基于粒形特征影响的月壤静力学及流动特性离散元研究

石安宁; 蒋明镜; 王思远; 林嘉禹

doi:10.11779/CJGE20230997

基于粒形特征影响的月壤静力学及流动特性离散元研究 English Version

1.
天津大学建筑工程学院土木工程系, 天津 300072
2.
苏州科技大学土木工程学院, 江苏苏州 215009

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

国家自然科学基金创新研究群体项目 42221002

详细信息

作者简介:
石安宁(1989—)，男，博士研究生，主要从事颗粒材料及太空土静力学及流动特性方面试验和数值模拟研究。E-mail: shianning0618@163.com

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

中图分类号: TU432
计量
- 文章访问数: 361
- HTML全文浏览量: 37
- PDF下载量: 92
出版历程
- 收稿日期: 2023-08-19
- 网络出版日期: 2024-11-10
- 刊出日期: 2025-03-31

Distinct element method for static and flow mobility characteristics of lunar regolith based on particle shape characteristics

1.
Department of Civil Engineering, Tianjin University, Tianjin 300072, China
2.
School of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, China

摘要

摘要: 由于月壤独特的颗粒形态及物理力学特性，研究其与不同材料间静力学及流动特性差异对于月球原位资源利用、基地选址及建造具有重要指导意义。基于真实月壤粒形特征数据，采用离散单元法对月壤静力学及流动特性进行了研究。首先基于嫦娥五号携带返回月壤样品粒形特征，使用三维完整接触模型，确定不同粒径月壤形状参数（抗转动系数β），以期反映真实月壤样品宏观静力学及流动性响应；随后对月壤、丰浦砂及玻璃珠等材料进行不同围压下三轴试验和不同转速下转筒试验离散元模拟；最后对3种材料的静力学及流动特性进行了对比分析。离散元模拟结果表明：在三轴试验模拟中，相较于其他材料，真实月壤表观黏聚力及内摩擦角明显偏大，且在剪切过程中表现出一定剪胀特性。在转筒试验模拟中，相较于其他材料，真实月壤工况稳态倾角和剖面孔隙比更大，而剖面剪切速率及配位数更小。在一定惯性数范围内，真实月壤有效摩擦系数最大，使其表现出较低的流动性。
- 嫦娥五号 /
- 月壤粒形特征 /
- 转筒 /
- 离散元 /
- 流动特性 /
- 有效摩擦系数 /
Abstract: Since it exhibits uniquely grain shape, physical and mechanical characteristics, the lunar regolith is extremely important for utilization of in-situ resources, selection of base station location and construction in lunar exploration. Based on the data of the shape characteristics of the lunar regolith, the distinct element method (DEM) is employed to study the static and flow mobility characteristics of the lunar regolith. Firstly, to reproduce the macroscopic static and flow behaviors of the lunar regolith sample, a complete three-dimensional contact model considering the grain shape characteristics of the Chang'E-5 mission is used, and then the corresponding shape parameters (coefficient of rolling resistance β) for different grain sizes are determined. Secondly, the triaxial tests under different confining pressures and the rotating drum tests under different rotating speeds are simulated using the DEM, and the samples include the lunar regolith, Toyoura sand, and glass beads. Finally, a contrastive analysis of the static and flow mobility characteristics of the three materials is conducted. The simulated results show that in the triaxial tests, compared with the other two materials, the lunar regolith has the largest apparent cohesion and internal friction angle, and it exhibits dilatancy in the shearing process. In the rotating drum tests, compared with the other two materials, the lunar regolith has the largest inclination angle and void ratio, and the smallest shearing rate and coordination number. Under a certain range of the inertia number, the lunar regolith has the largest effective friction coefficient compared with the other two materials, indicating that it has the smallest flow mobility.
- Chang'E-5 mission /
- lunar regolith /
- grain shape characteristic /
- rotating drum /
- DEM /
- flow mobility /
- effective friction coefficient

HTML全文

0. 引言

劲性水泥搅拌桩（SDCM column）也称“混凝土芯搅拌桩”,是一种由水泥搅拌桩(DCM column)壳和中心处较小面积预制混凝土芯桩组成的复合材料桩。按照芯桩与DCM桩壳二者长度间的相对关系,SDCM桩分为3种类型：芯桩长度小于DCM桩壳长度的短芯SDCM桩、芯桩长度等于DCM桩壳长度的等芯SDCM桩和芯桩长度大于DCM桩壳长度的长芯SDCM桩。较之传统的DCM桩,SDCM桩的竖向和水平向承载力高,沉降控制效果好。它既可作为桩基础,也可作为复合地基的竖向增强体,在国内外都得到了大量应用^[1-2]。

