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陕西榆林毛乌素沙漠南缘风积沙的湿陷规律及其影响因素

张曦, 骆建文, 潘俊义, 刘斌, 杨楠

张曦,骆建文,潘俊义,等. 陕西榆林毛乌素沙漠南缘风积沙的湿陷规律及其影响因素[J]. 中国地质灾害与防治学报,2024,35(4): 75-84. DOI: 10.16031/j.cnki.issn.1003-8035.202307023
引用本文: 张曦,骆建文,潘俊义,等. 陕西榆林毛乌素沙漠南缘风积沙的湿陷规律及其影响因素[J]. 中国地质灾害与防治学报,2024,35(4): 75-84. DOI: 10.16031/j.cnki.issn.1003-8035.202307023
ZHANG Xi,LUO Jianwen,PAN Junyi,et al. Collapse characteristics and influencing factors of wind-blown sands in the southern margin of Mu Us Desert, Yulin, Shaanxi Province[J]. The Chinese Journal of Geological Hazard and Control,2024,35(4): 75-84. DOI: 10.16031/j.cnki.issn.1003-8035.202307023
Citation: ZHANG Xi,LUO Jianwen,PAN Junyi,et al. Collapse characteristics and influencing factors of wind-blown sands in the southern margin of Mu Us Desert, Yulin, Shaanxi Province[J]. The Chinese Journal of Geological Hazard and Control,2024,35(4): 75-84. DOI: 10.16031/j.cnki.issn.1003-8035.202307023

陕西榆林毛乌素沙漠南缘风积沙的湿陷规律及其影响因素

基金项目: 长庆工程设计有限公司资助项目(CEDC-2021-026)
详细信息
    作者简介:

    张 曦(1989—),男,陕西西安人,工程地质专业,硕士研究生,工程师,主要从事岩土工程勘察设计及相关科研工作。E-mail:148374641@qq.com

    通讯作者:

    杨 楠(1998—),女,内蒙古通辽人,地质资源与地质工程专业,博士研究生,主要从事土动力学与岩土地震工程相关科研工作。E-mail:2020126125@chd.edu.cn

  • 中图分类号: P642.26

Collapse characteristics and influencing factors of wind-blown sands in the southern margin of Mu Us Desert, Yulin, Shaanxi Province

  • 摘要:

    随着中国干旱、半干旱地区的开发与发展,湿陷性沙土对工程建设的危害日益显著。为探明沙土的湿陷规律及其影响因素,文章以毛乌素沙漠南缘风积沙土为研究对象,首先,通过控制单因素室内压缩试验,研究不同工况下风积沙的湿陷规律;其次,采用 PFC3D(三维颗粒流软件)对风积沙土室内压缩试验进行数值模拟,探究不同孔隙率、不同颗粒组成对沙土湿陷性的影响。研究结果表明:沙土湿陷系数随压力呈先升后降的变化趋势,压力为 150 kPa 时取得湿陷系数最大值;随着干密度或含水率的增大,沙土湿陷系数减小。相较于含水率,干密度对沙土湿陷性的影响更大;风积沙土的湿陷系数与孔隙率之间呈正相关关系,毛乌素沙漠南缘风积沙土的湿陷起始孔隙率为 0.425;当 0.075~0.25 mm、0.25~0.5 mm两粒组颗粒含量之比为 0.35∶0.65 时,沙土湿陷性最大。研究结果较全面地描述了沙土室内压缩试验从宏观到微观的全过程,从多尺度揭示了沙土湿陷性的湿陷规律及其影响因素,可为毛乌素沙漠地区工程建设提供参考,同时为沙土在颗粒流数值模拟方面的研究提供了一定的思路和依据。

    Abstract:

    With the development of arid and semi-arid regions in China, the hazards posed by collapsible sands to engineering construction have become increasingly significant. In order to investigate the collapsibility regularity and its influencing factors of sand soils, this paper focuses on the wind-blown sands at the southern edge of the Maowusu Desert. Initially, by controlling the single factor laboratory compression tests, the collapsibility regularity of wind-blown sand under different working conditions was investigated. Subsequently, using PFC3D (three-dimensional particle flow software) for numerical simulation of the laboratory compression tests on wind-blown sands, the paper explores the effects of different porosities and particle compositions on the collapsibility of sandy soils. The research results indicate that the collapsibility coefficient of sandy soils shows a trend of first increasing and then decreasing with pressure, reaching its maximum value at 150 kPa. With the increase in dry density or moisture content, the collapsibility coefficient of sand decreases. Compared to moisture content, dry density has a greater impact on the collapsibility of sandy soils. There is a positive correlation between the collapsibility coefficient of wind-blown sand and its porosity. The initial porosity of the collapsibility of the wind-blown sand on the southern edge of the Maowusu Desert is 0.425. When the ratio of particle content between 0.075~0.25 mm and 0.25~0.5 mm is 0.35∶0.65, the collapsibility of sandy soils is maximized. The research results comprehensively describe the entire process of laboratory compression tests on sand from macro to micro levels, revealing the collapsibility regularity and its influencing factors on wind-blown sand from multiple scales. This can provide a reference for engineering construction in the Maowusu Desert and provide certain ideas and basis for the research on particle flow numerical simulation of sand.

