s_i} =$ $\sqrt {k_{\text{R}}^2 - k_{{\text{a}}i}^2}$ (i=1, 2)和 $\gamma = \sqrt {k_{\text{R}}^2 - k_{{\text{b1}}}^2}$ ，分别为压缩波和剪切波对应的衰减指数； ${k}_{{a}_{1}}^{2}=-{\zeta }_{11}^{2}, {k}_{{a}_{2}}^{2}=-{\zeta }_{12}^{2}，$ $k_{{b_{\text{1}}}}^2 =$ $- {a^2} + {\kappa _{\text{1}}}\frac{{{\rho _{\text{s}}}}}{{{G_{\text{s}}}}}{\omega ^2}$ 。

因此由式（13），结合边界条件即 ${\left. {{\tau _{rz}}} \right|_{z = 0}} = 0$ ， ${\left. {{u_r}} \right|_{z = L}} = {\left. {{u_\theta }} \right|_{z = L}} = 0$ 可知

$\left. \begin{array}{l} {B}_{0}={B}_{1}=0且\mathrm{cos}(aL)=0\text{ }\text{, }\;\\ {a}_{m}=\frac{(2m-1){\rm{ \mathsf{ π}}}}{2L}, m=1, 2, 3\text{ }。 \end{array} \right\}$

(20)

$\begin{array}{l} \varphi = [{A_{{\text{s1}}}}\exp ( - {s_1}r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta ) +\\ \;\;{A_{{\text{s2}}}}\exp ( - {s_2}r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta )]\sin ({a_m}z) \text{, }\; \end{array}$

(21)

$\psi = {B_{\text{s}}}\exp ( - \gamma r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta )\sin ({a_m}z) 。$

(22)

将式（21）代入式（10）得

$\begin{array}{l} \;\;\;\;{p_{\text{f}}} = \left[ { - \frac{{a_m^2}}{{{c_2}}} + \frac{{{c_1}}}{{{c_2}}}{{\left( {\frac{\omega }{{{V_{\text{s}}}}}} \right)}^2}} \right]\left[ {{A_{{\text{s1}}}}\exp \left( \begin{array}{l} - {s_1}r\sin \theta \hfill \\ - {\text{i}}{k_R}r\cos \theta \hfill \end{array} \right) + } \right. \hfill \\ \;\;\;\;\left. {{A_{{\text{s2}}}}\exp \left( \begin{array}{l} - {s_2}r\sin \theta \hfill \\ - {\text{i}}{k_{\text{R}}}r\cos \theta \hfill \end{array} \right)} \right]\sin ({a_m}z) + \hfill \\ \frac{{\eta _{\text{b}}^{\text{2}}}}{{{c_2}}}(s_1^2 - k_{\text{R}}^{\text{2}}){A_{{\text{s1}}}}\exp ( - {s_1}r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta )\sin ({a_m}z) + \\ \frac{{\eta _{\text{b}}^{\text{2}}}}{{{c_2}}}(s_2^2 - k_{\text{R}}^{\text{2}}){A_{{\text{s2}}}}\exp ( - {s_2}r\sin \theta - {\text{i}}{k_{\text{R}}}r\cos \theta )\sin ({a_m}z) 。\end{array}$

(23)

通过式（9）结合本构方程及式（21），（22）并代入边界条件 ${\left. {{\tau _{rz}}} \right|_{z = 0}} = 0, {\left. {{u_\theta }} \right|_{z = L}} = 0$ 可知

${A_{{\text{s2}}}} = {d_1}{A_{{\text{s}}1}}, {B_{\text{s}}} = {d_2}{A_{{\text{s1}}}} 。$

(24)

联立式（9）即可求得位移转角u_r、u_θ表达式。

因此自由场饱和土在瑞利波作用下位移由体积平均原理得

${\bar u_r} = (1 - n){u_r} + n{w_r} \text{, }\;$

(25)

${\bar u_\theta } = (1 - n){u_\theta } + n{w_\theta } 。$

(26)

3. 瑞利波作用下桩的动力响应

3.1 水平阻力

桩在瑞利波作用下的动力响应由桩周土体决定，采用动力Winkler模型来描述饱和土桩体系的水平动力响应，进而计算单位桩长上的水平阻力^[8-9]。因此设单位桩长上的水平阻力为

