基于分形级配方程的堆石料颗粒破碎SBG模型

准确预测堆石料在受剪过程中颗粒的破碎率以及相应的级配变化,是揭示堆石料在复杂应力状态下强度、渗透、变形等特性的基础。基于分形级配方程,建立了一个实现"应力应变—破碎指标—级配分布(SBG)"转换的模型。引入Einav破碎指标BE作为衡量颗粒破碎率的指标,对分形级配方程进行变形和积分,推导了颗粒破碎率B_E和分形维数D的数学转换,即"破碎指标—级配分布"的转换。对已有的三轴剪切试验数据进行分析,提出一个可以定量表示颗粒破碎率随剪应变和平均正应力变化的数学模型,模型共有3个参数a,b,c,参数b与土体的临界状态有关,根据临界剪应变可以直接确定。对两组不同的试验数据进行拟合,发现模型预测值与试验值具有较高的吻合度,实现"应力应变—破碎指标"的转换。将以上两种转变联立,成功预测了不同剪应变及平均正应力下堆石料的级配变化。     

粗粒土颗粒破碎的级配转移矩阵研究

级配转移矩阵通过建立颗粒破碎前后各粒径百分含量向量的关系,能有效地描述粗粒土破碎过程中的级配演化。现有的级配转移矩阵忽略了不同粒径组颗粒的破碎差异,且不能考虑颗粒发生诸如研磨等现象后其粒径分组未改变的情况。为此,提出一种新的级配转移矩阵求解方法:首先基于大量的单颗粒点荷载试验,提出能够描述单颗粒破碎后子颗粒粒径分布的Hill分布函数;在此基础上,将单颗粒的破碎演化规律引入到离散元模拟中,基于子颗粒替代法,对不同粒径组颗粒采用相应的阿波罗填充模式,开展一系列多粒径组试样的一维压缩试验,最后通过追踪各粒径子颗粒来源,求解土体级配转移矩阵。该研究克服了传统数值方法中子颗粒数量和粒径分布选择较为主观的缺点,可较好地反映不同粒径组颗粒的破碎演化规律。     

考虑细观单粒强度的堆石料破碎特性研究

颗粒破碎是影响堆石料力学性质的主要因素之一,但由于测试手段的限制,荷载作用过程中堆石的颗粒破碎难以实时度量,因而影响堆石料力学特性的深入研究。通过单粒强度试验,发现同一粒组的堆石料单粒强度较好地服从Weibull分布,而破碎后颗粒的粒径级配曲线基本服从分形分布。在此基础上,推求了堆石料三轴试验过程中级配的演化过程,给出了颗粒破碎的实时预测方法,与三轴试验结果比较,验证了本文方法的有效性。     

堆石料的颗粒破碎规律研究

粗颗粒土剪切过程中的颗粒破碎现象已被广泛认识,并且在试验和理论方面进行了大量研究。利用大型三轴仪开展了一系列不同级配、不同密度、不同围压条件下堆石料的排水剪切试验,并对试验前后的试样分别进行了颗粒分析,以探讨堆石料的颗粒破碎规律及其影响因素。试验结果表明:密度对颗粒破碎影响较小,而级配和围压的影响较大,围压越高则颗粒破碎越严重。对比试验前后的粒径分布曲线发现,颗粒破碎主要集中在粒径20 mm以上的颗粒范围内,粒径变化幅度随粒径的减小呈减小趋势。基于分形理论,建立了颗粒破碎分形维数与围压和颗粒级配之间的关系表达式,为进一步研究堆石料的强度、变形及剪胀特性提供依据。     

钙质砂临界状态随颗粒破碎演化规律分析

根据物理试验揭示的钙质砂颗粒破碎特征和发展规律,建立了可进行钙质砂三轴试验的离散元数值模型。首先通过预压均匀级配的钙质砂破碎生成不同初始级配的试样,进行不破碎三轴剪切过程的数值试验,以确定临界状态与固定级配的对应关系。结果表明,一个固定级配对应一条固定的临界状态线,在压缩平面内各固定级配临界状态线基本平行但是位置随颗粒级配的拓宽(颗粒破碎程度的增大)而逐渐降低。然后,采用相同均匀级配的试样,进行加载过程颗粒可破碎的三轴试验,以揭示实际三轴试验中临界状态线的变化机理。结果表明,在e–p–Br三维空间中,可破碎三轴试验的各临界状态点都落在由固定级配临界状态线所确定的破碎临界状态面上,说明临界状态由最终的颗粒级配决定,而与产生该颗粒级配的过程无关。实际物理试验中,不同围压和应力路径达到临界状态时颗粒破碎程度的不同是导致实测临界状态线出现复杂变化的机理;在三轴压缩剪切情况下,颗粒破碎程度基本随着有效球应力的增大而增大,所以实测的颗粒破碎临界状态线相对于固定级配的临界状态线呈现出旋转的变化。     