很多学者通过室内外试验和数值模拟等方法,从承载力、荷载传递机制和控沉效果等方面对短芯SDCM桩和短芯SDCM桩复合地基进行了较为系统的研究。凌光荣等^[3]、董平等^[4]和吴迈等^[5]通过现场单桩载荷试验研究了SDCM桩的轴向承载特性。试验发现,芯桩的插入使搅拌桩桩侧摩阻力充分发挥,SDCM桩的竖向承载力可高于混凝土灌注桩。Voottipruex等^[6]采用三维有限元法研究了芯桩长度和截面积等因素对SDCM桩竖向和水平向承载力、芯桩轴力和弯矩分布的影响。吴迈等^[7]、丁永君等^[8]和顾士坦等^[9]采用理论分析和现场实测芯桩桩身应力的方法研究了SDCM桩的荷载传递特性。Wonglert等^[10-11]基于室内模型试验成果,提出短芯SDCM桩有土体破坏、芯桩底部破坏和搅拌桩壳顶部破坏3种破坏模式,研究了芯桩长度和搅拌桩壳强度对悬浮SDCM桩竖向承载力和破坏模式的影响。Wang等^[12]通过现场荷载板试验,比较了刚性基础下SDCM桩复合地基与DCM桩复合地基的竖向承载力。Voottipruex等^[13]和Wang等^[14]进行了路堤下SDCM桩复合地基现场试验,比较了柔性基础下SDCM桩复合地基与DCM桩复合地基的沉降控制效果。叶观宝等^[15-16]提出了悬浮SDCM桩复合地基桩-土应力比和沉降的计算方法。杨涛等^[17]建立了端承短芯SDCM桩复合地基的固结计算模型。

近年来,随着长芯SDCM桩在中国的逐渐应用,其承载机理和设计理论的研究开始受到学术界的关注。陈华顺等^[18]和程博华^[19]分别提出了长芯SDCM桩桩侧摩阻力和竖向承载力的计算方法。杨涛等^[20]给出了端承长芯SDCM桩复合地基固结解析解,但该解答无法用于分析悬浮长芯SDCM桩复合地基的固结问题。有鉴于此,本文研究悬浮长芯SDCM桩复合地基的固结计算方法,分析悬浮长芯SDCM桩复合地基的固结特性,进一步完善SDCM桩复合地基的固结计算理论。

1. 固结模型与基本假定

1.1 轴对称固结模型

图1给出悬浮长芯SDCM桩复合地基轴对称固结模型,r和z分别是径向和竖向坐标。r_e为一根SDCM桩的影响区半径,可由桩的间距和布桩方式计算得到。水泥搅拌桩壳外半径和长度分别为r_p和L_p=H₁,上部SDCM桩的置换率为m（m=(r_p/r_e)²）,压缩模量为E_p。芯桩打穿水泥搅拌桩壳,其半径和长度分别为r_sp和L_sp（L_sp=H₁+H₂）,压缩模量为E_sp。芯桩的截面含芯率为ρ（ρ=(r_sp/r_p)²）。根据水泥搅拌桩壳和芯桩的长度将复合地基加固区分为Ⅰ和Ⅱ二部分,加固区Ⅰ内桩间土的厚度、渗透系数、固结系数和压缩模量分别为H₁,k_v1,c_v1,E_s1,加固区Ⅱ内桩间土的厚度、渗透系数、固结系数和压缩模量分别为H₂,k_v2,c_v2,E_s2。下卧层土厚度、渗透系数、固结系数和压缩模量分别为H₃,k_v3,c_v3,E_s3。复合地基总厚度H= H₁+H₂+H₃。

图 1 复合地基固结模型

Figure 1. Consolidation model for composite ground

下载: 全尺寸图片幻灯片

1.2 基本假定

本文公式推导采用如下假定：①地基土完全饱和,水的流动符合Darcy定律；②搅拌桩壳不排水；③芯桩桩端以下的下卧层土和搅拌桩壳以下芯桩桩端以上的土仅发生径向渗流；④芯桩与搅拌桩壳间无相对滑移,加固区中任意深度处的桩和土的竖向应变相等；⑤大面积均布荷载p瞬时施加,在待加固地基中引起的竖向附加应力沿深度均布；⑥土的渗透系数和压缩模量不随固结而变化。

2. 固结方程与定解条件

2.1 固结方程

基于前述基本假定,参考杨涛等^[20-21]的研究,可得到荷载p瞬时施加情况下悬浮长芯SDCM桩复合地基得固结方程如下：

${\begin{cases} \frac{\partial {\bar{u}}_{s 1}}{\partial t} = c_{v 1 e} \frac{\partial^{2} {\bar{u}}_{s 1}}{\partial z^{2}} \begin{matrix} \end{matrix} (0 \leq z < H_{1}), \\ \frac{\partial {\bar{u}}_{s 2}}{\partial t} = c_{v 2 e} \frac{\partial^{2} {\bar{u}}_{s 2}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} \leq z < H_{1} + H_{2}), \\ \frac{\partial {\bar{u}}_{s 3}}{\partial t} = c_{v 3 e} \frac{\partial^{2} {\bar{u}}_{s 3}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} + H_{2} \leq z \leq H) 。 \end{cases}$

(1)

$c_{v 1 e} = (1 + \frac{m [ρ E_{s p} + (1 - ρ) E_{p}]}{(1 - m) E_{s 1}}) c_{v 1}$ ,

(2)

$c_{v 2 e} = (1 + \frac{m ρ E_{s p}}{(1 - m ρ) E_{s 2}}) (\frac{1 - m}{1 - m ρ}) c_{v 2}$ ,

(3)

$c_{v 3 e} = (1 - m ρ) c_{v3} 。$

(4)

