应变软化及剪胀性土体中考虑大应变的孔扩张问题解析

采用应力跌落模型模拟土体的应变软化,以Mohr-couloub屈服准则和不相关联的流动法则考虑土体屈服塑性流动和剪胀特性,引进对数应变考虑土体的大变形,给出了应变软化及剪胀性土体中考虑大应变的孔扩张问题的弹塑性解析解,为了对比,还给出了小应变情况下位移的解析表达式.分析了大、小应变理论、不同剪胀特性、不同软化程度和考虑塑性区弹性变形与否对结果的影响.结果表明:在孔扩张压力较大时,用小应变理论会引起很大误差,必须考虑大应变;在相同扩张力作用下,土体的软化程度越高,扩张率越大,土体的剪胀角越大则扩张率越小.土体的软化和剪胀特性还影响极限扩张压力,软化越严重,极限扩张压力越小;剪胀角越大,极限扩张压力越大.     

弹塑脆性岩土材料中球形孔大应变扩张分析

在应力跌落模型基础上引进软化阈值,建立弹塑脆性模型,模拟岩土材料的脆性软化特性,采用双剪统一强度理论和不相关联流动法则,考虑软化区的大应变,对球形孔扩张问题进行求解,得出了扩张-压力的解析表达式。通过算例分析,得出软化阈值对扩张变形和塑性区范围影响显著,软化阈值越小,扩张变形和塑性区范围越大,且软化区占整个塑性区的比重越大;考虑中间主应力对屈服的影响与否,对解答也有明显的影响。     

嵌岩端承桩竖向承载的扩孔理论分析

探讨了嵌岩桩嵌岩段的应力路径及工作机理,应用圆孔扩张理论,分析了嵌岩桩的承载机理.随着桩周挤压应力p的增大,围绕柱形孔的柱形区域将由弹性状态进入塑性状态,塑性区随p的增大而不断扩大,塑性区以外土体将保持弹性状态.利用弹塑性理论和体积平衡原理,推导了嵌岩桩嵌岩段的极限强度以及嵌岩段的极限竖向承载力的计算公式,并将扩孔理论分析结果与实测试验资料进行分析对比,研究表明,该方法可以成为解决嵌岩桩实际工程问题的个性化工具.     

冲击载荷下磁铁矿石破碎的能量耗散特性

针对金属矿山企业破碎磁铁矿石时,存在着耗能巨大且能量利用率较低的工程问题. 利用分离式Hopkinson压杆装置和高速摄影技术,首先,研究了磁铁矿石在冲击载荷下的能量运移转化规律及其机理;其次,采用标准方孔砂石筛与GZS-1高频振筛仪,分析了不同耗散能下磁铁矿石破碎块度的分布规律、平均块度的变化情况、以及矿石冲击破碎模式的转变过程;然后,分析了随应变率提高,矿石能量耗散率与破碎程度的相关性问题;最后,结合影响矿石块度分布的基本因素,推导出了磁铁矿石平均块度的预测模型表达式. 结果表明:随入射能提高,矿石波阻抗的降低,改变了矿石与压杆间的透射系数与反射系数,影响着各能量在入射能中的占比分布,即能量耗散率和能量反射率增大,而能量透射率却减小;耗散能越高,磁铁矿石的破碎程度越重,当耗散能由14.79 J提高到121.18 J时,矿石破碎块度的主要分布区域由粗粒端（26.5 mm,37.5 mm）向细粒端（4 mm,16 mm）移动;耗散能与平均块度（d_s）呈减对数关系,d_s降低了56.04%;d_s存在着一个临界值,当d_s大于该值时,矿石能量耗散率和破碎程度呈正相关;反之,两者呈负相关;在该值处,磁铁矿石可实现最优破碎. 研究成果对于磁铁矿石破碎工序中的能耗控制具有一定参考价值.     

深部圆巷开挖围岩能量耗散特征数值模拟分析

深部高应力巷道岩爆灾变机理及其控制对策研究,是目前国内外采矿工程所急待解决的重点难题.应用UDEC计算程序,分析了深部圆巷随开挖半径大小、应力水平高低和应力不均匀程度,围岩内主应力分布和能量耗散特征,发现随应力水平由低至高和应力不均匀程度的加剧,巷道围岩能量耗散值和能量耗散率均成凹形特征曲线急增;随开挖半径由小至大,能量耗散值成凹形曲线急增,但能量耗散率变化却很小;随着应力水平不均匀程度的加剧,在巷道围岩内部形成的主应力差值封闭包核区,呈现由围岩浅部向围岩深部跃移现象;当水平应力大于垂直应力时,在巷道顶板产生主应力差值封闭包核区的范围和量值大小,相对于巷道两帮更为严重.     

Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion

On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.     

不同冲击荷载下花岗岩力学和能量耗散特性

为探究不同冲击荷载条件下花岗岩的动力学特性,采用分离式霍普金森压杆分别对花岗岩试样进行单次和重复冲击荷载试验,并对试样的应力-应变响应、应变率曲线特征、能量耗散特性以及破坏形态进行综合分析.结果表明:单次冲击下,试样动态抗压强度与比能量呈现对数函数关系,试样破坏程度随着比能量的增加而逐渐增大；随着入射波峰值应力的增加,应力-应变曲线峰后段的回弹现象逐渐减弱,应变率曲线呈现出愈加明显的“双峰”特征,其第2波峰逐渐高于第1波峰.重复冲击作用下,当试样未破坏时,应力-应变曲线基本经历弹性加载、损伤演化和峰后回弹3个阶段,当试样经历最后一次冲击时,应力-应变曲线峰后段形状与试样的破坏程度有关.此外,试样破坏时的累积比能量越大,其破坏越严重,应变率曲线由“单峰”逐渐向“双峰”过渡.     

基于广义八面体理论的混凝土多轴破坏准则综述

广义八面体单元体系（含衍生单元体）是在真三轴应力状态下,根据不同材料的破坏（屈服）面特征,依次采用3组破坏面对正六面单元体进行截取所得到的,而依据这些单元体所建立的各种理论模型即构成为广义八面体理论内容.因广义八面体理论的显著特点是对称性,所以基于这一理论的混凝土多轴破坏准则将具有简洁的特点.为此可通过特定试验方法探求混凝土新的损伤变量、确定表达混凝土本征的内在变量及其联系,并采用损伤-断裂等方法建立起混凝土的多轴破坏准则,其包括强度准则、变形准则和强度-变形准则,及其在应力空间和偏平面上的屈服演化规律等,以便更好地描述混凝土在多轴应力状态下的破坏行为.     

Response and energy dissipation of rock under stochastic stress waves

The response and energy dissipation of rock under stochastic stress waves were analyzed based on dynamic fracture criterion of brittle materials integrating with Fourier transform methods of spectral analysis. When the stochastic stress waves transmit through rocks, the frequency and energy ratio of harmonic components were calculated by analytical and discrete analysis methods. The stress waves in shale, malmstone and liparite were taken as examples to illustrate the proposed analysis methods. The results show the harder the rock, the less absorption of energy, the more the useless elastic waves transmitting through rock, and the narrower the cutoff frequency to fracture rock. When the whole stress energy doubles either by doubling the duration time or by increasing the amplitude of stress wave, ratio of the energy of elastic waves transmitting through rock to the whole stress energy (i.e. energy dissipation ratio) is decreased to 10%-15%. When doubling the duration time, the cutoff frequency to fracture rock remains constant. However, with the increase of the amplitude of stress wave, the cutoff frequency increases accordingly.     

基于四维离散数值方法的岩石圆环试样动态破坏及耗能规律

利用最新提出的四维离散弹簧元法（4D-LSM）对岩石圆环的动态抗变形及耗能特性进行研究。首先对4D-LSM用于描述岩石圆环试样破坏的适用性进行了验证,发现4D-LSM可以较好地再现岩石试样的孔径比与破坏形态和强度间的影响规律。在此基础上,对孔隙率、非均质性、厚径比等因素与抗变形及耗能间的规律进行研究,得到了对应的数学公式。利用4D-LSM模拟大变形方面的优势,发现当岩石材料的变形抵抗能力较大时,岩石圆环将表现出与传统仅考虑小变形情况下实验和数值计算不同的破坏形态,岩石圆环的材料抗拉强度与抗变形能力也分别呈现非线性关系。通过建立圆环阵列模型,研究了由多个岩环构成的组合结构的抗变形和能量抵抗能力以及对应的破坏形态。结果表明,组合结构中的圆环单元与单圆环受力的破裂形态有所不同,但单圆环的抗变形及耗能规律仍适用于岩环阵列结构的分析。     