${q_h} = ({k_h} + {i} {c_h}){u_{{\bar{\text p}}}} 。$

(27)

式中：k_h和c_h分别为Winkler模型中弹簧刚度和阻尼系数。

3.2 考虑竖向荷载影响的桩的动力响应

将式（25），（27）代入式（3），（4）并省略因子e^iωt得

$\frac{{{{\text{d}}^{\text{4}}}{{\bar u}_{\text{p}}}}}{{{\text{d}}{z^4}}} + W\frac{{{{\text{d}}^2}{{\bar u}_{\text{p}}}}}{{{\text{d}}{z^2}}} + J{\bar u_{\text{p}}} = {H_1}{A_{{\text{s1}}}}\sin ({a_m}z) \text{, }\;$

(28)

$\frac{{{{\text{d}}^4}{{\bar \theta }_{\text{p}}}}}{{{\text{d}}{z^4}}} + W\frac{{{{\text{d}}^2}{{\bar \theta }_{\text{p}}}}}{{{\text{d}}{z^2}}} + J{\bar \theta _{\text{p}}} = {H_2}{A_{{\text{s1}}}}\cos ({a_m}z) 。$

(29)

其中， $W = \frac{{{\rho _{\text{P}}}{\omega ^2}}}{{{E_{\text{p}}}}} + \frac{{{\rho _{\text{P}}}{\omega ^2}}}{{{k_{\text{0}}}{G_{\text{p}}}}} + \frac{{{A_{\text{p}}}P}}{{{E_{\text{p}}}{I_{\text{p}}}}} - \frac{{({k_{\text{h}}} + {\text{i}}{c_{\text{h}}})}}{{{k_{\text{0}}}{A_{\text{p}}}{G_{\text{p}}}}}$ ， $J =$ $\frac{{\rho _{\text{p}}^{\text{2}}{\omega ^4}}}{{{k_{\text{0}}}{G_{\text{p}}}{E_{\text{p}}}}} - \frac{{{\rho _{\text{P}}}{A_{\text{p}}}{\omega ^2}}}{{{E_{\text{p}}}{I_{\text{p}}}}} - \left( {\frac{{{\rho _{\text{P}}}{\omega ^2}}}{{{k_{\text{0}}}{A_{\text{p}}}{G_{\text{p}}}{E_{\text{p}}}}} - \frac{1}{{{E_{\text{p}}}{I_{\text{p}}}}}} \right)({k_{\text{h}}} + {\text{i}}{c_{\text{h}}})$

方程（28）、（29）对应的解设为

$\begin{array}{c} {\bar u_{\text{p}}} = {M_{\text{1}}}\cos ({\lambda _{\text{1}}}z) + {M_{\text{2}}}\sin ({\lambda _{\text{1}}}z) + {M_{\text{3}}}ch({\lambda _{\text{2}}}z) +\\ {M_{\text{4}}}sh({\lambda _{\text{2}}}z) + {b_{\text{1}}}{A_{{\text{s1}}}}\sin ({a_m}z) \text{, }\; \end{array}$

(30)

$\begin{array}{c} {\bar \theta _{\text{p}}} = {M_{\text{1}}}{\chi _{\text{1}}}\sin ({\lambda _{\text{1}}}z) + {M_{\text{2}}}{\chi _{\text{2}}}\cos ({\lambda _{\text{1}}}z) + {M_{\text{3}}}{\chi _{\text{3}}}sh({\lambda _{\text{2}}}z) +\\ {M_{\text{4}}}{\chi _{\text{4}}}ch({\lambda _{\text{2}}}z) + {b_{\text{2}}}{A_{{\text{s1}}}}\cos ({a_m}z) \text{, }\; \end{array}$

(31)