  • 国内外学者对黄土湿陷性及湿陷规律的探索从未间断[1],湿陷性沙土相关研究成果较少。国内针对湿陷性沙土的研究主要集中在对新疆、甘肃、宁夏、陕西等省份戈壁地区或沙漠地区沙土变形机理[2]、沙土湿陷性的影响因素及影响规律[38]、湿陷性沙土地基处理方法[910]的研究。但由于湿陷性沙土分布地区偏远,对沙土湿陷性的研究尚处于初探阶段,还未取得系统、显著的研究成果。

    湿陷性沙土在我国分布范围较广,但对沙土的湿陷特性认识不足,不利于湿陷性沙土地区工程建设的推进。随着我国“一带一路”倡议实施,国外工程建设也遇到湿陷性沙土,如非洲安哥拉罗安达市的“Quelo沙”[1115]、尼日尔某炼厂建设中的湿陷性风积沙土[16]、巴基斯坦塔尔沙漠工程建设区遇到的风积沙土[1718]。因此,进一步了解与掌握沙土的湿陷特性,对世界范围内湿陷性沙土地基中的工程建设具有重要的指导意义和应用价值。

    为确定湿陷系数,一般要在工程场地取样进行单线法或双线法湿陷实验,需要消耗大量的人力和时间[19],且对于沙土的研究仅停留在宏观参数的获得,无法了解试样内部颗粒的变化规律。为弥补室内试验中无法观测土颗粒变化的缺陷,许多学者采用三维颗粒流软件对沙土进行数值模拟。学者们应用PFC软件对沙土进行研究,大多是从强度和力学特性等方面着手,采用PFC2D、PFC3D数值软件进行双轴试验[20]、平面应变状态试验[21]、三轴试验[2224]、剪切试验[2526]的颗粒流数值模拟,分析了各种细观参数对宏观力学性质的影响,得到了数值试样在受力过程中的宏细观特征。显然,颗粒流方法已经逐渐成为国内外学者研究沙土的重要方法之一,但对于沙土湿陷试验的颗粒流模拟还未见报道。

    综上所述,目前湿陷性沙土相关研究成果较少,缺乏对不同成因湿陷性沙土的针对性分析,也极少关注沙土湿陷的细观过程。鉴于此,本文以毛乌素沙漠南缘风积沙为研究对象,采用室内试验、数值模拟对沙土湿陷特性进行研究。研究从现象与本质两方面入手,将沙土微观参数与宏观湿陷反应联系起来,可以对沙土湿陷过程有更深入的认识,并从多尺度揭示风积沙的湿陷规律及其影响因素。研究成果对在风积沙土地区的工程建设具有重要的参考意义和应用价值。

    取样地点为榆林市榆阳区小纪汗镇活洛滩村,距离榆林市政府30.3 km。该场地地势平坦,地层岩性分布较为简单,浅表地层均为第四系风积粉细沙,地下水位为4~6 m,区域年平均降雨量约280 mm,取样场地附近无地表河流发育。试样为淡黄色稍湿风积沙,其基本物理特性指标见表1。沙土孔隙比较大,含水率低。粒径级配曲线见图1,主要集中在0.075~0.25 mm、0.25~0.5 mm两粒径区间内,不均匀系数为3.2,曲率系数为0.903。沙土颗粒均匀,级配曲线不连续,为级配不良土。现场标准贯入试验测得场地密实程度为松散至稍密,且通过人工取样法取场地原状环刀样测得其湿陷系数大于0.015,场地湿陷性为轻微湿陷。

    表  1  场地基本物理特性指标
    Table  1.  Basic physical charecteristics of the site
    参数 密度/(g·m−3 含水率/% 干密度/(g·m−3 比重 孔隙比 饱和密度/(g·m−3 饱和度 最小干密度/(g·m−3 最大干密度/(g·m−3
    数值 1.587 4.5 1.519 2.616 0.722 1.938 16.3 1.38 1.77
    下载: 导出CSV 
    | 显示表格
    图  1  试验土样粒径级配曲线
    Figure  1.  Distribution curve of particle sizes

