描述砂性土宏细观力学关系的数学模型

土体等颗粒材料在外力作用下的细观颗粒层面的力学行为决定着其宏观力学性质.然而,目前已经提出的宏细观本构关系多基于对某一种试验数据的唯象总结,缺乏普适性.根据已有的理论研究成果,基于Hertz接触理论,采用颗粒流离散元程序(particle flow code,PFC3D)模拟了粒状砂性土的单轴压缩试验,推导了一种更具普...     

棒在颗粒物质中穿行时摩擦振荡行为的研究

实验发现，棒在颗粒物质中运动时滑动摩擦力具有准周期振荡性质. 根据颗粒物质的剪胀性对此现象进行了研究，提出相应的物理模型，建立了平均体积分数振荡方程和滑动摩擦力振荡变化关系式，理论计算分析结果与实验结果基本吻合.     

Contact force measurements and stress-induced anisotropy in granular materials

Interparticle forces in granular media form an inhomogeneous distribution of filamentary force chains. Understanding such forces and their spatial correlations, specifically in response to forces at the system boundaries, represents a fundamental goal of granular mechanics. The problem is of relevance to civil engineering, geophysics and physics, being important for the understanding of jamming, shear-induced yielding and mechanical response. Here we report measurements of the normal and tangential grain-scale forces inside a two-dimensional system of photoelastic disks that are subject to pure shear and isotropic compression. Various statistical measures show the underlying differences between these two stress states. These differences appear in the distributions of normal forces (which are more rounded for compression than shear), although not in the distributions of tangential forces (which are exponential in both cases). Sheared systems show anisotropy in the distributions of both the contact network and the contact forces. Anisotropy also occurs in the spatial correlations of forces, which provide a quantitative replacement for the idea of force chains. Sheared systems have long-range correlations in the direction of force chains, whereas isotropically compressed systems have short-range correlations regardless of the direction.     

Logarithmic rate dependence of force networks in sheared granular materials

Many models of slow, dense granular flows assume that the internal stresses are independent of the shearing rate. In contrast, logarithmic rate dependence is found in solid-on-solid friction, geological settings and elsewhere. Here we investigate the rate dependence of stress in a slowly sheared two-dimensional system of photoelastic disks, in which we are able to determine forces on the granular scale. We find that the mean (time-averaged) stress displays a logarithmic dependence on the shear rate for plastic (irreversible) deformations. However, there is no perceivable dependence on the driving rate for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate leads to an increase in the strength of the force network and stress fluctuations. Qualitatively, this behaviour resembles the changes associated with an increase in density. Increases in the shearing rate also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is suddenly stopped, stress relaxations occur with a logarithmic functional form over long timescales. This slow collective relaxation of the stress network provides a mechanism for rate-dependent strengthening.     

薄体位势边界条件识别反问题正则化边界元方法

针对二维薄体位势柯西边界条件识别反问题,提出了解析积分和奇异值分解联合正则化算法．解析积分用于薄体位势问题边界元法中几乎奇异积分的正则化．奇异值分解技术用来求解系统方程．数值算例研究了狭长比为1E-8和1E-7的薄体问题,计算结果表明该算法的有效性和精确性．     

考虑互层状岩体接触状态的地下洞室围岩稳定分析

层间剪切、挤压破碎带是影响互层状岩体地下洞室围岩稳定的重要因素.针对互层状岩体层间剪切、挤压破坏问题,引入界面单元模型模拟其接触特性.在此基础之上,对该接触面模型算法进行改进,针对接触面边界上节点可能存在的接触状态:黏结、滑移、张开和嵌入,建立了相应的接触状态判别准则和修正迭代算法,可以有效模拟互层状岩体层间非线性滑移破坏问题.将本文模型应用于巴基斯坦阿扎德帕坦水电站地下厂房围岩稳定性分析中,对比横观各向同性模型计算结果,表明考虑接触后在层间过渡处应力和位移呈现非连续性变化,且量值增大;层间出现了错动位移,在主厂房边墙侧中下部较为明显.     

苏州黏土的力学特性

为了研究结构性对土的力学特性的影响,对苏州黏土的原状样和人工制备样进行等向压缩试验、三轴固结排水剪切试验和不排水剪切试验.试验结果表明：在固结压力相同时,原状样比人工制备样具有更大的孔隙比、压缩指数C_c和膨胀指数C_s;剪切时的围压对人工制备样的应力比-应变曲线没有影响,而对原状样的应力-应变曲线有影响,即剪切围压小的试样得到的应力比较高;排水剪切围压相同时,人工制备样的强度高于原状样的强度,这是由于原状样的孔隙比大于人工制备样的孔隙比;孔隙比相同时,原状样的强度比人工制备样的要高.     