式中： ${\lambda }_{1}=\sqrt{\frac{W+\sqrt{{W}^{2}-4J}}{2}}, {\lambda }_{2}=\sqrt{\frac{-W+\sqrt{{W}^{2}-4J}}{2}}，$ M_i(1，2，3，4)为与桩的边界条件有关的待定系数。其中 ${\chi }_{\text{1}}=-{\chi }_{\text{2}}=-\frac{{k}_{0}{A}_{\text{p}}{G}_{\text{p}}{\lambda }_{\text{1}}+{A}_{\text{p}}P{\lambda }_{\text{1}}}{{k}_{0}{A}_{\text{p}}{G}_{\text{p}}+{\rho }_{\text{p}}{I}_{\text{p}}{\omega }^{2}+{E}_{\text{p}}{I}_{\text{p}}{\lambda }_{\text{1}}^{2}}，$ ${\chi _{\text{3}}} =$ ${\chi _{\text{4}}} = \frac{{{k_0}{A_{\text{p}}}{G_{\text{p}}}{\lambda _{\text{2}}} + {A_{\text{p}}}P{\lambda _{\text{2}}}}}{{{k_0}{A_{\text{p}}}{G_{\text{p}}} + {\rho _{\text{p}}}{I_{\text{p}}}{\omega ^2} - {E_p}{I_{\text{p}}}\lambda _{\text{1}}^2}},$ ${b_{\text{1}}} = \frac{{{H_{\text{1}}}}}{{a_m^4 - Wa_m^2 + J}}$ ， ${b_{\text{2}}} = \frac{{{H_2}}}{{a_m^4 - Wa_m^2 + J}}$ 。

沿桩身的弯矩和剪力可由弹性力学推导为

$\begin{array}{l} {\bar M_{\text{p}}} = {E_{\text{P}}}{I_P}\left[ {{M_1}{\chi _1}{\lambda _1}\cos ({\lambda _1}z) - {M_2}{\chi _2}{\lambda _1}\sin ({\lambda _1}z)} \right. +\\ {M}_{3}{\chi }_{3}{\lambda }_{2}ch({\lambda }_{2}z)+{M}_{4}{\chi }_{4}{\lambda }_{2}sh({\lambda }_{2}z)-{b}_{\text{2}}{a}_{m}{A}_{\text{s1}}\mathrm{sin}({a}_{m}z)]。 \end{array}$

(32)

$\begin{array}{l} {{\bar Q}_{\text{p}}} = {k_0}{A_{\text{P}}}{G_{\text{P}}}\left[ { - {M_1}({\lambda _1} + {\chi _1})\sin ({\lambda _1}z) + {M_2}({\lambda _1} - {\chi _2})} \right. \cdot \hfill \\ \cos ({\lambda _1}z) + {M_3}({\lambda _2} - {\chi _3})sh({\lambda _2}z) + {M_4}({\lambda _2} - {\chi _4})ch({\lambda _2}z) + \hfill \end{array} \left. \\ \;\;\;\;\;\;\;\;\;\;{({b_{\text{1}}}{a_m} - {b_{\text{2}}}){A_{s{\text{1}}}}\cos ({a_m}z)} \right] 。$

(33)

桩顶柔性状态下，桩端处于固定状态，桩的边界条件为：

$\left. \begin{array}{l} {\overline{M}}_{\text{p}}(z)={K}_{1}{\overline{\theta }}_{c}+{K}_{2}\left[{\overline{\theta }}_{\text{p}}(0)-{\overline{\theta }}_{c}\right]\text{, }\;z=0\text{ }\text{, }\;\\ {\overline{Q}}_{\text{p}}(z)-{A}_{\text{p}}P{\overline{\theta }}_{\text{p}}(z)+{\omega }^{2}{M}_{\text{0}}{\overline{u}}_{\text{p}}(z)=0, z=0\text{ }\text{, }\;\\ {\overline{u}}_{\text{p}}(z)=0\text{, }\;{\overline{\theta }}_{\text{p}}(z)=0, z=L\text{ }。 \end{array} \right\}$

(34)