式中 ${\bar{u}}_{s 1}$ , ${\bar{u}}_{s 2}$ , ${\bar{u}}_{s 3}$ 分别为加固区Ⅰ、Ⅱ中桩间土和下卧层土中任意深度z处的平均超静孔隙水压力；c_v1e,c_v2e,c_v3e分别为考虑劲性桩和芯桩影响的加固区Ⅰ、Ⅱ中桩间土和下卧层土的等效竖向固结系数。

2.2 定解条件

（1）边界条件

考虑复合地基上边界排水、下边界不排水的单面排水情况,边界条件如下：

$z = 0, {\bar{u}}_{s 1} = 0$ ,

(5)

$z = H, \frac{\partial {\bar{u}}_{s 3}}{\partial z} = 0$ 。

(6)

（2）孔压和水流连续性条件

考虑到 $(1 - m) {\bar{u}}_{s 1}$ 和 $(1 - m ρ) {\bar{u}}_{s 2}$ 分别为加固区Ⅰ和加固区Ⅱ内任意深度处的平均孔压,可得加固区Ⅰ与加固区Ⅱ分界面处、加固区Ⅱ与下卧层分界面处孔压和水流连续性条件如下：

z=H₁时,

$(1 - m) {\bar{u}}_{s 1} = (1 - m ρ) {\bar{u}}_{s 2}$ ,

(7)

$(1 - m) k_{v 1} \frac{\partial {\bar{u}}_{s 1}}{\partial z} = (1 - m ρ) k_{v 2} \frac{\partial {\bar{u}}_{s 2}}{\partial z}$ 。

(8)

z=H₁+H₂时,

$(1 - m ρ) {\bar{u}}_{s 2} = {\bar{u}}_{s 3}$ ,

(9)

$(1 - m ρ) k_{v 2} \frac{\partial {\bar{u}}_{s 2}}{\partial z} = k_{v 3} \frac{\partial {\bar{u}}_{s 3}}{\partial z}$ 。

(10)

（3）初始条件

荷载施加的瞬时,桩间土和下卧层土中没有竖向变形。参照杨涛等^[20-21]的研究,容易写出如下初始条件：

${\bar{u}}_{s 1} (z, 0) = \frac{p}{1 - m}$ ,

(11)

${\bar{u}}_{s 2} (z, 0) = \frac{p}{1 - m ρ}$ ,

(12)

${\bar{u}}_{s 3} (z, 0) = p$ 。

(13)

3. 固结解析解

3.1 方程与定解条件的函数变换

为便于求解,进行如下函数变换：

${\begin{cases} {\hat{u}}_{s 1} = (1 - m) {\bar{u}}_{s 1}, \\ {\hat{u}}_{s 2} = (1 - m ρ) {\bar{u}}_{s 2}, \\ {\hat{u}}_{s 3} = {\bar{u}}_{s 3} 。 \end{cases}$

(14)

显然, ${\hat{u}}_{s 1}$ 和 ${\hat{u}}_{s 2}$ 分别是复合地基上、下加固区任意深度处的平均超静孔隙水压力。将式（14）代入固结控制方程式（1）和定解条件式（5）～（13）,则变换后的复合地基固结控制方程和求解条件如下：

${\begin{cases} \frac{\partial {\hat{u}}_{s 1}}{\partial t} = c_{v 1 e} \frac{\partial^{2} {\hat{u}}_{s 1}}{\partial z^{2}} \begin{matrix} \end{matrix} (0 \leq z < H_{1}), \\ \frac{\partial {\hat{u}}_{s 2}}{\partial t} = c_{v 2 e} \frac{\partial^{2} {\hat{u}}_{s 2}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} \leq z < H_{1} + H_{2}), \\ \frac{\partial {\hat{u}}_{s 3}}{\partial t} = c_{v 3 e} \frac{\partial^{2} {\hat{u}}_{s 3}}{\partial z^{2}} \begin{matrix} \end{matrix} (H_{1} + H_{2} \leq z \leq H) 。 \end{cases}$

(15)

$z = 0 ： {\hat{u}}_{s 1} = 0$ ,

(16)

$z = H ： \frac{\partial {\hat{u}}_{s 3}}{\partial z} = 0$ ,

(17)

z=H₁,

${\begin{cases} {\hat{u}}_{s 1} = {\hat{u}}_{s 2} \\ k_{v 1} \frac{\partial {\hat{u}}_{s 1}}{\partial z} = k_{v 2} \frac{\partial {\hat{u}}_{s 2}}{\partial z} \end{cases}$ ,

(18)

z=H₁+H₂,

${\begin{cases} {\hat{u}}_{s 2} = {\hat{u}}_{s 3} \\ k_{v 2} \frac{\partial {\hat{u}}_{s 2}}{\partial z} = k_{v 3} \frac{\partial {\hat{u}}_{s 3}}{\partial z} \end{cases}$ ,

(19)

${\hat{u}}_{s 1} (z, 0) = {\hat{u}}_{s 2} (z, 0) = {\hat{u}}_{s 3} (z, 0) = p$ 。

(20)