接触行为对颗粒材料中应力波波速与能量的影响

采用离散单元法,研究线弹性接触模型、Hertz接触模型、线性平行粘结模型对不同排列颗粒材料中波传播的影响,分析了三种接触模型下波的波速变化和能量变化,同时也研究了弹性模量对颗粒材料中波传播的影响.最后对颗粒材料样本采用Hertz接触模型,探究了不同围压条件下颗粒材料中波的波速变化和能量衰减.研究结果表明:不同接触模型下波传播的波速和能量衰减率不同;当颗粒样本从规则排列到随机排列,波传播的波速变小,能量衰减率变大;随着颗粒弹性模量的增大,波速呈对数增大;在波传播过程中能量快速耗散,随着围压的增大,波速和能量衰减率都增大.     

基于SPH法的金属切削大变形数值模拟

采用光滑质点流体动力学法对金属切削过程中复杂的材料本构行为进行了数值模拟,进而分析了切削加工中的基本规律.模拟结果表明,切削过程是切削层材料受刀具的挤压而产生的以剪切滑移为主的塑性变形过程;堆积在刀尖处的材料屈服强度提高,接触应力增大,使得工件表面产生显微裂纹;切削过程中,切削力逐渐增大,最后保持在一定范围内平稳变动;形成切屑后,前刀面上的最大接触应力在距离切刃一定距离处上下变动,在该位置处刀具的磨损较为严重.     

非规则曲面的离散元法分析模型建模软件

在采用离散元法分析机械部件与颗粒材料接触作用时,需要建立机械部件（边界）的离散元法分析模型。分析可知,机械部件中与颗粒材料接触作用的零件表面,存在不能用初等解析函数表达的非规则曲面。为此,采用推进波前法（AFT：Advancing Front Technique）进行非规则曲面网格划分,把非规则曲面离散成三角形平面片的组合,同时添加运动属
性和材料特性参数,由此建立非规则曲面边界的离散元法分析模型。在对PRO/E软件进行二次开发的基础上,研制了非规则曲面边界建模软件。通过实例验证,初步证明了基于AFT边界建模方法和软件的可行性,为复杂结构机械部件工作过程的仿真分析奠定了基础。     

垃圾焚烧炉渣的力学特性和破碎特性试验研究

在不同的最大竖向压力(100~3 200 k Pa)下,对上海某生活垃圾焚烧厂炉渣进行了室内压缩试验和直剪试验,并在试验前后对所有试样进行了颗粒筛分。结果表明:炉渣的压缩破碎变形属于不可逆变化,在初始孔隙比一定的条件下,试样的最终压缩量受初始颗粒级配和颗粒大小的共同影响。此外,当炉渣受到的最大竖向压力小于其屈服应力时,压缩后试样的级配曲线较初始级配曲线变化不大;当炉渣受到的最大竖向压力超过其屈服应力时,颗粒破碎明显加剧,压缩后试样的级配曲线受最大竖向压力的影响较大。最后,对直剪试验后炉渣的破碎进行了分析,表明当压力达到一定大小后,由剪切作用产生的颗粒破碎将不再增长。     

不同胶结物粒间胶结三维仿微观力学试验

离散单元法被广泛应用于颗粒材料的力学特性研究,建立合理的胶结微观接触理论对实现胶结型岩土材料宏观、微观力学特性的数值分析显得尤为重要.首先通过室内三维接触试验方法制备由环氧树脂和高铝水泥胶结的铝球试样,并使用辅助加载装置进行拉伸、压缩、剪切、弯曲及扭转5种加载方式下的接触力学特性测试,为建立三维微观接触模型奠定试验基础.结果表明,胶结铝球颗粒的接触力学响应及强度包线与胶结物类型有关.在峰值前,胶结铝球的力-位移与力矩-转角变化关系曲线表现为线弹性;在峰值后,表现为环氧树脂偏塑性、高铝水泥偏脆性;法向作用力对胶结接触力学特性有重要影响,不同胶结铝球的抗剪、抗弯、抗扭能力随着法向作用力的增大呈现先增大后减小趋势,存在临界法向应力比;在不同荷载空间下,不同胶结铝球颗粒的归一化峰值强度包线(剪切强度、弯矩、扭矩-法向荷载)近似呈抛物线型.     

重塑上海软土的压缩特性试验

对上海第4层淤泥质软土重塑试样,进行等向压缩试验、K0试验及单向压缩试验.分析不同试验条件下压缩指数和膨胀指数的关系,给出不同试验条件下压缩指数Cc的大小.对8次等向压缩 回弹试验结果进行了分析,比较了膨胀指数Cs的大小.通过对2次K0试验结果的分析,给出重塑上海软土在加载-卸载-再加载过程中,K0随σv的变化规律及K0与OCR(超固结比)的关系.讨论在3种不同试验条件下,卸载过程中膨胀指数Cs与OCR的关系.通过室内试验对压缩性参数的确定,为进一步建立重塑上海软土的本构模型提供了基础.     