考虑颗粒破碎效应的粒状材料本构研究：进展及发展

颗粒破碎会引起材料的压缩性变大及强度软化，因此颗粒破碎对粒状材料力学特性影响的研究非常重要。首先从试验研究方面着手，总结了颗粒破碎的描述方法、不同加载条件下（一维及等向压缩、三轴剪切、扭剪及单剪）应力应变的颗粒破碎效应；接着总结了考虑颗粒破碎效应的粒状材料力学本构模拟方法，即一维及等向压缩模型、三维剪切模型及基于离散元法的微观土力学模型。最后，通过大量试验结果分析并结合笔者近年来的研究成果，指出可破碎颗粒材料在应力应变过程中的颗粒级配变化可由修正相对破碎指数来表示，可通过塑性功来确定，且塑性功确定法的优越性还体现在循环加载下的累积破碎评价；然后再通过修正相对破碎指数，来确定临界状态线的位置，进而可通过当前状态与临界状态线的相对位置来评价颗粒破碎对颗粒材料力学特性的影响。所提出的以修正相对破碎指数为关键变量的本构方程可直接应用于考虑颗粒破碎效应的粒状材料静动力本构模型的开发。     

一个考虑颗粒破碎的堆石料弹塑性本构模型

基于广义塑性理论建立了一个考虑堆石料颗粒破碎的弹塑性本构模型。模型采用随平均应力增加而减小的峰值摩擦角和特征点摩擦角来反映堆石料因颗粒破碎而表现出的峰值应力比与剪胀应力比的非线性,在此基础上确定塑性流动和加载方向向量;运用指数型压缩函数建立依赖于体积应变和平均应力的压缩参数 λ ,并构造随平均应力与剪应力水平而变化的塑性模量表达式。模型共有 8 个参数,均可通过等向或单向压缩和三轴压缩试验确定。为验证本文模型的合理性,依据试验资料确定了 3 种不同堆石料的本构模型参数,并对典型三轴压缩试验进行了模拟。 3 种材料的模型预测结果与试验数据均吻合良好,表明本文模型可合理反映了颗粒破碎对堆石料强度与变形特性的影响。     

染色石膏颗粒一维压缩破碎与粒径迁移

为研究粒状岩土材料粒组层面的破碎与粒径迁移规律,采用人工制备的染色石膏颗粒,进行不同应力和级配的单粒组及多粒组等比例混合试样的一维压缩试验。采用人工识别和图像识别软件相结合的方法进行破碎后的颗粒分离,得到各粒组破碎后的级配,据此分析颗粒破碎过程中的粒径迁移模式、粒组的破碎概率以及破碎重叠效应。分析结果表明,颗粒破碎与粒径迁移模式为分步多次破碎、依粒组次序迁移,因而破碎后粒组的级配是连续不间断的。与单粒组级配试样中颗粒破碎概率随粒径减小而减小不同,多粒组级配试样中颗粒的破碎概率随粒径减小而增大(窄级配试样)或先增后减(宽级配试样),但较单粒组级配试样整体上有所下降。破碎重叠效应表现为各粒组颗粒的绝对破碎量远大于相对破碎量,且随着应力的增加和粒径的减小更加明显。最后基于粒度熵的概念,建立了可以反映破碎重叠效应的绝对破碎率。该试验结果亦可为颗粒破碎的数值模拟提供参考。     

粒状岩土材料颗粒破碎演化规律的模型预测研究EI北大核心CSCD

荷载作用下粒状岩土材料的颗粒破碎改变了粒径分布,从而影响其力学特性。为了揭示应力水平对颗粒破碎的影响规律,利用一系列高压应力下的侧限压缩试验研究钙质砂和石英砂的压缩变形、应力–应变关系、粒径分布的演化和颗粒破碎特性。在此基础上,建立描述粒状岩土材料的应力水平与孔隙比、体应变、相对破碎率等相关关系的数学模型。研究结果显示:无论是钙质砂还是石英砂,随着应力水平的增加,一旦颗粒破碎增长致使砂粒趋向分形分布,体应变与相对破碎率的比值将保持恒定。恒定比值意味着基于体应变就可估算相对破碎率,其数值为石英砂大于钙质砂。如果颗粒分布发展至分形分布,其孔隙比、体应变、相对破碎率的增量随应力水平的变化规律,可以用形式统一的数学模型表达。基于试验获得的模型参数,该模型可用于预测颗粒在分形分布阶段的相对破碎率。     