将边界条件代入桩体水平位移、旋转角度沿桩身的弯矩和剪力表达式，由此可以导出所有未确定的待定参数M_i（i=1, 2, 3, 4），A_s1。

4. 数值分析及讨论

通过数值算例验证，分析竖向荷载及桩顶柔性约束下各参数对于桩身位移、转角和弯矩的影响。各相关参数属性： ${\rho _{\text{s}}}$ =2.7×10³ kg/m³， ${\rho _{\text{f}}}$ =2.2×10³ kg/m³，E_a=2×10⁹ Pa， ${\nu _{\text{0}}}$ =0.4，n=0.4，α=0.9，k_d=1×10^-8 m/s，K_s=3.6×10¹⁰ Pa，K_f=2×10⁹ Pa，G_s=2.5×10⁶ Pa，d=1 m，r_a=0.5 m，L=20 m， ${\rho _{\text{p}}}$ =2.5×10³ kg/m³，E_p= 2.5×10¹⁰ Pa，k₀=0.75，I_p=π/64，ν_p=0.2，A_p=0.25π，M₀=1×10⁵ kg，P=10×10⁶ Pa。引入无量纲频率a₀=ωL_a/v_s。

4.1 验证

为验证模型的准确性，将Makris^[10]解与模型进行比较。在相同条件下，对本文的计算模型进行验证。图 2将水平位移与Makris^[10]解的结果进行比较。可以看出两种解法有较高的一致性。

图 2 本文解与Makris解的比较

Figure 2. Comparison between authors' and Makris' solutions

下载: 全尺寸图片幻灯片

4.2 参数分析

图 3，4给出了瑞利波作用下，竖向荷载对单桩的水平动力响应的影响，其研究了桩长、竖向荷载大小和无量纲频率对桩基水平振动的影响。从图 3可以看出，随着竖向荷载的增加，位移、转角和弯矩都在增大，且增加的趋势也越来越大。随着深度的增加，竖向荷载改变所引起的变化不再明显，最终趋于稳定。

图 3 竖向荷载对单桩横向响应沿桩长变化的影响

Figure 3. Influences of vertical load on lateral response of a single pile along pile length

下载: 全尺寸图片幻灯片

图 4 竖向荷载对单桩水平响应随无因次频率变化的影响

Figure 4. Influences of vertical load on horizontal response of a single pile with dimensionless frequency

下载: 全尺寸图片幻灯片

图 4显示了垂直载荷对位移、转角和弯矩的影响。当频率等于固有频率时，发生共振。在共振区，当竖向荷载较小时，随竖向荷载的增大，桩顶位移和桩端弯矩整体呈增大趋势。随无量纲频率的增大，竖向荷载的改变引起水平位移和转角的变化将不再明显。

5. 结论

考虑竖向荷载对瑞利波作用下饱和软土中单桩结构水平动力响应的影响，建立瑞利波作用下饱和软土中桩顶柔性约束下单桩水平动力响应的计算模型。通过数值计算结果，得出以下3点结论。

（1）随深度的增加，位移和转角先减小后增大；弯矩整体呈减小趋势；最终接近桩端固结端时桩的水平动力响应趋于稳定。

（2）随无量纲频率的增加，位移、转角和弯矩在共振区发生共振后最终趋于稳定。

（3）随竖向荷载的增加，位移、转角和弯矩都在增大。但是这种改变所引起的变化随着深度的增加不再明显，最终趋于稳定。

图 1 团粒微观结构

Figure 1. Microstructure of aggregate

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图 2 接触力学响应

Figure 2. Mechanical responses of contact

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图 3 不同孔径介质中的水合物相平衡线

Figure 3. Hydrate phase equilibrium lines in media with different pore sizes

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图 4 参数c，d与孔径l的关系

Figure 4. Relationship between parameters c, d and pore size l

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图 5 团粒破碎的级配演化规律^[27]

Figure 5. Gradation evolution law of aggregate crushing^[27]

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图 6 离散元试样及粒径级配曲线

Figure 6. DEM sample and grain-size distribution curve

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图 7 不同围压及环境盐度下深海能源黏土的应力应变曲线

Figure 7. Stress-strain curves of methane hydrate bearing clay under different environmental salinities and confining pressure

下载: 全尺寸图片幻灯片

图 8 不同环境盐度下深海能源黏土的体变曲线

Figure 8. Volume strain curves of methane hydrate bearing clay under different environmental salinities

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图 9 不同围压及不同盐度下深海能源黏土的胶结破坏曲线

Figure 9. Bond failure of methane hydrate bearing clay under different environmental salinities and confining pressures

