Effect of particle shape on the dynamic deformation characteristics of artificially simulated rockfill material
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摘要:
堆石料作为土石坝的主要构筑材料,其在地震作用下的动变形特性受颗粒形状、级配和相对密度等影响。颗粒形状对堆石料力学特性影响的研究目前主要集中于静力特性,关于动力特性方面的研究相对较少。采用水泥净浆浇筑方法制备了不同形状的人工模拟堆石料并进行动力循环三轴试验,研究了颗粒形状对动残余应变和颗粒破碎的影响。结果表明:采用该方法制备的人工模拟堆石料可以近似反映天然堆石料的动变形特性;在低围压下,残余体积应变随形状系数的增大而减小,在高围压下则规律相反;轴向残余应变随形状系数的增大而先增后减;在相同应力条件下,形状系数越小,颗粒破碎率越低。另外,研究还建立了颗粒破碎率与颗粒形状系数和围压的关系。
Abstract:Rockfill material, as the primary construction material for earth-rock dams, exhibits dynamic deformation characteristics under seismic action that are influenced by particle shape, gradation, and relative density. Current research on the effect of particle shape on the mechanical properties of rockfill mainly focuses on static characteristics, with relatively limited studies on dynamic properties. Artificially simulated rockfill materials of various shapes were prepared using a cement paste casting method, followed by cyclic triaxial tests. The study investigated the effect of particle shape on dynamic residual strain and particle breakage. The results indicate that the artificially simulated rockfill material prepared by this method can approximate the dynamic deformation characteristics of natural rockfill. Under low confining pressure, residual volumetric strain decreases as the shape coefficient increases, whereas under high confining pressure, the opposite trend is observed. Axial residual strain first increases and then decreases with an increase in shape coefficient. Under identical stress conditions, a smaller shape coefficient corresponds to a lower particle breakage rate. Additionally, the study established a relationship between particle breakage rate, shape coefficient, and confining pressure.
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土石坝因其取材便利,成本较低,并且拥有着丰富的施工经验,在中国水利水电事业中得到广泛应用。目前,高土石坝所处地区大多地质情况较为复杂,地震发生的频率高且强度大,导致高土石坝出现坝体变形、坝基沉降过大等问题,堆石料是土石坝的主要构筑材料,研究堆石料的变形破坏尤为重要。