粒状岩土材料颗粒破碎演化规律的模型预测研究

 荷载作用下粒状岩土材料的颗粒破碎改变了粒径分布,从而影响其力学特性。为了揭示应力水平对颗粒破碎的影响规律,利用一系列高压应力下的侧限压缩试验研究钙质砂和石英砂的压缩变形、应力–应变关系、粒径分布的演化和颗粒破碎特性。在此基础上,建立描述粒状岩土材料的应力水平与孔隙比、体应变、相对破碎率等相关关系的数学模型。研究结果显示：无论是钙质砂还是石英砂,随着应力水平的增加,一旦颗粒破碎增长致使砂粒趋向分形分布,体应变与相对破碎率的比值将保持恒定。恒定比值意味着基于体应变就可估算相对破碎率,其数值为石英砂大于钙质砂。如果颗粒分布发展至分形分布,其孔隙比、体应变、相对破碎率的增量随应力水平的变化规律,可以用形式统一的数学模型表达。基于试验获得的模型参数,该模型可用于预测颗粒在分形分布阶段的相对破碎率。     

石英砂砾破碎过程中粒径分布的分形行为研究

荷载作用下粒状土的颗粒破碎改变土的粒径分布,从而影响其力学特性。试验证据显示随着颗粒破碎的增加,任何初始分布的土粒都将趋向一种自相似的分形分布。为了揭示土的粒径分布的分形转变机制,利用侧限压缩试验研究高压应力下石英砂砾的粒径分布演化规律和颗粒破碎特性,基于分形模型和粒径分布实测数据研究破碎过程中粒径分布的分形行为。研究发现:颗粒破碎增长导致粒状土趋向分形分布的过程与颗粒破碎量密切相关,并可以通过增大的分形维数来描述。尽管石英砂砾的初始分布和粒径有所不同,分形维数大于2.2的粒径分布实测数据均展示了较为严格的自相似性,因而该数值可作为分形分布的分形维数下限值。研究还发现:相同破碎状态下Hardin相对破碎率小于Einav相对破碎率,但二者对应力和体应变的响应规律是一致的。颗粒破碎发展至粒径分布成为分形分布时,体应变与相对破碎率的比值将保持恒定,并且受初始分布的均匀性和颗粒大小的影响很小。这一特点可用于分形分布的识别,并意味着试验中如果粒径分布是分形的,则无须为了粒径分析而终止试验,只需测量到体应变就可估计相对破碎率。     

Particle breakage in triaxial shear of a coral sand

This paper presents a laboratory experimental study to comprehensively investigate the characteristics of particle breakage using numerous triaxial tests on a coral sand. Coral is a highly crushable granular material which fills the gaps between more crushable and less crushable granular materials. The monotonic tests and cyclic tests were terminated at the designated axial strains and the designated cyclic numbers, respectively. The grain size distributions were measured by sieve analyses of the specimens after the triaxial tests were performed. The relative breakage and relative fractal dimension were used to quantify the particle breakage. The cause of particle breakage that increased with increasing isotropic consolidation stress was shown to be isotropic stress. An almost linear increase in particle breakage in relative breakage was found as axial strain increased, whereas the increase in particle breakage in relative fractal dimension showed upward convexity. More particle breakage occurred in denser samples. During consolidation to the identical mean effective stress, the anisotropic stress state played a bigger role in particle breakage than the isotropic stress state, but during shearing particle breakage occurred more sharply in the triaxial tests with the isotropic consolidation to the higher confining pressure. In the cyclic shearing, the particle breakage in relative breakage and relative fractal dimension increased in upward convexity as the cyclic number increased, but in upward concavity with increasing axial strain. A hyperbolic model was proposed to correlate the relative fractal dimension with the relative breakage for use with both monotonic and cyclic tests. In the monotonic tests, a hyperbolic model was proposed to correlate the particle breakage in relative breakage and relative fractal dimension with the plastic work per unit volume. It is proposed that the loading-mode-induced (i.e., monotonic loading and cyclic loading) different mechanism of particle breakage meant that this model could not be applicable in the cyclic tests. The results suggested that the hyperbolic correlation of the particle breakage in relative fractal dimension and the plastic work per unit volume is the most reliable method of interpreting the energy consumption characteristics of particle breakage. This approach takes the fractal nature of soil into consideration. A microscopic view of particle breakage is also effective for observing the evolution of particle breakage.     

Particle breakage evolution of coral sand using triaxial compression tests

Particle breakage continuously changes the grading of granular materials and has a significant effect on their mechanical behaviors.Revealing the evolution pattern of particle breakage is valuable for development and validation of constitutive models for crushable materials.A series of parallel triaxial compression tests along the same loading paths but stopped at different axial strains were conducted on two coral sands with different particle sizes under drained and undrained conditions.The tested specimens were carefully sieved to investigate the intermediate accumulation of particle breakage during the loading process.The test results showed that under both drained and undrained conditions,particle breakage increases continuously with increasing axial strain but exhibits different accumulating patterns,and higher confining pressures lead to greater particle breakage.Based on the test results,the correlations between particle breakage and the stress state as well as the input energy were examined.The results demonstrated that either the stress state or input energy alone is inadequate for describing the intermediate process of particle breakage evolution.Then,based on experimental observation,a path-dependent model was proposed for particle breakage evolution,which was formulated in an incremental form and reasonably considers the effects of the past breakage history and current stress state on the breakage rate.The path-dependent model successfully reproduced the development of particle breakage during undrained triaxial compression using the parameters calibrated from the drained tests,preliminarily demonstrating its effectiveness for different stress paths.     

