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Journal of Changjiang River Scientific Research Institute >

2025 , Vol. 42 >Issue 11: 103 - 110

DOI: https://doi.org/10.11988/ckyyb.20240964

Rock-Soil Engineering

Experimental Study on Damping Ratio Characteristics of Loose Silty Fine Sand at Different Saturations

  • YU Song , 1 ,
  • XU Meng-bing 2, 3 ,
  • FENG Zhi-guo 1 ,
  • ZHANG Jun-jie 1 ,
  • ZHANG Guo-chao 1 ,
  • WANG Yong 2
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  • 1 China Railway Major Bridge Reconnaissance & Design Institute Co., Ltd., Wuhan 430050, China
  • 2 State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China
  • 3 University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2024-09-10

  Revised date: 2024-11-14

  Online published: 2025-04-22

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Abstract

[Objective] Current research on the damping ratio evolution of silty fine sand under varying saturation conditions remains relatively limited, and in particular, systematic investigations revealing the mechanisms by which saturation variations influence damping ratios within the framework of unsaturated soil mechanics are still insufficient. To address this gap, typical loose silty fine sand from the Hangzhou Bay area is selected as the research subject. Utilizing a self-improved unsaturated soil resonant column testing system, the damping ratio evolution characteristics and underlying mechanisms along the desaturation path are thoroughly investigated. The findings aim to provide a scientific basis for analyzing dynamic properties and engineering applications of unsaturated soils. [Methods] An improved unsaturated soil resonant column apparatus was employed to conduct small-strain dynamic property tests under controlled drainage paths and saturation conditions. Test specimens were initially prepared with varying saturation levels and stress states. A stepwise desaturation process under constant net stress conditions was then applied to establish a series of samples with different saturation states. Subsequently, shear modulus and damping ratio measurements were performed across varying saturation levels and net stress conditions via resonant column loading. By integrating theoretical analyses of soil-water characteristic curves (SWCC) and pore water distribution states, distinct stages of damping ratio evolution were identified, and damping mechanisms induced by saturation variations were elucidated. [Results] The experimental results indicated that: (1) under identical saturation conditions, the damping ratio of silty fine sand gradually decreased with increasing net stress. (2) During saturation evolution, the damping ratio exhibited distinct stage-wise variations: when the soil approached full saturation, the damping ratio remained relatively stable. As saturation declined, the damping ratio rapidly attenuated and reached a minimum near the optimal saturation Sropt. Further saturation reduction led to a slight rebound in the damping ratio. (3) Based on the SWCC and pore water morphology evolution, the saturation-dependent damping ratio variations were categorized into three stages: boundary effect stage, transition stage, and residual saturation stage. [Conclusion] This study elucidates the damping ratio evolution mechanism of loose silty fine sand along desaturation paths. It demonstrates that the damping ratio is influenced not only by net stress but also closely associated with pore water distribution states, and that its minimum damping ratio occurs at the optimal saturation Sropt. The results reveal that saturation-dependent damping ratio changes can be categorized into three stages, each corresponding to distinct pore water morphology evolution processes. By employing the improved unsaturated soil resonant column, the complete damping ratio evolution process with saturation variation is observed. The principle of minimum damping ratio under “optimal saturation” control is proposed, and the three-stage evolution mechanism is revealed through SWCC analysis. These findings provide a foundation for refining unsaturated soil dynamic models and enhancing the scientific rigor of related engineering designs.

Key words： silty fine sand; damping ratio; resonant column; dynamic characteristics test; saturation; net stress

Cite this article

YU Song , XU Meng-bing , FENG Zhi-guo , ZHANG Jun-jie , ZHANG Guo-chao , WANG Yong . Experimental Study on Damping Ratio Characteristics of Loose Silty Fine Sand at Different Saturations[J]. Journal of Changjiang River Scientific Research Institute, 2025 , 42(11) : 103 -110 . DOI: 10.11988/ckyyb.20240964