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图 10 不同环境盐度下深海能源黏土的团粒破碎曲线

Figure 10. Aggregate crushing rates of methane hydrate bearing clay under different environmental salinities

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图 11 峰值强度包线

Figure 11. Peak strength envelopes

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表 1 深海能源黏土的接触参数及破碎参数^[23]

Table 1 Contact parameters and crushing parameters of methane hydrate bearing clay^[23]

类型	参数名称	数值
颗粒接触参数	颗粒接触等效模量E_p/MPa	700
	颗粒法切向刚度比ξ_p	1.5
	颗粒摩擦系数μ	0.5
	Hamaker常数A/J	7.5×10^-20
	表面电势ψ₀/mv	100
	双电层厚度1/κ/nm	5
	颗粒局部压碎系数ζ_c	2.1
	颗粒接触半径系数β	0.1
	力学接触截断距离d_mc/nm	0.9
	物理化学截断距离d_pc/nm	25
胶结参数	胶结法切向刚度比ξ_b	2.64
	临界胶结厚度系数g_c	0.1
	胶结半径系数λ_b	0.740
破碎参数	参考粒径d₀/um	10
	单团粒参考强度σ_{d, 0}/GPa	1.25
	团粒强度与粒径相关的指数参数m	0.25
	胶结强度尺寸相关的修正系数A_k	1200
	粒径相关的修正系数B_k	10
	强度随机数f_var的标准偏差值	6.9
	强度随机数f_var的上、下限值	9.0，0.25
	最小破碎粒径d_lim/um	2.5

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参考文献(31)