孔隙填充型深海能源土的离散元成样

针对孔隙填充型水合物的赋存形态,提出了一种新的制备孔隙填充型能源土试样的数值成样方法.孔隙填充型水合物的砂性能源土试样是由砂粒和水合物颗粒混合而成的特殊的散粒体材料,具有明显的非连续特征.在土骨架的孔隙中,将水合物块体视为由颗粒通过强胶结作用凝聚而成的团簇整体,随机填充生成不同水合物饱和度的沉积物试样,开展能源土宏观力学特性的离散元固结排水三轴压缩试验模拟,并从应力应变、体变、接触组构等方面进行分析.结果表明,水合物饱和度的增大对低饱和度的孔隙填充型能源土试样的初始弹性模量和强度影响较小.有效围压相同时,孔隙填充型能源土试样的体积剪缩量随着水合物饱和度的增大而减小;而水合物饱和度相同时,能源土试样强度及体积剪缩量随着有效围压的增大而增大.能源土试样的剪胀角随有效围压的增大而近似线性减少,随水合物饱和度的增大而趋于线性增大.颗粒间接触方向随着轴向应变的增大而朝竖直方向偏转.     

Sound scattering in dense granular media

The sound propagation in a dense granular medium is basically characterized by the ratio of wavelength to the grain size. Two types of wave transport are distinguished： one corresponds to coherent waves in the long wavelength limit, the other to short-wavelength scattered waves by the inhomogeneous contact force networks. These multiply scattered elastic waves are shown to exhibit a diffusive characteristics of transport over long distances of propagation. Determination of the transport mean free path l^＊ and the inelastic absorption （Q^-1） allows the inference of the structural properties of the material such as the heterogeneity and internal dissipation. The relevance of our experiments for seismological applications is discussed. Moreover, we apply the correlation technique of the configuration-specific sound scattering to monitoring the dynamic behaviour of the granular medium （irreversible rearrangements） under strong vibration, shearing and thermal cycling, respectively.     

弹性支承功能梯度圆板轴对称弯曲问题精确解

对周边为弹性支承边界条件下的功能梯度材料圆板轴对称弯曲问题进行了分析.将位移函数写成傅立叶贝塞尔级数的形式,根据各向同性功能梯度材料基本方程,并针对指数函数形式的梯度分布情况,对功能梯度圆板轴对称弯曲问题的位移和应力进行了精确分析.通过具体算例,分析了在圆板上、下表面荷载作用下,材料性质的不同梯度变化对圆板结构响应的影响.分析结果表明,材料性质的梯度变化对圆板的力学性能有显著影响.     

磁电弹圆柱中轴对称压缩波的传播

为研究无限长横观各向同性磁电弹圆柱中轴向对称压缩波的传播,考虑16种边界条件,得出广义频散方程,并讨论不同边界条件下波的频散特性.数值结果表明边界条件对磁电弹圆柱中轴向对称压缩波的传播特性有着显著的影响.     

Jamming by shear

A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu-Nagel jamming concept has attracted intensive theoretical and modelling interest but has prompted less experimental effort. In the Liu-Nagel framework, jammed states of athermal systems exist only above a certain critical density. Although numerical simulations for particles that do not experience friction broadly support this idea, the nature of the jamming transition for frictional grains is less clear. Here we show that jamming of frictional, disk-shaped grains can be induced by the application of shear stress at densities lower than the critical value, at which isotropic (shear-free) jamming occurs. These jammed states have a much richer phenomenology than the isotropic jammed states: for small applied shear stresses, the states are fragile, with a strong force network that percolates only in one direction. A minimum shear stress is needed to create robust, shear-jammed states with a strong force network percolating in all directions. The transitions from unjammed to fragile states and from fragile to shear-jammed states are controlled by the fraction of force-bearing grains. The fractions at which these transitions occur are statistically independent of the density. Jammed states with densities lower than the critical value have an anisotropic fabric (contact network). The minimum anisotropy of shear-jammed states vanishes as the density approaches the critical value from below, in a manner reminiscent of an order-disorder transition.     

拉压弹性常数不同对梁的弯曲强度的影响

岩石类材料(包括混凝土材料)在受拉与受压状态的弹性模量和泊松比是有明显差异的,本文推导了拉压弹性模量不同的矩形截面梁纯弯曲情况下弹性力学的解答.结果表明,不考虑拉压弹性模量的差异会引起较大误差.     

考虑固结路径影响的天然沉积土不排水剪切试验研究

针对传统等向固结剪切试验不能反映实际工程中的非等向变形和强度特性的局限,采用GDS应力路径三轴试验仪,对天然沉积结构性软黏土进行了不同固结条件下的不排水剪切试验,探讨不同应力路径对天然沉积土不排水剪切特性的影响.结果表明:相同的平均有效固结应力下土体偏压固结后剪切阶段应力-应变关系曲线的峰值强度大于等向固结的峰值强度;固结过程偏应力的存在提高了土体的总应力强度指标,当控制固结压力终值的剪应力相同时,偏压固结的强度包线相对于等向固结将平行上移;等向固结下当固结压力大于结构屈服压力时,有效应力路径与屈服面具有相似性,剪切屈服破坏后有效应力路径沿着临界状态线下滑;偏应力固结后剪切过程中有效应力路径的走向相对于等向固结发生了向右偏转.