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0 引言

在工程实践中,地震荷载、机械振动、交通荷载、波浪荷载等振动荷载会对基础设施造成相当大的破坏,造成较高的安全风险和经济损失[1-4]。阻尼比作为反映土体动力特性的基本参数,其取值的合理性将直接影响到工程结构的安全性和经济性[5-7]。
目前,已有不少学者对砂土的阻尼比特性开展了卓有成效的试验研究[6,8-9]。对于干砂而言,干砂的阻尼比受颗粒间的摩擦和碰撞机制主导, Panyan等[10]对不同颗粒形状的干砂进行共振柱试验,提出了包含颗粒形状和级配影响的干砂小应变阻尼比预测模型。Senetakis等[11]考虑了不同振动模式下细粒含量对干砂阻尼比的影响,研究表明:随着细粒含量的增加,砂土的弯曲和扭转阻尼比比值减小,并收敛至粉土的对应取值。饱和砂土在动力荷载下,由于孔隙水的存在,其阻尼比还受到孔隙水压力、黏滞效应等多种机制的共同影响,展现出不同于干砂的动力响应特性[12]。如王体强等[13]基于超重力模型试验,对干砂和饱和砂进行了对比试验,结果表明干砂阻尼比随剪应变变化具有良好的规律性,而饱和砂相较于干砂随剪应变规律不明显,离散性大。王勇等[14]、Cheng等[15]对不同细粒含量饱和砂土分别进行了一系列动三轴和共振柱试验,发现饱和砂土阻尼比随细粒含量的增加呈现先增大后减小的趋势。江洎洧等[16]对饱和粉细砂开展了动三轴试验,研究表明Hardin公式[17]可以很好拟合阻尼比与动应变的关系。对于非饱和砂土而言,其阻尼比的变化更为复杂,受到含水率、孔隙结构、颗粒排列等多种因素的共同控制[8,12,18]。薛龙[19]开展了非饱和粉细砂的动三轴试验,认为非饱和粉质砂土的阻尼比随动应变的增大而逐渐增大,随着饱和度的增大阻尼比亦有增加的趋势。王晋宝等[20]基于共振柱试验,对砂土开展了从干燥到饱和状态3种不同饱和度时阻尼比特性的试验研究,给出了Martin-Davidenkov模型[21]以及阻尼比经验公式的拟合方程参数值。王海东等[22]利用循环单剪试验研究了饱和度和粒径对非饱和砂土动力特性的影响,结果表明,在饱和度为0.3~0.7范围内,阻尼比随饱和度的变化整体较为平稳,差异性不大,说明在该饱和度区间饱和度并不是影响砂土阻尼比的主导因素。然而,上述研究试验中对砂土饱和度的控制多是通过控制含水率计算得到,目前鲜有文献报道在严格控制基质吸力条件下实现砂土全饱和度区间阻尼比特性变化规律的研究。
本文采用自主改进的非饱和土共振柱系统对杭州湾粉细砂开展不同饱和度下的小应变动力特性试验,严格控制砂样基质吸力,探究全饱和度范围内粉细砂阻尼比随剪应变、净应力的演化规律,并尝试阐明饱和度对粉细砂阻尼比的影响机理。

1 试验研究

1.1 测试材料与SWCC曲线

试验粉细砂样品采自杭州湾近海海域,埋深25~30 m。土样取回后置于烘箱中,保持温度105 ℃,烘干12 h。过孔径2 mm筛,装袋封存。根据《土工试验方法标准》(GB/T 50123—2019)对试验土样进行基本物理性质测定,试验结果见表1。试验土样的颗粒分布曲线如图1所示,砂样粒径主要分布在0.1~0.5 mm之间,约占91.61%。不均匀系数Cu为2.69,曲率系数Cc为1.428,细粒(粒径d<0.075 mm)含量为7.22%。根据《土的工程分类标准》(GB/T 50145—2007),土样属于含细粒土砂。
表1 粉细砂的基本物理特性

Table 1 Basic physical properties of silty fine sand

相对
密度		 最小干密度/
(g·cm-3)		 最大干密度/
(g·cm-3)		 平均粒径
(d50/mm)		 最小孔
隙比emin		 最大孔
隙比emax
2.69 1.26 1.56 0.198 0.724 1.135
Fig.1 粉细砂的颗粒级配曲线
Particle size distribution curve of silty fine sand 试验过程中,粉细砂样的相对密实度控制在30%,相应的干密度<i>ρ</i><sub>d</sub>为1.337 g/cm<sup>3</sup>。采用压力板仪测量粉细砂的土-水特征曲线(Soil-Water Characteristic Curve, SWCC),并采用van Genuchten(VG)模型<sup>[<a href="javascript:;" class="mag_content_a" onclick="piaofuRef(this,'b23')" rid="b23">23</a>]</sup>拟合实测数据,如<a href="javascript:;" class="mag_content_a mag_xref_fig" onclick="clickFigXref(this,'F2')" rid="F2">图2</a>所示。
图2 VG模型的预测SWCC曲线