3.2 固结解析解

显然,式（15）,（16）～（20）分别是瞬时荷载p作用在由复合地基上、下加固区复合土和下卧层土组成的三层土系统固结问题的固结方程和定解条件。与瞬时荷载p作用下的三层天然地基固结问题相比,只是各层天然地基土的固结系数c_v1,c_v2和c_v3分别被c_v1e,c_v2e和c_v3e代替而已。设三层土系统中土层i的渗透系数为k_vi(i=1,2,3),则其压缩模量为E_sie=c_vier_w/k_vi (i=1,2,3）。

为使计算公式得以简化,定义5个无量纲参数：

$\begin{array}{l} a_{i} = \frac{k_{v i}}{k_{v 1}}; b_{i} = \frac{E_{s 1 e}}{E_{s i e}}; c_{i} = \frac{H_{i}}{H_{1}}; μ_{i} = \sqrt{\frac{b_{i}}{a_{i}}} (i = 1, 2, 3) ； \\ d_{i} = \sqrt{\frac{a_{i - 1} b_{i - 1}}{a_{i} b_{i}}} \begin{matrix} \end{matrix} (i = 2, 3) 。 \end{array}}$

(21)

根据谢康和^[22]的研究,容易得到：

（1）各加固区和下卧层的平均超静孔压

${\begin{cases} {\hat{u}}_{s 1} (z, t) = p \sum_{m = 1}^{\infty} C_{m} s i n (λ_{m} \frac{z}{H_{1}}) e^{- λ_{m}^{2} T_{v1e}}, \\ {\hat{u}}_{s 2} (z, t) = p \sum_{m = 1}^{\infty} C_{m} [s i n (λ_{m}) c o s (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}}) + \\ d_{2} c o s (λ_{m}) s i n (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}})] e^{- λ_{m}^{2} T_{v1e}}, \\ {\hat{u}}_{s 3} (z, t) = p \sum_{m = 1}^{\infty} \frac{C_{m} A_{m}}{c o s (μ_{3} c_{3} λ_{m})} c o s (μ_{3} λ_{m} \frac{H - z}{H_{1}}) e^{- λ_{m}^{2} T_{v1e}}, \end{cases}$

(22)

$T_{v1e} = c_{v1e} t / H_{1}^{2}$ 。

(23)

（2）桩间土和下卧层土的平均孔压

将式（14）代入式（22）,可得悬浮长芯SDCM桩复合地基上、下部加固区中桩间土和下卧层土平均超静孔隙水压力：

${\begin{cases} {\bar{u}}_{s 1} (z, t) = \frac{p}{1 - m} \sum_{m = 1}^{\infty} C_{m} s i n (λ_{m} \frac{z}{H_{1}}) e^{- λ_{m}^{2} T_{v 1 e}}, \\ {\bar{u}}_{s 2} (z, t) = \frac{p}{1 - m ρ} \sum_{m = 1}^{\infty} C_{m} [s i n (λ_{m}) c o s (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}}) + \\ d_{2} c o s (λ_{m}) s i n (μ_{2} λ_{m} \frac{z - H_{1}}{H_{1}})] e^{- λ_{m}^{2} T_{v1e}}, \\ {\bar{u}}_{s 3} (z, t) = p \sum_{m = 1}^{\infty} \frac{C_{m} A_{m}}{c o s (μ_{3} c_{3} λ_{m})} c o s (μ_{3} λ_{m} \frac{H - z}{H_{1}}) e^{- λ_{m}^{2} T_{v1e}}, \end{cases}$

(24)

$C_{m} = \frac{2 d_{2} s i n (2 μ_{3} c_{3} λ_{m})}{λ_{m} [s i n (2 μ_{3} c_{3} λ_{m}) (d_{2} + μ_{2} c_{2} F_{m}) - μ_{3} c_{3} D_{m}]}$ ,

(25)

$A_{m} = s i n (λ_{m}) c o s (μ_{2} c_{2} λ_{m}) + d_{2} c o s (λ_{m}) s i n (μ_{2} c_{2} λ_{m})$ ,

(26)

$D_{m} = s i n (2 μ_{2} c_{2} λ_{m}) E_{m} - d_{2} s i n (2 λ_{m}) c o s (μ_{2} c_{2} λ_{m})$ ,

(27)

$E_{m} = s i n^{2} (λ_{m}) - d_{2}^{2} c o s^{2} (λ_{m})$ ,

(28)

$F_{m} = s i n^{2} (λ_{m}) + d_{2}^{2} c o s^{2} (λ_{m})$ 。

(29)

按下面方程求解出特征值 $λ_{m}$ ：

$A_{m} + d_{3} c o t (μ_{3} c_{3} λ_{m}) B_{m} = 0$ ,

(30)

$B_{m} = s i n (λ_{m}) s i n (μ_{2} c_{2} λ_{m}) - d_{2} c o s (λ_{m}) c o s (μ_{2} c_{2} λ_{m})$ 。

(31)

（3）复合地基整体平均固结度

参考谢康和^[22]的研究,容易得到悬浮长芯SDCM桩复合地基按沉降定义和按孔压定义的整体平均固结度U_s和U_p的计算公式：

$U_{s} = 1 - \sum_{m = 1}^{\infty} \frac{C_{m}}{λ_{m} (1 + b_{2} c_{2} + b_{3} c_{3})} e^{- λ_{m}^{2} T_{v1e}}$ ,