球形孔洞膨胀动态问题的弹性-损伤力学分析

研究了材料还没有出现塑性变形、仅含弹性区和损伤区的球形孔洞动态扩展问题．首先通过对弹性区的研究以及初始损伤分析获得弹性区的场量分布,并给出弹性／损伤区交界处的边界连续条件;然后在自相似假设条件下,推导出动态扩展时损伤区需满足的控制方程;最后通过打靶法进行数值求解．数值分析表明,许多材料参数如ν、n、m都对弹性区和损伤区的场量分布有影响．     

常吸力下非饱和土柱孔扩张弹塑性解及饱和度响应

为研究非饱和土中常吸力条件下圆孔扩张的应力-应变特性及饱和度响应,基于非饱和土临界状态模型(UCSM)和考虑水力滞回的土水特征曲线(SWCC),引入常吸力下饱和度随孔隙比非线性变化模型,推导非饱和土中柱孔扩张问题的排水半解析解。根据柱孔周围土单元平衡微分方程,考虑边界条件,引入辅助坐标将问题转化为以3个主应力分量、孔隙比和饱和度为基本未知量的一阶微分方程组进行求解。本解答充分考虑基质吸力和超固结比对柱孔扩张响应的影响,探究扩张过程中柱孔周围土体的应力分布和体积变化,以及扩张过程中饱和度的演化规律。结果表明：非饱和土常吸力柱孔扩张过程中,呈现吸力硬化特性,且吸力硬化特性随着吸力增大而趋于稳定;孔壁及周围土体饱和度在扩张过程中变化显著,且受吸力大小的影响较大;当吸力较低时,饱和度主要受含水量变化的影响;当吸力较高时,饱和度主要受孔隙比变化的影响。本文的解答可以很好地捕捉非饱和土体不同应力历史和水力状态下的饱和度响应,可为非饱和土中静力触探试验等原位试验的解释提供指导。     

非达西渗流作用下饱和黏土压密注浆扩孔理论分析

为研究软土注浆过程中在渗流作用下小孔扩张引起的土体力学响应,基于广义Tresca屈服准则和非相关联流动准则,考虑非线性渗流和应变软化等因素的综合影响,结合弹塑性边界条件推导饱和软黏土地层注浆扩孔问题的弹塑性解答.通过算例对比分析了是否考虑地下水渗流作用时孔周土体渗流场、应力场、位移场的计算结果的差异,进一步讨论了非线性...     

基于球孔扩张理论的软黏土中载体桩桩端挤密加固效应

载体桩是近年来出现的一种新桩型,其主要利用柱锤对深层土体进行填料夯实,形成桩端扩大载体,从而大大提高桩体竖向承载力。虽然载体桩在实际工程中广泛应用,但目前仍缺乏较为严格的理论分析,特别在关于评价载体的加固范围和载体对土体的挤密效应方面,仍然研究较少,这大大制约了载体桩的推广和发展。针对该问题,将柱锤对填料夯实的过程简化为球孔扩张力学模型,软黏土采用修正剑桥模型的本构关系来模拟,建立球孔扩张偏微分控制方程组,通过相似变换的求解技术将偏微分方程转化为常微分方程组,利用微分方程数值求解技术获得常微分方程组的数值解。开展参数分析,探讨球孔扩张过程中孔周土体强度和刚度的变化、孔周土体挤密区的范围等,从理论角度揭示载体桩载体成形过程中的加固机理,为建立考虑桩端挤密效应的载体桩竖向承载力计算方法提供理论基础。     

应力应变关系对双向应力J积分守恒性的影响

分析了双向应力下应力应变关系对J积分守恒性的影响 ,结果表明 :增量理论弹塑性有限元的应力应变关系曲线是影响J积分守恒性的重要原因 .     