Fig.2 SWCC curve predicted by VG model

在保持净应力不变的条件下,通过控制基质吸力,可以得到不同饱和度的试样。VG模型拟合公式为
${S}_{r}={S}_{c}+\frac{1-{S}_{c}}{\left[1\right.+{\left(\alpha \psi \right)}^{n}{]}^{m}}　。$
式中:Sr为饱和度;Sc为残余饱和度; $\psi $为基质吸力(kPa);α、m、n为模型参数(本文α=0.234,m=12.69, n=0.116)。

1.2 测试仪器

试验采用自主改进的非饱和土共振柱仪。基于Stokoe型共振柱饱和底座,在中心位置安装一块进气值为200 kPa的陶土板,陶土板下方设置环形凹槽,保证水流通畅,在陶土板与金属底座的接触部位以环氧树脂粘结,室温条件下固结24 h完成胶结。图3为改造共振柱底座实物图。改造后的共振柱底座可以在控制基质吸力的条件下,对同一土样在脱湿或者吸湿路径下土体的小应变特性开展共振柱试验测试。改进后的共振柱测试单元如图4所示。
图3 改造共振柱底座

Fig.3 Modified resonance column base

图4 非饱和土共振柱测试单元示意图

Fig.4 Schematic diagram of unsaturated soil resonant column test unit

共振柱测量阻尼比的原理是根据自由振动衰减曲线的对数衰减率来进行计算的。利用加速度传感器测得的自由振动波幅的衰减计算得出土样的阻尼比[7]为
$D=\sqrt{\frac{{\delta }^{2}}{4{\pi }^{2}+{\delta }^{2}}}　。$
式中:D为阻尼比; $\delta $为衰减对数。

1.3 试样制备和试验方案

现场原状砂样的相对密实度为31.2%,为与实际工程接近,室内重塑砂样的相对密实度控制为30%。试样制备尺寸为50 mm×100 mm(直径×高),干密度ρd=1.337 g/cm3,孔隙率n'=0.5。根据研究目标,即在控制基质吸力情况下,研究全饱和区间内松散粉细砂土小应变动力特性。干砂试样的制备采用落雨法,将预先称量好的干燥粉细砂在共振柱饱和底座上分为5层振捣成样。制备非饱和粉细砂时,以SWCC为依据来控制粉细砂试样的饱和度。首先,采用烘干砂和无气水制备含水量为5%的砂样,将试样置于密闭容器中12 h,使水分均匀。使用振动击实法在饱和器中形成5层样品的砂样。将初始含水率为5%的粉细砂在三轴饱和器中分5层压实,每层表面刨毛后,再填下一层。重复上述步骤至最后一层,整平表面。在真空缸内使用真空饱和法对样品进行饱和。将饱和砂试样快速冷冻,避免外部因素扰动,然后快速安装在测试系统的底座上。试件解冻后,基于非饱和土轴平移技术,将围压设置为150 kPa,孔隙气压设置为50 kPa,试样的反压和净应力分别保持在50 kPa和100 kPa,加压时间均设置为120 min。试样的净应力和反压保持不变,孔隙气压和围压根据轴向平移技术而变化。当达到吸力平衡(即8 h的排(吸)水量<0.1 cm3[24-26])时,对不同饱和度的试样进行阻尼比试验测试。不同基质吸力与饱和度的对应关系如表2所示。按照相同的方法,在净应力分别为200、300、400 kPa的砂试样进行阻尼比试验测试。
表2 基质吸力与饱和度之间的对应关系

Table 2 Correspondence between matric suction and saturation

饱和度/% 100 92 65 50 40 30 20 17 0
基质吸力/kPa 0 4 6 8 10 15 40 200 0

2 测试结果与分析

2.1 松散粉细砂阻尼比随应变的变化规律

图5给出了饱和度Sr在0~1区间内,净应力分别为400、300、200、100 kPa应力状态下阻尼比随动剪应变的变化曲线。其中,散点为测量值。由图5可看出,随着动剪应变增大,松散粉细砂阻尼比逐渐增大。
图5 不同应力水平下各饱和度松散粉细砂的阻尼比变化

Fig.5 Variation of damping ratio for loose silty fine sand at different saturations under different stress levels