(32)

$\begin{matrix} U_{p} = 1 - \sum_{m = 1}^{\infty} \frac{\sqrt{a_{2} b_{2}} B_{m} (b_{3} - b_{2}) + b_{2} b_{3} + (b_{3} - b_{2} b_{3}) c o s (λ_{m})}{λ_{m}^{} b_{2} c_{3} (1 + c_{2} + c_{3})} \cdot \\ C_{m} e^{- λ_{m}^{2} T_{v1e}} 。 \end{matrix}$

(33)

4. 算例验证

算例中,H=20 m,r_e=1.1 m；芯桩：r_sp=0.175 m,L_sp= H₁+ H₂=12 m,E_sp=20 GPa,泊松比μ_sp=0.17。搅拌桩壳：r_p=0.35 m,L_p=H₁=8 m,E_p=150 MPa,泊松比μ_p=0.25。地基土：H₃=8 m,E_s1=E_s2=3 MPa,E_s3=9 MPa,k_v1=k_v2=k_v3=10^-8 m/s,泊松比μ_s=0.35。为了在数值计算中近似模拟等应变条件,在复合地基表面铺设0.5 m厚的混凝土板,板上荷载p=68 kPa瞬时施加。混凝土板压缩模量和泊松比与芯桩相同。地基土、芯桩、搅拌桩壳和混凝土板均采用线弹性模型。在各材料的弹性模量E和压缩模量E₁之间按E= (1+ μ)(1-2μ)E₁/(1-μ)近似换算,μ为泊松比。图2为悬浮长芯SDCM桩复合地基轴对称有限元模型。模型左、右侧边界上约束径向位移,不排水。模型底边界上径向和竖向均约束,不排水。复合地基表面自由,排水。

图 2 有限元模型

Figure 2. FEM model

下载: 全尺寸图片幻灯片

采用ABAQUS有限元软件进行算例固结分析。混凝土板、芯桩和搅拌桩壳采用4结点四边形单元（CAX4）剖分,桩间土采用应力-孔压耦合4结点四边形单元（CAX4P）剖分。芯桩-土交界处设置摩擦接触对,摩擦系数取0.42。模型共剖分2466个单元,结点总数2742个。

图3给出本文解析解计算的悬浮长芯SDCM桩复合地基整体平均固结度（U_s）曲线与有限元计算结果的比较,时间轴采用无量纲时间因数T_u=c_v1t/H²。图3表明,本文解析解与有限元计算结果较为接近,解析解数值略大于数值解,二者差值最大不超过3.0%。计算表明,解析解有较高的计算精度。

图 3 解析解和有限元解的比较

Figure 3. Comparison between analytical results and FEM results

下载: 全尺寸图片幻灯片

5. 复合地基结性状分析

采用的几何和力学参数基准值如下：H=20 m,H₁=10 m,H₂=5 m,H₃=5 m。m=0.1, $ρ$ =0.25。E_p=150 MPa,E_sp=20 GPa。E_s1=E_s2=3 MPa,E_s3=9 MPa。k_v1=k_v2=k_v3=10^-8 m/s。

（1）桩的贯入比的影响

图4给出长芯SDCM桩贯入比 $β$ =L_sp/H的变化对复合地基固结速率的影响,计算时地基土为均质土,E_s3=3 MPa,搅拌桩壳长度与芯桩长度的比值 $β_{1}$ =L_p/ L_sp=0.67保持不变。图4表明,复合地基的固结速率随着长芯SDCM桩贯入比的增加逐渐增大,当 $β$ >0.75以后,复合地基固结速率的增加率显著增大。

图 4 β对固结速率的影响

Figure 4. Influences of β on consolidation rate

下载: 全尺寸图片幻灯片

（2）搅拌桩壳的刚度和几何尺寸的影响

图5～7分别给出上部SDCM桩置换率m、搅拌桩壳长度与芯桩长度之比 $β_{1}$ =L_p/L_sp和搅拌桩壳压缩模量E_p的变化对复合地基固结速率的影响。在图5固结度曲线计算中,芯桩截面积保持不变,即m_iρ_i=mρ=0.025,m越大表示搅拌桩壳的厚度越大。图5～7计算结果表明,搅拌桩壳的厚度、长度和压缩模量的变化对悬浮长芯SDCM桩复合地基的固结速率没有影响。

图 5 　m对固结速率的影响

Figure 5. Influences of m on consolidation rate

下载: 全尺寸图片幻灯片

图 6 β₁对固结速率的影响

Figure 6. Influences of β₁ on consolidation rate

下载: 全尺寸图片幻灯片

图 7 E_p对固结速率的影响

Figure 7. Influences of E_p on consolidation rate

下载: 全尺寸图片幻灯片

（3）芯桩刚度和含心率的影响

图8,9分别给出芯桩的截面含芯率 $ρ$ 和压缩模量E_sp的变化对复合地基固结速率的影响。图8表明,芯桩含芯率 $ρ$ 的变化对悬浮长芯SDCM桩复合地基固结速率近乎没有影响。当含芯率 $ρ$ 增大时,仅在固结前期复合地基的固结速率会略微减小,但降幅非常小,可以忽略不计。从图9中可见,芯桩压缩模量E_sp的变化对悬浮长芯SDCM桩复合地基前期的固结速率有一定影响。随着E_sp数值的增加,前期复合地基固结速率随之减小,但降幅并不大。总的来看,芯桩刚度的变化对复合地基固结速率的影响不大。