循环荷载作用下堆石料的颗粒破碎特性

通过大型动力三轴试验,研究了循环荷载作用下堆石料的颗粒破碎特性及其影响因素,首次根据堆石颗粒在混合料中所发挥的作用以及堆石料发生颗粒破碎后不同粒径范围颗粒含量的变化量,将堆石料的颗粒破碎形式划分为棱角破碎和骨架破碎。进而,基于堆石料发生颗粒破碎前后级配的分形维数定义了堆石料的颗粒破碎率,建立了循环荷载作用下堆石料颗粒破碎率与其动剪应变及体积应变关系表达式。     

循环三轴应力路径下钙质砂颗粒破碎演化规律

钙质砂广泛分布于中国南海区域,是吹填造陆的重要材料。钙质砂颗粒容易破碎,使得其力学特性相比于普通的陆源硅质砂有显著差异。对取自中国南海西沙群岛某岛礁的钙质砂开展了三轴排水循环剪切试验,研究了围压、循环应力比、循环振次对钙质砂颗粒破碎发展过程的影响。在试验所采用的围压范围内,钙质砂在固结过程中产生的颗粒破碎较少,但是在随后的循环剪切过程中产生了显著的颗粒破碎。在循环剪切作用下,钙质砂的颗粒破碎形式主要是尖角的磨损,剪切后试样的颗粒中出现了一些碎屑和微细颗粒,大颗粒的棱角有一定程度的磨圆,但粒径无明显减小。在常围压下的等幅循环剪切中,颗粒破碎程度随着循环剪切次数的增大而增加,增长速率逐渐降低,可以采用对数曲线来描述相对破碎指数的发展过程。再考虑围压和循环应力比的影响规律,初步建立了一个描述颗粒破碎演化过程的数学模型。     

Effects of initial particle gradation and rock content on crushing behaviors of weathered phyllite fills——A case of eastern Ankang section of Shiyan—Tianshui highway,China

The objective of this paper is to investigate the effects of initial particle gradation and rock content on the crushing behavior(i.e.grain size before and after crushing) of weathered phyllite fills.Compaction tests were conducted on weathered phyllite fills with rock contents of 35%,45%,55%,65% and 75%(by weight).First,the particle size distributions(PSDs) were observed before and after compaction,and then the particle breakage of weathered phyllite fills was analyzed by fractal dimension.Relative fractal dimension was proposed to evaluate the effects of initial rock content and initial gradation on the particle breakage.It was found that the fractal dimension method can well characterize the crushing behaviors of the weathered phyllite fills.The finer the fills were,the more they were compacted.That is,after the first compaction,the relative fractal dimension of the weathered phyllite fills increased as the rock content increased,reaching the values of 0.013,0.016,0.024,0.037 and 0.08,respectively.After the second compaction,these relative fractal dimension values,dominated by the initial particle gradation,became 0.059,0.072,0.052,0.095 and 0.118,respectively.In conclusion,the weathered phyllite fills with 55% rock content exhibited the least breakage and were most suitable for filling the subgrade.Findings in this paper will provide significant guidance for the construction of weathered phyllite filling subgrade in future projects.     

基于粒度熵概念的贝壳砂颗粒破碎特性描述

对取自福建莆田湄洲湾海域的贝壳砂进行了不同围压、不同相对密度下的三轴排水剪切试验,同时考虑了尺寸效应的影响。依据试样试验前后粒径分布资料,在统计熵概念基础上提出颗粒破碎粒度熵模型对其破碎率进行了度量,并与Hardin颗粒破碎模型进行了比较,结果表明：贝壳砂颗粒破碎率与围压、相对密度及试样尺寸均有关系,在相同试验条件下,贝壳砂颗粒破碎程度随着试样尺寸的增加而增大,随着围压的增加而增大;当相对密度较低时,颗粒破碎率呈增大趋势;相对密度增加到较高值时,颗粒破碎程度减弱;贝壳砂三轴压缩前后的级配曲线均可以通过粒度熵模型参数表征,其中相对基础熵参数（NB）较好地反映了颗粒破碎程度大小,破碎率愈高,NB值愈小,NB与Hardin破碎率存在显着的线性关系。贝壳砂颗粒破碎粒度熵参数能较好地描述其颗粒破碎行为,为岩土介质材料的颗粒破碎分析提供了一个新的量化指标。