关于阻尼比的合理表征,迄今已提出了很多经验公式,比较经典的是Hardin等[17]基于试验结果提出的关于剪切模量的阻尼比经验公式。以往研究表明,Hardin-Drnevich双曲线模型具有参数少、物理意义明确的优点,但将Hardin-Drnevich双曲线模型直接应用于阻尼比拟合时,结果往往效果不佳[27]。
Hardin-Drnevich公式为
$D={D}_{max}\left(1-\frac{G}{{G}_{max}}\right)　。$
式中:Dmax为最大阻尼比;G为小应变剪切模量;Gmax为最大剪切模量。
陈国兴等[28]通过开展共振柱试验研究了大量江苏苏南地区新近沉积土的小应变动力特性,基于Hardin-Drnevich公式进行修正,给出下列经验公式来描述土体阻尼比,即
$D={D}_{min}+{D}_{max}{\left(1-\frac{G}{{G}_{max}}\right)}^{n″}　。$
式中:Dmin为最小阻尼比,是土体的基本阻尼比,与土的性质、固结状态等因素有关;n″为与土性有关的拟合参数,该参数决定了阻尼比曲线的形状。
本文采用式(4)对试验数据进行拟合,并将实测数据与拟合结果展示于图5。由实测数据和拟合曲线可以得知,式(4)能够较好地描述本文松散粉细砂土的阻尼比特性。

2.2 净应力对阻尼比的影响

由图5 实测数据和拟合曲线可得,在较小应变范围 (应变γ<10-3)内,不同净应力状态下阻尼比随剪应变变化幅度很小,随着应变增大(γ>10-3),阻尼比开始迅速增大,且在剪应变幅值相同的情况下,阻尼曲线随净应力的增大逐渐向右下方移动,表明阻尼比随净应力的增大而减小,较高应力状态抑制了阻尼比增大的趋势。这主要是因为净应力水平越高,有效应力越大,土颗粒之间的接触和咬合越紧密,相同条件下对能量的耗散越低,其阻尼比也就越小。
为了分析在小应变条件下净应力对松散粉细砂阻尼特性的影响特性,选取动剪应变参考值为γr=10-5,根据图5所示拟合曲线方程进行计算,得到不同饱和度的粉细砂阻尼比随净应力的关系,如图6所示。由图6可看出,不同饱和度松散粉细砂的阻尼比在小应变条件下随净应力水平的提高均呈现出轻微程度的减小趋势,但总体变化量值不大,说明净应力对松散粉细砂阻尼比的影响并不十分显著。
图6 不同饱和度下阻尼比随净应力的变化规律

Fig.6 Variation patterns of damping ratio with net stress at different saturations

2.3 饱和度对阻尼比的影响

图7给出了相同净应力下,不同饱和度对松散粉细砂阻尼比影响的实测值和拟合曲线。结果表明,同一净应力状态下松散粉细砂阻尼比随剪应变的变化曲线均随饱和度的增大而逐渐上移,这表明当动剪应变幅值相同时,随着饱和度的增加,松散粉细砂的阻尼比略微增大,可以发现在低剪应变(γ<10-3)范围内,阻尼比整体上随饱和度的增加变化幅度并不大、相对较稳定;但是随着剪应变的增加,饱和度越高,阻尼比的增长速度越快。这是因为振动或能量在土体中传播时,引起了水与颗粒之间的相对运动,导致波在传播过程中能量损耗增大[29]。含水率越高其耗散能量会越大;动剪应变幅值越大,土体颗粒之间的剪切滑动摩擦消耗的能量就会越多,阻尼比也随之越大。
Fig.7 饱和度对松散粉细砂阻尼比的影响
Influence of saturation on damping ratio of loose silty fine sand 为了分析在小应变条件下饱和度对松散粉细砂阻尼特性的影响特性,同样选取<i>γ</i><sub>r</sub>=10<sup>-5</sup>作为动剪应变参考值,根据<a href="javascript:;" class="mag_content_a mag_xref_fig" onclick="clickFigXref(this,'F7')" rid="F7">图7</a>所示拟合曲线方程进行计算,得到不同应力状态下松散粉细砂阻尼比随饱和度的关系,如<a href="javascript:;" class="mag_content_a mag_xref_fig" onclick="clickFigXref(this,'F8')" rid="F8">图8</a>所示。从<a href="javascript:;" class="mag_content_a mag_xref_fig" onclick="clickFigXref(this,'F8')" rid="F8">图8</a>可以看出,在同一净应力状态下松散粉细砂阻尼比随饱和度的变化阶规律大致可分为3个阶段:在边界效应阶段(Ⅰ),阻尼比对饱和度的变化并不敏感 ;当饱和度减小至65%,进入到过渡阶段(Ⅱ)后,随着饱和度的减小,孔隙气体逐渐占据更大的孔隙空间,松散粉细砂阻尼比随饱和度降低而减小的速率明显加快,这种趋势一直持续到饱和度为17%左右,其阻尼比达到最小;进入到残余饱和阶段(Ⅲ),阻尼比略微增大。Wu等<sup>[<a href="javascript:;" class="mag_content_a" onclick="piaofuRef(this,'b18')" rid="b18">18</a>]</sup>基于共振柱试验研究了毛细管力对砂土小应变模量<i>G</i><sub>max</sub>的影响,提出了最优饱和度<i>S</i><sub>ropt</sub>的概念。本文试验得出的最优饱和度约为16%,此时粉细砂的阻尼比达到最小值。
图8 不同净应力状态下阻尼比随饱和度的变化规律