图 8 ρ对固结速率的影响

Figure 8. Influence of ρ on the consolidation rate

下载: 全尺寸图片幻灯片

图 9 E_sp对固结速率的影响

Figure 9. Influences of E_sp on consolidation rate

下载: 全尺寸图片幻灯片

（4）下卧层土体刚度的影响

图10给出下卧层土压缩模量E_s3取不同数值情况下悬浮长芯SDCM桩复合地基的U_s-T_u曲线。图10表明,复合地基的固结速率随下卧层土刚度的增加而增大。这说明,将芯桩的桩端置于承载力较大的持力层上可加速复合地基的固结。

图 10 E_s3对固结速率的影响

Figure 10. Influences of E_s3 on consolidation rate

下载: 全尺寸图片幻灯片

6. 结论

（1）本文固结解析解是基于加固区等竖向应变假定获得的,因此,它更适用于刚性基础下悬浮长芯SDCM桩复合地基的固结分析。

（2）桩的贯入比和下卧层土的刚度是影响悬浮长芯SDCM桩复合地基固结快慢的主要因素。桩的贯入比和下卧层土的压缩模量越大,悬浮长芯SDCM桩复合地基的固结越快。

（3）芯桩截面含芯率的变化不会影响悬浮长芯SDCM桩复合地基的固结速率。芯桩刚度的增加会略微减小固结前期复合地基的固结速率,对后期复合地基的固结速率没有影响。

（4）搅拌桩壳的厚度、长度和刚度的变化对悬浮长芯SDCM桩复合地基的固结速率没有影响。

图 1 三维完整接触模型力学响应图^[21]

Figure 1. Mechanical responses of three-dimensional complete contact model^[21]

下载: 全尺寸图片幻灯片

图 2 月壤颗粒球度与直径间关系^[22]

Figure 2. Relationship between sphericity and diameter of lunar regolith ^[22]

下载: 全尺寸图片幻灯片

图 3 月壤直径与抗转动系数间关系^[22]

Figure 3. Relationship between diameter of lunar regolith and rolling resistance coefficient^[22]

下载: 全尺寸图片幻灯片

图 4 DEM模拟颗粒级配

Figure 4. Grain-size distribution curves for DEM simulations

下载: 全尺寸图片幻灯片

图 5 离散元试样示意图

Figure 5. Sketch of numerical specimen for DEM simulations

下载: 全尺寸图片幻灯片

图 6 测量球位置示意图

Figure 6. Sketch of measuring spheres for DEM simulations

下载: 全尺寸图片幻灯片

图 7 偏应力及体变演化规律

Figure 7. Evolution of deviatoric stress and volume change

下载: 全尺寸图片幻灯片

图 8 黏聚力和内摩擦角

Figure 8. Cohesion and internal friction angle

下载: 全尺寸图片幻灯片

图 9 转筒倾角演化规律

Figure 9. Evolution of inclination angle in rotating drum

下载: 全尺寸图片幻灯片

图 10 转筒剖面速度图

Figure 10. Normalized velocity profile of rotating drum

下载: 全尺寸图片幻灯片

图 11 转筒剖面孔隙比图

Figure 11. Normalized porosity profile of rotating drum

下载: 全尺寸图片幻灯片

图 12 转筒剖面配位数图

Figure 12. Normalized coordination number profile of rotating drum

下载: 全尺寸图片幻灯片

图 13 转筒剖面平均粒径图

Figure 13. Normalized mean particle diameter profile of rotating drum

下载: 全尺寸图片幻灯片

图 14 转筒剖面惯性数图

Figure 14. Normalized inertial number profile of rotating drum

下载: 全尺寸图片幻灯片

图 15 有效摩擦系数与惯性数关系

Figure 15. Relationship between effective friction coefficient and inertial number

下载: 全尺寸图片幻灯片

表 1 转筒离散元数值试样的材料参数

Table 1 Material parameters of DEM specimens for rotating drum

参数	颗粒密度/ (kg·m^-3)	接触等效模量/MPa	接触刚度比	摩擦系数	抗转动系数	破损系数	法向黏滞阻尼	切向黏滞阻尼
玻璃珠	2500	6.5	1.5	0.15	0.01	2.1	0.13	0.13
丰浦砂	2655	7.0	5.0	0.5	0.25	4.0	0.4	0.4
月壤	2320	8.0	5.0	0.5	详见表 2	4.0	0.8	0.8

下载: 导出CSV

表 2 不同粒径月壤抗转动系数^[22]

Table 2 Rolling resistance coefficient for lunar regolith with different diameters^[22]