    为探明风积沙的湿陷规律,以《土工试验方法标准》(GB/T 50123—2019)[27]为标准制取含水率(ω) 3%、6%、9%,干密度(ρd)1.40,1.45,1.5,1.55 g/cm3,粒径区间为 0.075~0.25 mm的不同组合重塑环刀试样,遵循控制变量原则进行了重塑土室内压缩试验,试验采用双线法,压力取25,50,100,150,200 kPa,共计试验12组。

    风积沙土质相对较均匀,较少混有其他成因土层,而且可以取得原状样,所以对其湿陷性的评价仍可按《湿陷性黄土地区建筑规范》[28]的有关规定进行。室内压缩试验结果见表2

    表  2  室内压缩试验结果
    Table  2.  Laboratory compression test results
    试样
    编号
    干密度
    /(g·cm−3
    含水率/% 粒径区间/mm 湿陷系数 湿陷等级
    1 1.40 3 0.075~0.250 0.02650 轻微湿陷
    2 1.45 3 0.075~0.250 0.02225 轻微湿陷
    3 1.50 3 0.075~0.250 0.01625 轻微湿陷
    4 1.55 3 0.075~0.250 0.00100 无湿陷
    5 1.40 6 0.075~0.250 0.02550 轻微湿陷
    6 1.45 6 0.075~0.250 0.02200 轻微湿陷
    7 1.50 6 0.075~0.250 0.01725 轻微湿陷
    8 1.55 6 0.075~0.250 0.00050 无湿陷
    9 1.40 9 0.075~0.250 0.02450 轻微湿陷
    10 1.45 9 0.075~0.250 0.02050 轻微湿陷
    11 1.50 9 0.075~0.250 0.01850 轻微湿陷
    12 1.55 9 0.075~0.250 0.00050 无湿陷
    下载: 导出CSV 
    | 显示表格

    等间距选取表2 中的试验结果,分析试样的湿陷性系数(p )−压力($ {\delta _{\rm{s}}} $)曲线,土样湿陷系数随压力的变化曲线如图2 所示。

    图  2  $ p - {\delta _{\rm{s}}} $曲线
    Figure  2.  $ p - {\delta _{\rm{s}}} $ curves

    图2 可知,随着压力的增大,$ p - {\delta _{\rm{s}}} $曲线呈现出先升后降的趋势,在压力为 150 kPa 时取得湿陷系数最大值。这是因为在峰值压力之前,风积沙土处于孔隙填充挤密阶段,仍然保持较稳定的多孔结构,随压力增大,内部孔隙被水和细小颗粒填充的趋势随之增大,故湿陷性变大。而当压力超过峰值压力后,在高压和水的作用下,沙土天然微观结构基本被破坏,沙土试样反而呈现出膨胀的趋势,故湿陷系数减小。此外,随着干密度、含水率的增大,湿陷系数减小。干密度的增加使土样更密实,孔隙率减小,含水率的增加使一部分孔隙被水填充,进一步减小了孔隙率,故干密度、含水率同时增大时,土的湿陷性会明显减弱。为比较干密度、含水率对风积沙土湿陷特性的影响程度,分别分析湿陷系数随含水率的变化规律、湿陷系数随干密度的变化规律(图3)。

    图  3  $ p - {\delta _{\rm{s}}} $曲线
    Figure  3.  $ p - {\delta _{\rm{s}}} $ curves

    当干密度为1.4 g/cm3时,含水率从 3% 增至 9%,最大湿陷系数(压力为 150 kPa 时的湿陷系数)仅减小了0.0043;当含水率为 3% 时,干密度从1.4 g/cm3增至1.45 g/cm3,最大湿陷系数减小了0.007。可见,虽然含水率的增大会使湿陷系数减小,但明显干密度才是影响风积沙土湿陷性的主控因素。

    颗粒流程序(particle flow code,PFC) 是在著名学者 Peter Cundal1 主持下采用颗粒流理论开发的一种数值计算平台。该软件利用球形粒子之间的连续相互作用运动,计算粒子位置和相对位移以及每个时步下粒子重叠量,通过力—位移定律计算粒子间的接触力、能量传递以及消耗[29]。已有许多学者采用PFC2D 对沙土的变形和强度性质进行了数值模拟,但 PFC2D 仅可以定性地研究沙土的细观力学行为。二维模拟与实际试验有着本质区别,主要体现在二维模型的孔隙率无法反应真实情况的孔隙率,故无法采用 PFC2D 获取沙土宏细观参数间的定量关系。本文采用 PFC3D 颗粒流软件进行数值模拟试验,试验分为以下两个步骤:

    (1)成样

    数值试样的生成包括试样尺寸的确定、颗粒的填充、接触模型的选择三个步骤:①根据实际室内压缩试验规模确定数值试样的大小和形状。数值试样墙体的形状、尺寸与实际室内压缩试验的规模完全相同,是由一个圆柱形墙面以及上下两墙面组成。为了避免颗粒在加载过程中,从墙体的缝隙中飞出,需对墙体的高度及上下墙面适当延伸。②颗粒的填充。在 PFC3D 中合成材料土样是由球形颗粒组装而成,如果采用与实际风积沙土大小完全相同的粒径会生成过多的颗粒,影响计算机运算速率。为加快运算速率,可采用级配平移、放大粒径的方法来减少颗粒数目[30],同时通过在 PFC 成样程序中根据实际颗粒分析试验结果设置不同粒组,并控制粒组含量,使数值试样的颗粒组成成分尽可能接近实际沙样。③对于不考虑黏聚力的沙土,采用线性接触模型[31],该接触模型力学元件如图4 所示。室内压缩试验计算模型如图5 所示。

    图  4  三维线性接触模型物理元件图
    Figure  4.  Physical model diagram of the three-dimensional linear contact model
    图  5  室内压缩试验计算模型三视图
    Figure  5.  Three views of the calculation model for laboratory compression test

    (2)加载

    整个加载过程是用球形颗粒的运动来模拟土颗粒的运动变化情况,通过顶面墙体来控制施加压力, 圆柱形墙面与底面墙体保持不动。在PFC3D中,加载不是通过给顶面墙体一个力,而是通过给顶面墙体一个轴向的速度实现加载,轴向速度的大小为给定应变率与数值试样高度的乘积(图6)。

    图  6  试样加荷示意图
    Figure  6.  Schematic diagram of specimen loading

    加载过程中实时监测试样高度的变化,用数值试样原始高度减沉降稳定后的试样高度,即为在该压力下的下沉量。试样的轴向应变为上下两面墙体的相对位移除以试样的初始高度,应力的大小为作用在顶面墙体上的力除以的圆柱形墙体的底面积。

    本文颗粒流数值模拟的对象为沙土,颗粒间的接触模型选择线性接触模型。因此,PFC程序中需要确定的参数如下:①模型的半径($ r $)与高($ h $);②比重($ {G_{\rm{s}}} $);③加载压力($ p $);④孔隙率($ n $);⑤粒径范围与含量;⑥摩擦系数($ \mu $);⑦法向接触刚度($ {k_{\rm{n}}} $);⑧切向接触刚度($ {k_{\rm{s}}} $)。

    根据已有的基本物理力学参数与室内湿陷试验结果确定上述宏、细观参数。上述参数中模型的半径($ r $)与高($ h $)、比重($ {G_{\rm{s}}} $)、加载压力($ p $)、孔隙率($ n $)、粒径范围与含量可以通过换算或直接与基本物理力学参数相对应。而PFC软件中试样的宏、细观参数之间没有直接联系[32],摩擦系数($ \mu $)、法向接触刚度($ {k_{\rm{n}}} $)、切向接触刚度的确定首先需要遵循控制变量原则分析各参数对风积沙土变形特性的影响规律,然后根据所得规律标定细观参数,参数标定的依据为12组重塑土室内压缩试验结果。

    (1)模型的半径($ r $)与高($ h $

    根据实际室内压缩试验规模确定数值试样的大小和形状。室内压缩试验所用的环刀内径为61.8 mm,半径为30.9 mm,高为20 mm。数值试样约束墙体的形状、尺寸与实际室内压缩试验的规模完全相同,即r = 30.9 mm、h = 20 mm。

    (2)颗粒比重($ {G_{\rm{s}}} $

    颗粒比重取值与比重试验所得结果相同,即$ {G_{\rm{s}}} $= 2.616。

    (3)压力($ p $

    室内压缩试验压力取25,50,100,150,200 kPa,数值模拟加载程序中压力取值与室内试验相同。

    (4)孔隙率($ n $

    已知土样的干密度($ {\rho _{\rm{d}}} $)、比重($ {G_{\rm{s}}} $),可由下式计算出模型的孔隙率($ n $):

    $$ n=1-\frac{{\rho }_{{\mathrm{d}}}}{{G}_{{\mathrm{s}}}{\rho }_{{\mathrm{w}}}^{4\text{°C}}} $$ (1)

    式中:$ n $——孔隙率;

    $ {\rho _{\rm{d}}} $——干密度/(g·cm−3),土颗粒的质量除以土的 体积;

    $ {G_{\rm{s}}} $——比重;