Fig.8 Variation patterns of damping ratio with saturation under different net stress states

图9 土颗粒周围水的分布示意图

Fig.9 Schematic diagram of water distribution around soil particles

土颗粒表面水分的分布由近至远可分为结构水、吸附膜、吸附水、毛细水及自由水,如图9所示。结构水存在于矿物晶层内,一般视为土颗粒的一部分;吸附膜则主要通过电荷吸附作用附着于土颗粒表面,高温110 ℃无法烘干去除,但可在颗粒表面移动;吸附水则通过静电引力、及范德华力等附着于土颗粒表面;而毛细水则是由表面张力引起,常温下即可蒸发;自由水为可自由流动的孔隙水。
对于不同饱和度的松散粉细砂而言,在边界效应阶段(Ⅰ),土体大部分孔隙被水充满,土颗粒被水完全包裹,且土颗粒接触点处的水相连续,孔隙气体仅以小气泡形式赋存在孔隙水中,随水流动,因此该阶段毛细作用力变化很小,土体的有效应力基本保持不变,故此时孔隙水形态的变化对土体阻尼比的影响不大,阻尼比与饱和状态下粉细砂的阻尼比基本一致。但随着饱和度的持续减小,重力水不断排出,进入到过渡阶段(Ⅱ),气体开始占据孔隙的主要空间,孔隙水逐渐减少并聚集在土颗粒间的接触角隅位置,弯液面形成并逐渐增多,毛细作用力对有效应力的贡献开始发挥并增大,导致土体的刚度增大,阻尼特性减弱,这种趋势一直持续到最优饱和度Sropt附近,土体的刚度达到最大,阻尼比达到最小。随后,转入残余饱和阶段(Ⅲ),土颗粒接触点处的弯液面毛细水逐渐被排尽,此时粒间相互作用已由毛细作用力转变为如双电层斥力、范德华力及静电力等复杂的物理化学作用力,但是与黏性土不同,粉细砂颗粒间距离较大,脱湿过程对土体变形并不显著,且石英颗粒表面也不会同黏土颗粒一样表面附着有大量的剩余电荷,其物理化学吸附作用力很弱(相比重力可以忽略不计),毛细增强效应迅速减弱,其对有效应力的贡献也迅速减小,总体上造成有效应力减小,进而导致粉细砂的阻尼特性略微增大响应。

3 结论

研究饱和度对松散粉细砂阻尼比特性的影响对于场地动力响应特性分析具有重要的意义。基于自主改进的非饱和土共振柱,研究了松散粉细砂阻尼比随净应力和饱和度的演化规律,并从土颗粒、孔隙水形态及相互作用角度阐述了引起其变化的内在机制。主要结论如下:
(1)在小应变范围内(10-5~10-3),不同净应力水平下粉细砂的阻尼比变化趋势基本相同;随着剪应变增加,粉细砂的阻尼比迅速增大;初始应力水平越高,阻尼比增长越慢;在相同饱和度和剪应变条件下,净应力对粉细砂阻尼比的影响不显著。
(2)在小应变条件下,粉细砂阻尼比整体上随饱和度的增加变化幅度并不大、相对较稳定;随着剪应变幅值的增加,饱和度越高,阻尼比的增长速度越快。在小剪应变幅值固定不变时,粉细砂阻尼比随饱和度的变化规律大致可分为3段:边界效应阶段,阻尼比对饱和度的变化并不敏感;过渡阶段,阻尼比随饱和度降低而减小,这种趋势一直持续到最优饱和度Sropt附近,其阻尼比值达到最小;残余饱和阶段,阻尼比随饱和度的降低则略有增大。
(3)松散粉细砂阻尼比随饱和度变化曲线的3个阶段与颗粒内部孔隙水的细观形态演化以及毛细作用引起的粒间应力变化密切相关。边界效应阶段毛细作用力变化很小,孔隙水形态变化对阻尼比的影响微弱;过渡阶段,毛细作用对有效应力的贡献增大,土体阻尼特性减弱;进入残余饱和阶段,毛细效应迅速减弱,阻尼比略微增大。

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