组数	颗粒直径/mm	抗转动系数β	组数	颗粒直径/ mm	抗转动系数β
1	0.36	1.009	13	0.216	0.589
2	0.35	0.923	14	0.207	0.576
3	0.316	0.917	15	0.195	0.573
4	0.305	0.910	16	0.184	0.562
5	0.293	0.818	17	0.175	0.558
6	0.282	0.810	18	0.165	0.558
7	0.271	0.781	19	0.156	0.533
8	0.268	0.757	20	0.136	0.533
9	0.254	0.755	21	0.127	0.518
10	0.247	0.733	22	0.114	0.356
11	0.235	0.711	23	0.106	0.335
12	0.225	0.615

下载: 导出CSV

表 3 不同倾角变化规律

Table 3 Variation for different types of inclination angles

转筒弗劳德数 F_r	内摩擦角/ (°)	倾角类型
转筒弗劳德数 F_r	内摩擦角/ (°)	启滑角θ_l/(°)	休止角θ_r/(°)	差值 θ_l-θ_r	稳态倾角θ_s/(°)
1.0×10^-2	16.42	42.72	26.21	16.51	28.99
		69.39	37.31	32.08	42.37
		81.23	44.06	37.17	47.69
7.5×10^-3	31.7	41.12	25.80	15.32	28.48
		68.88	37.87	31.01	41.93
		81.21	41.99	39.22	47.20
5.0×10^-3	38.1	39.88	25.38	14.50	28.05
		67.69	37.11	30.58	41.79
		79.58	43.17	36.41	46.89

下载: 导出CSV

参考文献(35)