[1]	ZHANG W, LIANG J Q, SU P B, et al. Distribution and characteristics of mud diapirs, gas chimneys, and bottom simulating reflectors associated with hydrocarbon migration and gas hydrate accumulation in the Qiongdongnan Basin, northern slope of the South China Sea[J]. Geological Journal, 2019, 54(6): 3556-3573. doi: 10.1002/gj.3351
[2]	LIANG J Q, ZHANG W, LU J A, et al. Geological occurrence and accumulation mechanism of natural gas hydrates in the eastern Qiongdongnan Basin of the South China Sea: insights from site GMGS5-W9-2018[J]. Marine Geology, 2019, 418: 106042. doi: 10.1016/j.margeo.2019.106042
[3]	王淑云, 罗大双, 张旭辉, 等. 含水合物黏土的力学性质试验研究[J]. 实验力学, 2018, 33(2): 245-252. WANG Shuyun, LUO Dashuang, ZHANG Xuhui, et al. Experimental study of mechanical properties of hydrate clay[J]. Journal of Experimental Mechanics, 2018, 33(2): 245-252. (in Chinese)
[4]	石要红, 张旭辉, 鲁晓兵, 等. 南海水合物黏土沉积物力学特性试验模拟研究[J]. 力学学报, 2015, 47(3): 521-528. SHI Yaohong, ZHANG Xuhui, LU Xiaobing, et al. Experimental study on the static mechanical properties of hydrate-bearing silty-clay in the South China Sea[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(3): 521-528. (in Chinese)
[5]	ZHANG X H, LU X B, SHI Y H, et al. Study on the mechanical properties of hydrate-bearing silty clay[J]. Marine and Petroleum Geology, 2015, 67: 72-80. doi: 10.1016/j.marpetgeo.2015.04.019
[6]	SONG Y C, ZHU Y M, LIU W G, et al. The effects of methane hydrate dissociation at different temperatures on the stability of porous sediments[J]. Journal of Petroleum Science and Engineering, 2016, 147: 77-86. doi: 10.1016/j.petrol.2016.05.009
[7]	LI Y H, SONG Y C, YU F, et al. Experimental study on mechanical properties of gas hydrate-bearing sediments using Kaolin clay[J]. China Ocean Engineering, 2011, 25(1): 113-122. doi: 10.1007/s13344-011-0009-6
[8]	LI Y H, SONG Y C, YU F, et al. Effect of confining pressure on mechanical behavior of methane hydrate-bearing sediments[J]. Petroleum Exploration and Development, 2011, 38(5): 637-640. doi: 10.1016/S1876-3804(11)60061-X
[9]	LI Y, SONG Y, LIU W, et al. Analysis of mechanical properties and strength criteria of methane hydrate-bearing sediments[J]. International Journal of Offshore and Polar Engineering, 2012, 22(4): 290-296.
[10]	YUN T S, SANTAMARINA J C, RUPPEL C. Mechanical properties of sand, silt, and clay containing tetrahydrofuran hydrate[J]. Journal of Geophysical Research: Solid Earth, 2007, 112(B4): 106-118.
[11]	LI Y H, SONG Y C, LIU W G, et al. A new strength criterion and constitutive model of gas hydrate-bearing sediments under high confining pressures[J]. Journal of Petroleum Science and Engineering, 2013, 109: 45-50. doi: 10.1016/j.petrol.2013.08.010
[12]	LI T, LI L Q. DEM analyses of cemented hydrate's effect on the compression behavior of fine-grained sediments[J]. IOP Conference Series: Earth and Environmental Science, 2021, 643(1): 012111. doi: 10.1088/1755-1315/643/1/012111
[13]	LI T, LI L Q, LIU J J, et al. Influence of hydrate participation on the mechanical behaviour of fine-grained sediments under one-dimensional compression: a DEM study[J]. Granular Matter, 2021, 24(1): 32.
[14]	蒋明镜, 李涛, 胡海军. 结构性黄土双轴压缩试验的离散元数值仿真分析[J]. 岩土工程学报, 2013, 35(增刊2): 241-246. http://cge.nhri.cn/article/id/15388 JIANG Mingjing, LI Tao, HU Haijun. Numerical simulation of biaxial tests on structured loess by distinct element method[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(S2): 241-246. (in Chinese) http://cge.nhri.cn/article/id/15388
[15]	韩振华, 张路青, 周剑, 等. 黏土矿物颗粒特征对含水合物的沉积物力学特性影响研究[J]. 工程地质学报, 2021, 29(6): 1733-1743. HAN Zhenhua, ZHANG Luqing, ZHOU Jian, et al. Effect of clay mineral grain characteristics on mechani-cal behaviours of hydrate-bearing sediments[J]. Journal of Engineering Geology, 2021, 29(6): 1733-1743. (in Chinese)
[16]	MAKOGON Y F. Hydrates of Natural Gas[M]. Oklahoma: PennWell Books Tulsa, 1981.
[17]	ANDERSON R, LLAMEDO M, TOHIDI B, et al. Characteristics of clathrate hydrate equilibria in mesopores and interpretation of experimental data[J]. The Journal of Physical Chemistry B, 2003, 107(15): 3500-3506. doi: 10.1021/jp0263368
[18]	UCHIDA T, EBINUMA T, TAKEYA S, et al. Effects of pore sizes on dissociation temperatures and pressures of methane, carbon dioxide, and propane hydrates in porous media[J]. The Journal of Physical Chemistry B, 2002, 106(4): 820-826. doi: 10.1021/jp012823w
[19]	SEO Y, LEE H E, UCHIDA T. Methane and carbon dioxide hydrate phase behavior in small porous silica gels: three-phase equilibrium determination and thermodynamic modeling[J]. Langmuir, 2002, 18(24): 9164-9170. doi: 10.1021/la0257844
[20]	SMITH D H, WILDER J W, SESHADRI K. Methane hydrate equilibria in silica gels with broad pore-size distributions[J]. AIChE Journal, 2002, 48(2): 393-400. doi: 10.1002/aic.690480222
[21]	CHA M J, HU Y, SUM A K. Methane hydrate phase equilibria for systems containing NaCl, KCl, and NH 4 Cl[J]. Fluid Phase Equilibria, 2016, 413: 2-9. doi: 10.1016/j.fluid.2015.08.010
[22]	JIANG M J, SUN R H, ARROYO M, et al. Salinity effects on the mechanical behaviour of methane hydrate bearing sediments: a DEM investigation[J]. Computers and Geotechnics, 2021, 133: 104067. doi: 10.1016/j.compgeo.2021.104067
[23]	NIU M Y, JIANG M J. DEM modeling mechanical behaviors of remolded and structured clays under constant stress ratio compression tests[M]// Smart Geotechnics for Smart Societies. London: CRC Press, 2023.
[24]	蒋明镜, 孙若晗, 李涛, 等. 一个非饱和结构性黄土三维胶结接触模型[J]. 岩土工程学报, 2019, 41(增刊1): 213-216. doi: 10.11779/CJGE2019S1054 JIANG Mingjing, SUN Ruohan, LI Tao, et al. A three-dimensional cementation contact model for unsaturated structural loess[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(S1): 213-216. (in Chinese) doi: 10.11779/CJGE2019S1054
[25]	SHEN Z F, JIANG M J. DEM simulation of bonded granular material: Part Ⅱ extension to grain-coating type methane hydrate bearing sand[J]. Computers and Geotechnics, 2016, 75: 225-243. doi: 10.1016/j.compgeo.2016.02.008
[26]	蒋明镜, 刘阿森, 李光帅. 南海北部陆坡区深海软土宏微观特征与力学特性研究[J]. 岩土工程学报, 2023, 45(3): 618-626. doi: 10.11779/CJGE20220081 JIANG Mingjing, LIU Asen, LI Guangshuai. Macro- and micro-characteristics and mechanical properties of deep-sea sediment from South China Sea[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(3): 618-626. (in Chinese) doi: 10.11779/CJGE20220081
[27]	CIANTIA M O, ARROYO M, CALVETTI F, et al. An approach to enhance efficiency of DEM modelling of soils with crushable grains[J]. Géotechnique, 2015, 65(2): 91-110. doi: 10.1680/geot.13.P.218
[28]	ZHAO Y P, KONG L, XU R, et al. Mechanical properties of remolded hydrate-bearing clayey-silty sediments[J]. Journal of Natural Gas Science and Engineering, 2022, 100: 104473. doi: 10.1016/j.jngse.2022.104473
[29]	牛昴懿. 基于团粒破碎的结构性黏土力学特性的三维离散元模拟研究[D]. 上海: 同济大学, 2022. NIU Maoyi. Three-Dimensional Discrete Element Simulation of Mechanical Properties of Structural Clay Based on Particle Breakage[D]. Shanghai: Tongji University, 2022. (in Chinese)
[30]	JIANG M J, KONRAD J M, LEROUEIL S. An efficient technique for generating homogeneous specimens for DEM studies[J]. Computers and Geotechnics, 2003, 30(7): 579-597. doi: 10.1016/S0266-352X(03)00064-8
[31]	PANDA A P, RAO S N. Undrained strength characteristics of an artificially cemented marine clay[J]. Marine Georesources & Geotechnology, 1998, 16(4): 335-353.