    $ \rho _{\mathrm{w}}^{{4\text{°C} }} $——$ {4\text{°C} } $时纯蒸馏水的密度/(g·cm−3)。

    因为$ {\rho }_{{\mathrm{w}}}^{4\text{°C}} $ = 1.0 g/cm3,比重试验测得土的比重为$ {G_{\rm{s}}} = 2.616 $,由式 (1) 可得干密度$ {\rho _{\rm{d}}} $ = 1.4 g/cm3$ {\rho _{\rm{d}}} $ = 1.45 g/cm3$ {\rho _{\rm{d}}} $ = 1.50 g/cm3$ {\rho _{\rm{d}}} $ = 1.55 g/cm3对应的模型孔隙率分别为$ n = 0.465 $$ n = 0.446 $$ n = 0.427 $$ n = 0.407 $

    (5)粒径范围与含量

    采用级配平移、放大粒径的方法来减少颗粒数目。本文颗粒粒径放大系数为20。颗粒分析试验结果得到的是不同粒组颗粒的质量占比,比重试验测出颗粒比重。已知质量与密度,体积的计算公式为:

    $$ V = \frac{m}{\rho } $$ (2)

    式中:$ V $——体积/cm3

    $ m $——质量/g;

    $ \rho $——密度/(g·cm−3),土颗粒和水的质量除以土的体积。

    由式 (2) 可得,颗分试验所得颗粒的质量占比可以在PFC3D中等价为体积占比,所以可以通过控制不同粒组颗粒的体积占比使数值试样的颗粒组成成分尽可能接近实际沙样。

    (6)摩擦系数(μ

    沙土内摩擦角取值范围一般为15°~40°[33],尹成薇等[34]通过研究建立了PFC中沙土内摩擦角与颗粒间摩擦系数的线性相关关系:

    $$ \varphi = 0.73\arctan \mu + 7.85 $$ (3)

    式中:$ \varphi $——沙土内摩擦角/(°);

    $ \mu $——颗粒间摩擦系数。

    由式 (3) 可以推出,颗粒间摩擦系数的取值范围为0.1~0.9。

    重塑土室内压缩试验采用双线法,一组试验2个环刀样。一个试样在天然含水率下分级加荷,加至最后一级压力,下沉稳定后浸水饱和;另一个试样则是在浸水饱和后分级加荷。颗粒流数值模拟中水对摩擦系数影响较大[35],故在参数标定过程中将数值试样饱和后的摩擦系数统一定为最小值。PFC3D软件中无法模拟数值试样含水率的变化,仅能根据含水率增大,颗粒间摩擦系数减小的规律来体现含水率的变化。天然含水率下数值试样的摩擦系数大于饱和后数值试样的摩擦系数,用天然含水率条件下的数值模拟结果减去饱和条件下数值模拟结果即可得到湿陷量。据此规则,接触刚度保持不变,根据前文所述生成试样并加载,进行不同摩擦系数下的数值模拟[3637]。湿陷系数(δs)随摩擦系数(μ)的变化如图7所示。

    图  7  湿陷系数随摩擦系数的变化曲线
    Figure  7.  Curve of collapse factor with variation of friction coefficient

    图7可知,湿陷系数随摩擦系数的增大整体呈不断增大的趋势,在摩擦系数小于0.4时,湿陷系数增长速率较快,摩擦系数大于0.4后,湿陷系数增长速率减缓。摩擦系数较小时,试样受压颗粒越容易克服摩擦力发生移动[3839];摩擦系数增大,颗粒克服摩擦力发生滑动的难度加大,故湿陷系数增长速率减缓。

    (7)接触刚度(k

    文献[24]研究结果表明,对于线性接触模型,切向刚度与法向刚度的比值对于压缩模量的影响不大,因此本文取1.0,即细观参数标定过程中法向接触刚度($ {k_{\rm{n}}} $)=切向接触刚度(${k_{\rm{s}}} $)。摩擦系数保持不变,进行数值模拟,湿陷系数随接触刚度的变化如图8所示。

    图  8  湿陷系数随接触刚度的变化曲线
    Figure  8.  Curve of collapse factor with variation of contact stiffness

    图8可知,湿陷系数随接触刚度的增大整体呈下降趋势。接触刚度在小于$ 1.1 \times {10^7} $时,湿陷系数下降速率较快;接触刚度处于$ 1.1 \times {10^7} $$ 1.4 \times {10^7} $之间,湿陷系数下降速率减缓;接触刚度大于$ 1.4 \times {10^7} $后,试样湿陷性迅速丧失。接触刚度较小时,颗粒间相互作用较小,颗粒容易产生位移使土样整体下沉量大;而后,土样下沉量增大的速率减缓,当颗粒间相互作用足够大时,颗粒几乎不产生大的位移,试样便不具有湿陷性。