关于颗粒形状对土体的影响,国内外学者展开了大量试验和数值模拟研究,发现颗粒形状对砂土、砂砾等材料的强度和变形特性有显著影响[1-5]。堆石料作为典型的散粒体材料,颗粒尺寸较大、形状各异,构成复杂,其强度和变形特性同样受颗粒形状影响。徐德龙等[6-8]等通过室内试验探究了颗粒形状对强度特性的影响,发现在相同颗粒直径下,球度指标越大,抗剪强度和内摩擦角越小。在颗粒破碎方面,邹德高等[9]研究表明在相同颗粒直径下,球度指标越大,试样颗粒破碎率越低。关于颗粒形状对堆石料力学特性影响研究,目前主要集中于天然堆石料,在研究过程中对颗粒形状的影响主要还是定性研究,未能定量研究颗粒形状与静力特性参数的关系。孔德志等[10]提出了采用水泥净浆浇筑的方法,制备特定形状的堆石料,进行人工堆石料力学特性的研究。在此基础上,许建宝等[11-12]开展了颗粒形状对颗粒破碎特性的研究,结果表明颗粒破碎率与形状参数指标呈现线性关系;杨贵等[13]开展了颗粒形状对变形特性和强度的研究,得出堆石料的颗粒形状对峰值强度和内摩擦角增量有显著影响,其关系近似呈线性。
相较于研究颗粒形状对堆石料静力特性的影响,动力特性方面的试验研究更少。Yang等[14]采用人工模拟堆石料开展了颗粒形状对剪切模量和颗粒破碎的研究,结果表明剪切模量随颗粒形状系数的增大而减小,颗粒破碎率和最大剪切模量随颗粒形状系数的增大而增大。基于此,本文采用水泥净浆浇筑不同形状的人工模拟堆石料颗粒,通过循环三轴试验研究颗粒形状对人工模拟堆石料动变形特性的影响,并探寻建立颗粒破碎率与颗粒形状系数和围压的关系。
1. 试验方法
选用英国GDS生产的HCA动力三轴试验系统,其最大加载围压为1 MPa,最大频率加载为5 Hz,波形可以选择正弦波、半正弦波、三角波、方波,也可以设定人工波。试样直径为100 mm,高为200 mm,每种形状的颗粒质量相等,每个试样所包含的颗粒数都为450,初始孔隙比为0.61。
本文采用水泥净浆浇筑的方法成型不同形状的颗粒,其制备过程如下:充分搅拌水泥浆,其组成包括质量占比为73%的普通硅酸盐水泥、9.1%的硅粉、14.6%的水和3.3%的聚羧酸高效减水剂,相应质量分别为
1000 、125.6、200和44.8 g;水灰比为0.2。将水泥浆置入对应形状的有机玻璃脱模箱,静置一段时间,待水泥呈塑性,将其表面的水泥刮净,使用有机玻璃顶块将水泥顶出,然后在养护室经过24 h养护后形成3种形状的颗粒(正三棱柱、立方体和圆柱体),如图1所示的3种颗粒体积相同。为了研究颗粒形状对残余应变和颗粒破碎的影响,进行了动三轴循环试验,固结比为2.0,围压分别为100、300 和500 kPa,动应力比为0.4,振动次数为50,振动频率为0.1 Hz,波形选用正弦波,振动结束后,对试样进行风干、筛分和称量。
目前已有的颗粒形状量化方法较多,如涂新斌等[15]提出的S11、孔亮等[3]提出的形状系数、邹德高等[9]提出的平均球度、许建宝[11]使用的球度、郅彬等[16]提出的平均球形模量、Garboczi[17]提出的球谐函数、Masad等[18-20]提出的纹理指数等。本文采用形状系数Q量化颗粒形状,此方法同时考虑了颗粒的圆球度(Y)和颗粒的凹凸度(A),其定义为:
$$ Q = \alpha Y + \beta A $$ (1) $$ Y=S_{\text{d}}/S_{\mathrm{r}} $$ (2) $$ A=S_{\text{n}}/S\mathrm{_r} $$ (3) 式中:Q为形状系数;Y为圆球度;A为凹凸度;参数α、β取0.5;Sd为与颗粒等体积圆球体的表面积;Sr为颗粒的实际表面积;Sn为颗粒最大内接圆球体的表面积。
部分颗粒量化参数见表1。
表 1 颗粒形状量化参数Table 1. Quantitative parameters of particle shape颗粒形状 圆球度 凹凸度 形状系数 平均球形模量 平均球度 圆柱体 0.87 1.29 1.08 0.53 0.95 正方体 0.81 1.57 1.19 0.36 0.93 三棱柱 0.74 1.95 1.35 0.28 0.90 圆球体 1.00 1.00 1.00 1.00 1.00 2. 结果分析
2.1 残余应变和循环振次曲线分析
图2给出了人工模拟堆石料与天然堆石料[21]归一化残余应变曲线对比结果。从图2可以看出:即使相对密度、孔隙比、级配等物理特性有所不同,两者残余应变的整体发展规律仍具有较高的相似性。已有的研究[22]也表明不同相对密度堆石料残余应变的发展规律基本一致,均随循环振次的增大而增大。