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0. 引言
1. 计算模型
1.1 问题描述
1.2 基本方程
2. 方程的求解
3. 瑞利波作用下桩的动力响应
3.1 水平阻力
3.2 考虑竖向荷载影响的桩的动力响应
4. 数值分析及讨论
4.1 验证
4.2 参数分析
5. 结论

不同盐度下深海能源黏土宏微观力学特性离散元分析 English Version

作者简介: 李政(1997—)，男，研究生，主要从事深海能源土宏微观数值分析研究。E-mail: lz02181998@163.com

通讯作者: 蒋明镜, E-mail: mingjing.jiang@mail.usts.edu.cn

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出版历程

Discrete element analysis of macro- and micro-mechanical properties of methane hydrate-bearing clay under different salinities

0. 引言

1. 计算模型

1.1 问题描述

1.2 基本方程

2. 方程的求解

3. 瑞利波作用下桩的动力响应

3.1 水平阻力

3.2 考虑竖向荷载影响的桩的动力响应

4. 数值分析及讨论

4.1 验证

4.2 参数分析

5. 结论

其他相关附件

PDF格式

计量

出版历程

目录

0. 引言

1. 计算模型

1.1 问题描述

1.2 基本方程

2. 方程的求解

3. 瑞利波作用下桩的动力响应

3.1 水平阻力

3.2 考虑竖向荷载影响的桩的动力响应

4. 数值分析及讨论

4.1 验证

4.2 参数分析

5. 结论

作者简介:
李政(1997—)，男，研究生，主要从事深海能源土宏微观数值分析研究。E-mail: lz02181998@163.com

通讯作者:
蒋明镜, E-mail: mingjing.jiang@mail.usts.edu.cn