    据前文中颗粒流数值模型的确定方法与所得规律对重塑土的室内压缩试验进行数值模拟,数值模拟结果见表3

    表  3  数值模拟结果
    Table  3.  Numerical simulation results
    试样编号 颗粒比重 干密度/(g·cm−3 含水率/% 湿陷系数 模拟湿陷系数 孔隙率 粒径区间/mm 法向接触刚度 切向接触刚度 摩擦系数
    1 2.65 1.40 3 0.02650 0.02700 0.465 0.075~0.250 $ 1.109 \times {10^7} $ $ 1.109 \times {10^7} $ 0.350
    2 2.65 1.45 3 0.02225 0.02243 0.446 0.075~0.250 $ 1.284 \times {10^7} $ $ 1.284 \times {10^7} $ 0.370
    3 2.65 1.50 3 0.01625 0.01633 0.427 0.075~0.250 $ 1.473 \times {10^7} $ $ 1.473 \times {10^7} $ 0.360
    4 2.65 1.55 3 0.00100 0.00110 0.407 0.075~0.250 $ 1.590 \times {10^7} $ $ 1.590 \times {10^7} $ 0.350
    5 2.65 1.40 6 0.02550 0.02580 0.465 0.075~0.250 $ 1.109 \times {10^7} $ $ 1.109 \times {10^7} $ 0.270
    6 2.65 1.45 6 0.02200 0.02230 0.446 0.075~0.250 $ 1.284 \times {10^7} $ $ 1.284 \times {10^7} $ 0.270
    7 2.65 1.50 6 0.01725 0.01733 0.427 0.075~0.250 $ 1.473 \times {10^7} $ $ 1.473 \times {10^7} $ 0.273
    8 2.65 1.55 6 0.00050 0.00070 0.407 0.075~0.250 $ 1.590 \times {10^7} $ $ 1.590 \times {10^7} $ 0.271
    9 2.65 1.40 9 0.02450 0.02500 0.465 0.075~0.250 $ 1.109 \times {10^7} $ $ 1.109 \times {10^7} $ 0.232
    10 2.65 1.45 9 0.02050 0.02020 0.446 0.075~0.250 $ 1.284 \times {10^7} $ $ 1.284 \times {10^7} $ 0.230
    11 2.65 1.50 9 0.01850 0.01820 0.427 0.075~0.250 $ 1.473 \times {10^7} $ $ 1.473 \times {10^7} $ 0.230
    12 2.65 1.55 9 0.00050 0.00030 0.407 0.075~0.250 $ 1.590 \times {10^7} $ $ 1.590 \times {10^7} $ 0.231
    下载: 导出CSV 
    | 显示表格

    表3可知,数值模拟结果与室内重塑土湿陷试验结果较吻合。参数标定过程中发现,摩擦系数受含水率影响较大,随着含水率的增大,摩擦系数减小;接触刚度受干密度影响较大,随着干密度的增大,接触刚度增大。选取表2中干密度为1.4 g/cm3、含水率为3%和干密度为1.5 g/cm3、含水率为9%的两组试验进行数值模拟,按照25,50,100,150,200 kPa分级加荷,湿陷系数随压力的变化曲线($ p - {\delta _{\rm{s}}} $曲线)如图9 所示。

    图  9  室内试验、数值模拟$ p - {\delta _{\rm{s}}} $曲线对比
    Figure  9.  Comparison of laboratory test and numerical simulation $ p - {\delta _{\rm{s}}} $ curves

    图9中,数值模拟结果较好反映室内试验结果。真实土颗粒与球形颗粒存在差别,真实土颗粒形状不规则,在高压作用下还会破碎,这导致室内试验与数值模拟结果存在误差,数值模拟所得曲线相对平滑[4042]

    孔隙率是试样内部颗粒相对位移和试样变形规律的一个重要参数。借助PFC内置measure记录方法监测试样孔隙率在加载过程中的变化,在试样内部布置半径为10 mm的测量球共9个,以监测加载过程中试样的孔隙率,取9个测量球测得孔隙率的平均值代表数值试样下沉稳定后的孔隙率。对数值试样加压至200 kPa,孔隙率随压力的变化如图10所示。

    图  10  孔隙率随压力的变化曲线
    Figure  10.  Curve of porosity variation with pressure

    孔隙率随压力的变化曲线呈先降后升的趋势,该演化规律与湿陷系数随压力先增后减的规律相对应。孔隙率在150 kPa时最小,而后压力增大,土颗粒间相互作用力增大,出现膨胀现象。

    变化不同的初始孔隙率,进行数值模拟试验,孔隙率对风积沙土湿陷性的影响如图11所示。

    图  11  湿陷系数随孔隙率的变化曲线
    Figure  11.  Curve of collapse factor variation with porosity

    风积沙土的湿陷性与初始孔隙率之间呈正相关关系,当孔隙率$ n < 0.425 $时,沙土不具有湿陷性;当孔隙率$ n > 0.476 $时,沙土具有中等湿陷性。因此,可将孔隙率0.425界定为沙土出现湿陷性的湿陷起始孔隙率。