[1]	刘建忠, 李雄耀, 朱凯, 等. 月球原位资源利用及关键科学与技术问题[J]. 中国科学基金, 2022, 36(6): 907-918. LIU Jianzhong, LI Xiongyao, ZHU Kai, et al. Key science and technology issues of lunar in situ resource utilization[J]. Bulletin of National Natural Science Foundation of China, 2022, 36(6): 907-918. (in Chinese)
[2]	蒋明镜, 张鑫蕊, 司马军, 等. 壤基材料加筋月壤技术在月球基地建设中的应用[J]. 苏州科技大学学报(自然科学版), 2023, 40(3): 11-20, 53. JIANG Mingjing, ZHANG Xinrui, SIMA Jun, et al. Future application of lunar-textile composite/reinforced regolith to the construction of lunar bases[J]. Journal of Suzhou University of Science and Technology (Natural Science Edition), 2023, 40(3): 11-20, 53. (in Chinese)
[3]	蒋明镜, 王思远, 姜朋明, 等. 月球基地的建设远景与挑战[J]. 山东大学学报(工学版), 2024, 54(2): 114-125. JIANG Mingjing, WANG Siyuan, JIANG Pengming, et al. The long-range perspective and challenges for the construction of lunar base[J]. Journal of Shandong University (Engineering Science), 2024, 54(2): 114-125. (in Chinese)
[4]	FATERI M, COWLEY A, BERNILLON C, et al. Flowability of Lunar Regolith Simulant[C]// European Planetary Science Congress. Riga. 2017.
[5]	LIU X Y, HU Z, WU W N, et al. DEM study on the surface mixing and whole mixing of granular materials in rotary drums[J]. Powder Technology, 2017, 315: 438-444.
[6]	BRANDAO R J, LIMA R M, SANTOS R L, et al. Experimental study and DEM analysis of granular segregation in a rotating drum[J]. Powder Technology, 2020, 364: 1-12.
[7]	YAMAMOTO M, ISHIHARA S, KANO J. Evaluation of particle density effect for mixing behavior in a rotating drum mixer by DEM simulation[J]. Advanced Powder Technology, 2016, 27(3): 864-870.
[8]	BRUCKS A, ARNDT T, OTTINO J M, et al. Behavior of flowing granular materials under variable G[J]. Statistical, Nonlinear, and Soft Matter Physics (Physical Review E), 2007, 75: 032301.
[9]	KLEINHANS M G, MARKIES H, DE VET S J, et al. Static and dynamic angles of repose in loose granular materials under reduced gravity[J]. Journal of Geophysical Research (Planets), 2011, 116(E11): E11004.
[10]	KLEIN S P, WHITE B R. Dynamic shear of granular material under variable gravity conditions[J]. AIAA Journal, 1990, 28(10): 1701-1702. doi: 10.2514/3.10461
[11]	CUNDALL P A, STRACK O D L. A discrete numerical model for granular assemblies[J]. Géotechnique, 1979, 29(1): 47-65. doi: 10.1680/geot.1979.29.1.47
[12]	蒋明镜. 现代土力学研究的新视野: 宏微观土力学[J]. 岩土工程学报, 2019, 41(2): 195-254. doi: 10.11779/CJGE201902001 JIANG Mingjing. New paradigm for modern soil mechanics: Geomechanics from micro to macro[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(2): 195-254. (in Chinese) doi: 10.11779/CJGE201902001
[13]	WALTON O R, JOHNSON S M. DEM simulations of the effects of particle shape, interparticle cohesion, and gravity on rotating drum flows of lunar regolith[C]//Earth and Space 2010: Engineering, Science, Construction, and Operations in Challenging Environments. 2010: 36-41. [13] WALTON O R, JOHNSON S M. DEM simulations of the effects of particle shape, interparticle cohesion, and gravity on rotating drum flows of lunar regolith[C]//Earth and Space 2010. Honolulu, 2010.
[14]	NAKASHIMA H, SHIOJI Y, KOBAYASHI T, et al. Determining the angle of repose of sand under low-gravity conditions using discrete element method[J]. Journal of Terramechanics, 2011, 48(1): 17-26. doi: 10.1016/j.jterra.2010.09.002
[15]	CHEN H, CHEN Y X, WEI Q S, et al. Effect of gravity on repose angle and contact forces of particulate pile composed of non-monodispersed particles[J]. International Journal of Aerospace Engineering, 2019, 2019: 8513149.
[16]	SUNDAY C, MURDOCH N, TARDIVEL S, et al. Validating N-body code chrono for granular DEM simulations in reduced-gravity environments[J]. Monthly Notices of the Royal Astronomical Society, 2020, 498(1): 1062-1079. doi: 10.1093/mnras/staa2454
[17]	KARAPIPERIS K, MARSHALL J P, ANDRADE J E. Reduced gravity effects on the strength of granular matter: DEM simulations versus experiments[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2020, 146(5): 06020005. doi: 10.1061/(ASCE)GT.1943-5606.0002232
[18]	ANTONY S J, AROWOSOLA B, RICHTER L, et al. Modeling the flow characteristics of granular materials under low gravity environments using discrete element method[C]// Proceedings of the Earth and Space 2021, Reston, 2021: 12-21.
[19]	ELEKES F, PARTELI E J R. An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments[J]. Proceedings of the National Academy of Sciences of the United States of America, 2021, 118(38): e2107965118.
[20]	JIANG M J, MAO H, XI B L, et al. Three-dimensional DEM analysis of granular flows under different gravity levels in rotating cylinders[C]// Proceedings of GeoShanghai 2018 International Conference: Fundamentals of Soil Behaviours. Singapore, 2018.
[21]	JIANG M J, SHEN Z F, WANG J F. A novel three- dimensional contact model for granulates incorporating rolling and twisting resistances[J]. Computers and Geotechnics, 2015, 65: 147-163. doi: 10.1016/j.compgeo.2014.12.011
[22]	王思远, 蒋明镜. 基于嫦娥五号月壤粒形特征的离散元模拟方法[J]. 岩土工程学报, 2024, 46(4): 833-842. doi: 10.11779/CJGE20230040 WANG Siyuan, JIANG Mingjing. Lunar regolith simulations with discrete element method based on Chang'E-5 mission's lunar soil particle morphology[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(4): 833-842. (in Chinese) doi: 10.11779/CJGE20230040
[23]	WOOD J A, DICKEY J S, MARVIN U B, et al. Lunar anorthosites and a geophysical model of the moon[J]. Apollo 11 Science Conference, 1970: 965-988.
[24]	月球与深空探测科学数据与样品发布系统[EB/OL]. http://202.106.152.98:8081/moondata/web/datainfo/main.action#,2007-10-24/2023-01-02. Lunar and Deep Space Exploration Scientific Data and Sample Release Syslem[EB/OL]. http://202.106.152.98:8081/moondata/web/datainfo/main.action#,2007-10-24/2023-01-02. (in Chinese)
[25]	WU K, WU K, PIZETTE P, et al. Experimental and numerical study of cylindrical triaxial test on mono-sized glass beads under quasi-static loading condition[J]. Advanced Powder Technology, 2017, 28: 155-166.
[26]	HÄRTL J, OOI J Y. Experiments and simulations of direct shear tests: porosity, contact friction and bulk friction[J]. Granular Matter, 2008, 10(4): 263-271.
[27]	LOMMEN S, SCHOTT D, LODEWIJKS G. DEM speedup: Stiffness effects on behavior of bulk material[J]. Particuology, 2014, 12: 107-112. http://d.g.wanfangdata.com.cn/Periodical_zgklxb-e201401013.aspx
[28]	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.
[29]	KOMOSSA H, WIRTZ S, SCHERER V, et al. Transversal bed motion in rotating drums using spherical particles: comparison of experiments with DEM simulations[J]. Powder Technology, 2014, 264: 96-104.
[30]	ARNTZ M M H D, BEEFTINK H H, DEN OTTER W K, et al. Segregation of granular particles by mass, radius, and density in a horizontal rotating drum[J]. AIChE Journal, 2014, 60(1): 50-59.
[31]	MELLMANN J. The transverse motion of solids in rotating cylinders: forms of motion and transition behavior[J]. Powder Technology, 2001, 118(3): 251-270.
[32]	土工试验方法标准: GB/T 50123—2019[S]. 北京: 中国计划出版社, 2019. Standard for Geotechnical Testing Method: GB/T 50123—2019[S]. Beijing: China Planning Press, 2019. (in Chinese)
[33]	THORNTON C. Numerical simulations of deviatoric shear deformation of granular media[J]. Géotechnique, 2000, 50(1): 43-53.
[34]	KOVAL G, ROUX J N, CORFDIR A, et al. Annular shear of cohesionless granular materials: from the inertial to quasistatic regime[J]. Statistical, Nonlinear, and Soft Matter Physics (Physical Review E), 2009, 79: 021306.
[35]	JOP P, FORTERRE Y, POULIQUEN O. A constitutive law for dense granular flows[J]. Nature, 2006, 441(7094): 727-730.