2.2 颗粒形状对残余应变的影响
图3为不同围压下颗粒形状对体积残余应变$ {\varepsilon _{{\text{vr}}}} $的影响。可见不同围压下的规律基本一致,体积残余应变随着振次的增大而增大,循环振动前10次产生的残余应变增长速度较快,后续加载过程中逐渐稳定。图4为100 kPa下循环振次和残余体积应变占最终残余体积应变比值,循环振动前10次产生的体积残余应变占比较大,占总体积残余应变的70%~75%,前20次占总残余应变的75%~85%,前30次占总残余应变的85%~90%。
表2为不同形状颗粒振动50次下体积残余应变统计。从表2可以看出,在低围压情况下,圆柱体颗粒残余应变占比最大,为0.318%,三棱柱颗粒和圆柱体颗粒残余应变占比较小,分别为0.258%和0.259%;高围压情况下,三棱柱颗粒残余应变占比最大,圆柱体颗粒残余应变占比最小,正方体颗粒介于两者之间。
表 2 不同颗粒形状振动50次下体积残余应变Table 2. Volumetric residual strain after 50 vibrations for different particle shapes围压/kPa 不同颗粒形状的体积残余应变/% 圆柱体 正方体 三棱柱 100 0.318 0.259 0.258 300 0.315 0.392 0.411 500 0.402 0.436 0.447 发生这种现象的原因是:堆石料的残余应变主要包括动力荷载过程中颗粒的滚动和错动,以及动力加载过程中的颗粒破碎。在低围压情况下,残余应变主要由颗粒本身的位移决定,所以形状系数Q越大,其颗粒之间咬合力越强,进而抵抗错动翻滚的能力更加突出,残余应变越小;在高围压情况下,试样会发生一定的颗粒破碎,颗粒破碎程度成为残余应变的主要影响因素,故颗粒形状系数Q越大,颗粒破碎程度越高,残余应变越大,这和王晓鹤[23]结论一致。
图5给出了不同围压下颗粒形状对轴向残余应变$ {\varepsilon _{\text{a}}} $的影响。从图5可以看出,轴向残余应变和体积残余应变规律相似,轴向残余应变随围压的升高而增大,且在相同荷载下,圆柱形颗粒的残余应变始终最小,正方体颗粒的残余应变始终最大。结合形状系数可推论:当形状系数在一定范围内时,试样的轴向残余应变随着颗粒形状系数的增大而增大,超过范围后,试样的轴向残余应变随着颗粒形状系数的增大而减小。
从图5可知,在围压为100 和300 kPa时,圆柱体和三棱柱的残余应变较为接近,正方体颗粒残余应变最大;而在围压500 kPa时,正方体颗粒和三棱柱颗粒残余应变加大,且较为接近,圆柱体颗粒残余应变最小。因为在围压100 和300 kPa时圆柱体和三棱柱颗粒破碎程度较低,而正方体颗粒破碎程度较高;在高围压500 kPa时,三棱柱颗粒破碎程度显著增大,和正方体颗粒相近,圆柱体颗粒破碎程度增加较少。
图6给出了围压100 kPa下循环振次和轴向残余应变占最终轴向残余应变比值。从图6可知,轴向残余应变所占比例随振动次数的增加而减小,循环振动前10次产生的轴向残余应变占总轴向残余应变的90%以上,10~20次轴向残余应变约占总轴向残余应变的4.3%,20~30次轴向残余应变约占总轴向残余应变的2.5%,后续变形所占比例较小。结合体积残余应变可知残余应变主要发生在振动前期。
目前关于循环振次和残余应变的模型主要有两种,一是沈珠江等[24]提出的残余应变和循环振次应符合半对数衰减规律;二是傅华等[25]提出残余应变和循环振次的关系近似符合幂函数,其中以沈珠江模型在工程应用中较为广泛,故本文使用沈珠江模型计算残余剪应变参数$ {C_{{\text{dr}}}} $和残余体积应变参数$ {C_{{\text{vr}}}} $,其计算公式如下:
$$ {\varepsilon _{{\text{vr}}}} = {C_{{\text{vr}}}}\lg (1 + N) $$ (4) $$ {\gamma _{\text{r}}} = {C_{{\text{dr}}}}\lg (1 + N) $$ (5) 式中:$ {\varepsilon _{{\text{vr}}}} $为体积残余应变;N为循环振次;$ {C_{{\text{vr}}}} $为体积残余应变参数;$ {\gamma _{\text{r}}} $为残余剪应变;$ {C_{{\text{dr}}}} $为残余剪应变参数。
图7给出了归一化围压$ {\sigma _3}/{P_{\mathrm{a}}} $和颗粒形状系数Q对$ {C_{{\text{vr}}}} $的影响,其相互关系可以表示为:
$$ {C_{{\text{vr}}}} = {m_1}Q{\left(\frac{{{\sigma _3}}}{{{P_{\text{a}}}}}\right)^{0.5}} + {m_2} $$ (6) 式中:m1、m2为拟合参数,本文m1为0.07,m2为0.08;σ3为围压(kPa);Pa 为大气压(kPa)。
图8给出了形状系数Q及归一化围压σ3/Pa对残余剪应变系数Cdr的影响,可用以下公式进行拟合:
$$ {C}_{\text{dr}}={m}_{3}Q\left(\frac{{\sigma }_{3}}{{P}_{\text{a}}}\right)^{0.5}+{m}_{4} $$ (7) 式中:m3、m4为拟合参数,本文取m3为0.07,m4为0.12。
2.3 颗粒形状对颗粒破碎的影响
试样在承受动力加载过程中,达到一定应力后内部颗粒会发生破碎,进而导致级配、孔隙率、颗粒形状等相关性质发生改变。为研究颗粒形状对颗粒破碎的影响,对颗粒破碎后的形态进行了如下划分:完全破碎、边角破碎及断裂破碎,如图9所示。
本文使用颗粒破碎率Br对颗粒破碎进行量化,其定义为颗粒破碎质量占初始质量的百分比。具体的统计标准为:以原颗粒体积的1/2为标准,小于等于原颗粒体积1/2的颗粒为破碎体,大于原颗粒体积1/2的颗粒还能较好发挥功能,故不在统计范围内。由于围压100 kPa下的颗粒破碎现象并不明显,极少量的破碎可能由统计误差所致,故只列出300和500 kPa围压下的破碎率统计结果。
图10为不同围压下颗粒形状对颗粒破碎率Br的影响。从图10可知:(1)颗粒破碎率随围压升高而增大,如形状系数Q为1.1时,围压300和500 kPa下的颗粒破碎率分别为1.14%和1.58%。(2)相同围压下,颗粒形状系数Q越大,颗粒破碎率越高,此结果与静力加载条件下颗粒破碎率随颗粒形状量化指数(球度、平均球形模量和平均球度)的增大而减小的规律相反[9,11,16]。其主要原因为:本文使用的颗粒形状系数Q与其他颗粒形状量化指数在定义上有所差异,形状系数Q越大,平均球形模量、平均球度和球度越小,因此与静力加载下的结论相反,具体数据见表1。
图11给出了形状系数Q及围压对颗粒破碎率(颗粒破碎质量和试样结束装样时的质量百分比)Br的关系,可用以下公式进行拟合:
$$ {B}_{\rm r}=kQ\left(\frac{{\sigma }_{3}-{\sigma }_{0}}{{P}_{\text{a}}}\right) $$ (8) 式中:Br为颗粒破碎率;k为拟合参数,本文取 0.57;σ0为颗粒破碎开始的围压,与颗粒破碎强度[10]和动应力大小相关,本文σ0为100 kPa。
3. 结 语
通过对水泥浇筑的人工模拟堆石料进行动三轴试验,研究了颗粒形状对堆石料动变形特性方面的影响,所得结论如下:
(1)使用水泥净浆浇筑方法所制备的人工模拟堆石料与天然堆石料动残余变形规律相似,可以反映天然堆石料动变形特性。
(2)残余应变主要发生在循环振动的前10次,其中体积残余应变和轴向残余应变分别占最终应变的70%~75% 和87%~92%。轴向残余应变随形状系数的增大而先增后减;体积残余应变略有不同,在低围压下体积残余应变随形状系数的增大而减小,在高围压下则相反。
本文研究中只考虑了试验围压的影响,未能充分考虑固结应力比、动应力幅值和母岩强度等对试验结果的影响,后续将进一步开展研究。
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表 1 颗粒形状量化参数
Table 1 Quantitative parameters of particle shape
颗粒形状 圆球度 凹凸度 形状系数 平均球形模量 平均球度 圆柱体 0.87 1.29 1.08 0.53 0.95 正方体 0.81 1.57 1.19 0.36 0.93 三棱柱 0.74 1.95 1.35 0.28 0.90 圆球体 1.00 1.00 1.00 1.00 1.00 表 2 不同颗粒形状振动50次下体积残余应变
Table 2 Volumetric residual strain after 50 vibrations for different particle shapes
围压/kPa 不同颗粒形状的体积残余应变/% 圆柱体 正方体 三棱柱 100 0.318 0.259 0.258 300 0.315 0.392 0.411 500 0.402 0.436 0.447 -
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