    室内试验所取试样粒径主要分布在0.075~0.25 mm、0.25~0.5 mm两粒径区间内,两者总量超过 95%,基本上可以忽略黏粒对湿陷性的影响。为反映颗粒级配对湿陷性的影响,在PFC3D成样程序中,设置两个粒径区间,并将两粒径区间内颗粒含量占比分别设置成:①0∶1;②0.15∶0.85;③0.25∶0.75;④0.35∶0.65;⑤0.45∶0.55;⑥0.55∶0.45;⑦0.65∶0.35;⑧0.75∶0.25;⑨0.85∶0.15;⑩1∶0,得到不同颗粒组成情况下湿陷系数的变化曲线(图12)。

    图  12  不同颗粒组成情况下湿陷系数变化曲线
    Figure  12.  Curves of collapse coefficient variation under different particle compositions

    图12可知,当 0.075~0.250 mm、0.25~0.50 mm两粒径区间内颗粒含量比为0.35∶0.65时,沙土的湿陷性最强;当 0.25~0.50 mm区间内颗粒含量大于65%时,湿陷系数随 0.075~0.250 mm颗粒含量的增多而增大;当 0.25~0.50 mm区间内颗粒含量小于65%时,湿陷系数随 0.075~0.250 mm颗粒含量的增多而减小;0.075~0.250 mm 或 0.25~0.50 mm两粒径区间内颗粒含量过多时,湿陷系数均较低。粒径较大的颗粒起骨架作用,骨架颗粒间点与点接触,骨架颗粒间的摩擦力阻碍颗粒移动,造成大量的架空孔隙,提供了湿陷空间,在压缩过程中粒径较小的颗粒充填于架空的大孔隙中导致试样下沉。0.075~0.250 mm颗粒含量过多时(大于35%),大颗粒无法形成稳固的联通骨架,骨架颗粒易于发生移动,土中孔隙剧烈减少,导致沙土湿陷系数减小。0.25~0.50 mm颗粒含量过多时(大于 65%),大颗粒形成联通骨架,联通骨架不再压缩是湿陷系数减小的原因。

    (1)风积沙土湿陷系数随试验压力的增大呈现先增大后减小的趋势,湿陷系数可取到峰值时的压力为150 kPa。

    (2)随着干密度或含水率的增大,湿陷系数减小,但干密度对风积沙土湿陷系数的影响更大。

    (3)孔隙率随压力的变化曲线呈先降后升的趋势,该演化规律与湿陷系数随压力先增后减的规律相对应;当初始孔隙率大于0.425时,风积沙土开始具有湿陷性,且湿陷系数与初始孔隙率之间呈正相关关系。

    (4)当0.075~0.250 mm、0.25~0.50 mm两粒径区间内颗粒含量比为0.35∶0.65时,风积沙土的湿陷性最强。粒径较大的颗粒形成联通骨架,造成大量架空孔隙,粒径较小的颗粒充填于架空的大孔隙提升了湿陷空间。0.075~0.250 mm 或 0.25~0.50 mm两粒径区间内颗粒含量过多时,湿陷系数均较低。

    (5)本文采用的室内压缩试验数量有限,这导致未建立宏观参数与细观参数间定量的相关关系,此外数值模拟过程中,仅用单一的球形颗粒单元无法全面揭示沙土颗粒不规则形状对工程力学性质的影响。为此,今后的研究中可以引入更多的室内试验结果,由此建立起宏观参数与细观参数间定量关系,并建立不规则的颗粒集合刚体,有望得到更好的结果。

  • 图  1   试验土样粒径级配曲线

    Figure  1.   Distribution curve of particle sizes

    图  2   $ p - {\delta _{\rm{s}}} $曲线

    Figure  2.   $ p - {\delta _{\rm{s}}} $ curves

    图  3   $ p - {\delta _{\rm{s}}} $曲线

    Figure  3.   $ p - {\delta _{\rm{s}}} $ curves

    图  4   三维线性接触模型物理元件图

    Figure  4.   Physical model diagram of the three-dimensional linear contact model

    图  5   室内压缩试验计算模型三视图

    Figure  5.   Three views of the calculation model for laboratory compression test

    图  6   试样加荷示意图

    Figure  6.   Schematic diagram of specimen loading

    图  7   湿陷系数随摩擦系数的变化曲线

    Figure  7.   Curve of collapse factor with variation of friction coefficient

    图  8   湿陷系数随接触刚度的变化曲线

    Figure  8.   Curve of collapse factor with variation of contact stiffness

    图  9   室内试验、数值模拟$ p - {\delta _{\rm{s}}} $曲线对比

    Figure  9.   Comparison of laboratory test and numerical simulation $ p - {\delta _{\rm{s}}} $ curves