Energy dissipation rate: An indicator of coal deformation and failure under static and dynamic compressive loads

Dynamic disasters in Chinese coal mines pose a significant threat to coal productivity. Thus, a thorough understanding of the deformation and failure processes of coal is necessary. In this study, the energy dissipation rate is proposed as a novel indicator of coal deformation and failure under static and dynamic compressive loads. The relationship between stress-strain, uniaxial compressive strength, displacement rate, loading rate, fractal dimension, and energy dissipation rate was investigated through experiments conducted using the MTS C60 tests(static loads) and split Hopkinson pressure bar system(dynamic loads). The results show that the energy dissipation rate peaks are associated with stress drop during coal deformation, and also positively related to the uniaxial compressive strength. A higher displacement rate of quasi-static loads leads to an initial increase and then a decrease in energy dissipation rate, whereas a higher loading rate of dynamic loads results in larger energy dissipation rate. Theoretical analysis indicates that a sudden increase in energy dissipation rate suggests partial fracture occurring within coal under both quasi-static and dynamic loads. Hence, the energy dissipation rate is an essential indicator of partial fracture and final failure within coal, as well as a prospective precursor for catastrophic failure in coal mine.     

Analysis of progressive failure of pillar and instability criterion based on gradient-dependent plasticity

A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity.In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hooke‘s law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stressaverage deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically using instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.     

预测砌体墙板破坏荷载的广义应变能密度方法

为了揭示新板与基础板破坏荷载之间的关系,从面外均布荷载作用下砌体墙板的有限元模型中提取各单元的应变能密度,给出墙板的广义应变能密度概念．通过分析新板与基础板的广义应变能密度分布模式,提出了基于广义应变能密度预测砌体墙板破坏荷载的方法．算例分析表明,本文发展的方法与有限元的分析方法相比,虽然预测精度接近,但该方法具有建模过程简单、不受材料性质参数影响的优点;与屈服线方法相比,预测精度有较大提高．该方法能直接应用现有的试验数据或记录来预测新板的破坏荷载,为砌体墙板破坏荷载的预测提供一个新途径．     

三维动静组合加载下花岗岩能量耗散试验研究

利用改造的三维霍普金森试验系统(split Hopkinson pressure bar, SHPB),选取4个轴压水平(25, 50, 75和100 MPa)和4个围压水平(0, 5, 10和15 MPa),对应开展4种应变率(约70, 90, 110和130 s^-1)下花岗岩三维动静组合加载试验研究,分析静载轴压、静载围压和应变率对花岗岩受冲击过程中能量耗散的影响规律,并讨论其破坏模式。试验结果表明:轴压增大时,花岗岩破坏时单位体积吸收能逐渐降低;围压或应变率增大时,单位体积吸收能逐渐升高。岩石储能极限在能量耗散过程中发挥关键作用,且不同情况下具体表现不同:储能极限与初始储能的差值影响岩石受冲击时的吸能值;当岩石在静载下进入损伤阶段初期时,储能极限与初始储能的比值决定岩石受冲击时的释能值;当岩石在静载下进入损伤阶段后期甚至发生屈服时,储能极限值正比于岩石释能值。此外,岩石破坏模式与单位体积耗散能关系密切:应变率相似静载组合变化时,破碎程度与单位体积吸收能变化呈负相关;静载组合确定应变率梯度变化时,破碎程度与单位体积吸收能变化呈正相关。     

Effect of specimen size on energy dissipation characteristics of red sandstone under high strain rate简

In this experiment, red sandstone specimens, having slenderness ratios of 0.5, 0.7, 0.9 and 1.1 respectively, were subjected to blow tests using a Split Hopkinson Pressure Bar (SHPB) system at a pressure of 0.4 atmospheres. In this paper, we have analyzed the effect of slenderness ratio on the mechanical properties and energy dissipation characteristics of red sandstone under high strain rates. The processes of compaction, elastic deformation and stress softening deformation of specimens contract with an increase in slenderness ratio, whilst the nonlinear deformation process extends correspondingly. In addition, degrees of damage of specimens reduced gradually and the type of destruction showed a transformation trend from stretching failure towards shear failure when the slenderness ratio increased. A model of dynamic damage evolution in red sandstone was established and the parameters of the constitutive model at different ratios of length to diameter were determined. By comparison with the experimental curve, the accuracy of the model, which could reflect the stress–strain dynamic characteristics of red sandstone, was verified. From the view of energy dissipation, an increase in slenderness ratio of a specimen decreased the proportion of energy dissipation and caused a gradual fall in the capability of energy dissipation during the specimen failure process. To some extent, the study indicated the effects of slenderness ratios on the mechanical properties and energy dissipation characteristics of red sandstone under the high strain rate, which provides valuable references to related engineering designs and academic researches.