    图  10   孔隙率随压力的变化曲线

    Figure  10.   Curve of porosity variation with pressure

    图  11   湿陷系数随孔隙率的变化曲线

    Figure  11.   Curve of collapse factor variation with porosity

    图  12   不同颗粒组成情况下湿陷系数变化曲线

    Figure  12.   Curves of collapse coefficient variation under different particle compositions

    表  1   场地基本物理特性指标

    Table  1   Basic physical charecteristics of the site

    参数 密度/(g·m−3 含水率/% 干密度/(g·m−3 比重 孔隙比 饱和密度/(g·m−3 饱和度 最小干密度/(g·m−3 最大干密度/(g·m−3
    数值 1.587 4.5 1.519 2.616 0.722 1.938 16.3 1.38 1.77
    下载: 导出CSV

    表  2   室内压缩试验结果

    Table  2   Laboratory compression test results

    试样
    编号
    干密度
    /(g·cm−3
    含水率/% 粒径区间/mm 湿陷系数 湿陷等级
    1 1.40 3 0.075~0.250 0.02650 轻微湿陷
    2 1.45 3 0.075~0.250 0.02225 轻微湿陷
    3 1.50 3 0.075~0.250 0.01625 轻微湿陷
    4 1.55 3 0.075~0.250 0.00100 无湿陷
    5 1.40 6 0.075~0.250 0.02550 轻微湿陷
    6 1.45 6 0.075~0.250 0.02200 轻微湿陷
    7 1.50 6 0.075~0.250 0.01725 轻微湿陷
    8 1.55 6 0.075~0.250 0.00050 无湿陷
    9 1.40 9 0.075~0.250 0.02450 轻微湿陷
    10 1.45 9 0.075~0.250 0.02050 轻微湿陷
    11 1.50 9 0.075~0.250 0.01850 轻微湿陷
    12 1.55 9 0.075~0.250 0.00050 无湿陷
    下载: 导出CSV

    表  3   数值模拟结果

    Table  3   Numerical simulation results

    试样编号 颗粒比重 干密度/(g·cm−3 含水率/% 湿陷系数 模拟湿陷系数 孔隙率 粒径区间/mm 法向接触刚度 切向接触刚度 摩擦系数
    1 2.65 1.40 3 0.02650 0.02700 0.465 0.075~0.250 $ 1.109 \times {10^7} $ $ 1.109 \times {10^7} $ 0.350
    2 2.65 1.45 3 0.02225 0.02243 0.446 0.075~0.250 $ 1.284 \times {10^7} $ $ 1.284 \times {10^7} $ 0.370
    3 2.65 1.50 3 0.01625 0.01633 0.427 0.075~0.250 $ 1.473 \times {10^7} $ $ 1.473 \times {10^7} $ 0.360
    4 2.65 1.55 3 0.00100 0.00110 0.407 0.075~0.250 $ 1.590 \times {10^7} $ $ 1.590 \times {10^7} $ 0.350
    5 2.65 1.40 6 0.02550 0.02580 0.465 0.075~0.250 $ 1.109 \times {10^7} $ $ 1.109 \times {10^7} $ 0.270
    6 2.65 1.45 6 0.02200 0.02230 0.446 0.075~0.250 $ 1.284 \times {10^7} $ $ 1.284 \times {10^7} $ 0.270
    7 2.65 1.50 6 0.01725 0.01733 0.427 0.075~0.250 $ 1.473 \times {10^7} $ $ 1.473 \times {10^7} $ 0.273
    8 2.65 1.55 6 0.00050 0.00070 0.407 0.075~0.250 $ 1.590 \times {10^7} $ $ 1.590 \times {10^7} $ 0.271
    9 2.65 1.40 9 0.02450 0.02500 0.465 0.075~0.250 $ 1.109 \times {10^7} $ $ 1.109 \times {10^7} $ 0.232
    10 2.65 1.45 9 0.02050 0.02020 0.446 0.075~0.250 $ 1.284 \times {10^7} $ $ 1.284 \times {10^7} $ 0.230
    11 2.65 1.50 9 0.01850 0.01820 0.427 0.075~0.250 $ 1.473 \times {10^7} $ $ 1.473 \times {10^7} $ 0.230
    12 2.65 1.55 9 0.00050 0.00030 0.407 0.075~0.250 $ 1.590 \times {10^7} $ $ 1.590 \times {10^7} $ 0.231
    下载: 导出CSV
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  • 收稿日期:  2023-07-12
  • 修回日期:  2024-01-10
  • 录用日期:  2024-03-04
  • 网络出版日期:  2024-05-25
  • 刊出日期:  2024-08-24

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