Effect of height of rock specimen on strain localization, precursor to failure and entire deformationai characteristics

Patterns of shear band, precursors to shear failure occurring in strain-softening stage, axial, lateral and volumetric strains as well as Poisson＇s ratio of plane strain rock specimens in compression for different heights were investigated by use of Fast Lagrangian Analysis of Continua（FLAC）. A material imperfection closer to the lower-left corner of the specimen was prescribed. For finer mesh, the imperfection was modeled by four null elements, while it was modeled by a null element for coarser mesh. FISH functions were written to calculate the entire deformational characteristics of the specimen. In elastic stage, the adopted constitutive relation was linear elastic; in strain-softening stage, a composite Mohr-Coulomb criterion with tension cut-off and a post-peak linear constitutive relation were adopted. Height of rock specimen does not influence shear band＇s pattern （including the thickness and inclination angle of shear band）. The slopes of the post-peak stress-axial strain curve, stress-lateral strain curve, lateral strain-axial strain curve, Poisson＇s ratio-axial strain curve and volumetric strain-axial strain curve depend on the height. Hence, the slopes of these curves cannot be considered as material properties. Nonlinear deformation prior to the peak stress is a kind of precursors to shear failure, which is less apparent for shorter specimen. For the same axial strain, lower lateral expansion is reached for shorter specimen, leading to lower Poisson＇s ratio and higher volumetric strain. The maximum volumetric strain of longer specimen is less than that of shorter specimen. The conclusions drawn from numerical results using finer mesh qualitatively agree with those using coarser mesh.     

Ti-6Al-4V剪切带内部的应变、温度分布及演变研究

采用梯度塑性理论，考虑了峰值剪切应力之后的材料承载能力缓慢降低的过程及承载能力快速降低的过程，推导了剪切带内部的剪切变形、应变及温度分布的公式。计算了Ti-6Al-4V剪切带内部塑性剪切应变，温度的分布及演变。在剪切带内部，塑性剪切应变及温度分布是高度不均匀的，这种不均匀性随着施加的塑性剪切应变的增加而增加。随着流动剪切应力的降低，剪切带内部的最大塑性剪切应变线性增加，最高温度非线性增加。由于微结构效应，基于梯度塑性理论的剪切带内部的最大塑性剪切应变及最高温度的预测值高于经典理论的预测值。将Ti-6Al-4V剪切带内部的剪切变形及应变的理论结果与根据前人高速摄影实验图片的计算结果进行了对比，理论与实验结果的趋势非常吻合，在数值上，剪切带内部的最大剪切应变的理论值仍低于实测值。     

多孔介质岩土材料剪切带孔隙特征研究(2)——最大孔隙比分析

在流动剪切应力为残余剪切强度时，对剪切带内部的局部孔隙比和平均孔隙比进行了理论分析。对于应变软化阶段剪胀的岩土材料，基于梯度塑性理论验证了在剪切带内部存在最大孔隙比的客观事实，最大孔隙比具有两层含义，即局部(和坐标有关)最大孔隙比和平均最大孔隙比，分别解释了相关的实验现象。对影响剪切带内部平均最大孔隙度的因素进行了分析；给出了剪切软化模量、残余剪切强度及扩容角对剪切带内部最大孔隙度的影响规律。在软化过程中，剪切带中部最大孔隙度逐渐增加，直至残余强度剪切带中部最大孔隙度达到最大值。研究结果为流固耦合多孔介质岩土材料的稳定性研究奠定了初步的理论基础。     

Shear stress distribution and characteristics of deformation for shear band-elastic body system at pre-peak and post-peak

The distributed shear stress and the displacement across shear band, the evolution of plastic zones, and the load-carrying capacity of rock specimen were investigated in plane strain direct shear test according to Fast Lagrangian Analysis of Continua （FLAC）. And then the shear displacement distribution in normal direction of system composed of localized shear band and elastic rock was analyzed based on gradient-dependent plasticity. The adopted failure criterion was a composite of Mohr-Coulomb criterion, that is, the relation between tension cut-off and postpeak constitutive of rock was linear strain-softening. Numerical results show that shear stress field approximately undergoes three different stages. At first, shear stress is only concentrated in the middle of top and base of specimen. Next, shear stress in the middle of specimen tends to increase, owing to superposition of shear stresses. Interestingly, two peaks of shear stress appear far from the loading ends of specimen, and the peaks approach with the increase in timestep until elements at the center of specimen yield. Finally, relatively lower shear stress level is reached in large part of specimen except in the regions near the two ends. As flow stress decreases, the analytical shear displacement distribution in shear band based on gradient-dependent plasticity becomes steeps outside the band, it is linear and its slope tends to decrease. These theoretical results qualitatively agree with that of the present numerical predicted results. Main advantage of the analytical solution over the numerical results according to FLAC is that it is continuous, smooth and non-linear （except at elastic stage）.     

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.     

孔隙压力对岩样全部变形特征的影响

目的 研究了孔隙压力对剪切带图案及岩样全部变形特征的影响．方法 利用FLAC内嵌语言编制的FISH函数计算平面应变压缩岩样轴向、侧向、体积应变及泊松比．在峰前及峰后，岩石的本构模型分别取为线弹性模型及莫尔库仑剪破坏与拉破坏复合的应变软化模型．结果 随着孔隙压力的增加，岩样的破坏区域越来越广泛；剪切带倾角都接近于Arthur倾角；峰值强度及所对应的轴向、体积应变及侧向应变的大小均降低．当孔隙压力较低时，峰后应力-轴向应变曲线及应力-侧向应变曲线软化段斜率基本保持不变，根据单轴压缩条件下的解析解，这是由于岩样的破坏模式不随孔隙压力的增加而改变．结论当孔隙压力较高时，大量的单元发生破坏将消耗较多的能量，这使应力-轴向应变及侧向应变曲线软化段变平缓；岩样在轴向应变较低时就可获得较高的侧向变形量及泊松比，甚至负的体积应变．岩样失稳破坏的前兆的明显程度不随孔隙压力的改变而改变．     

扩容角对初始随机材料缺陷岩石试样破坏过程及力学行为的影响

在单轴平面应变压缩条件下，采用FLAC模拟扩容角对具有初始随机材料缺陷的光滑端面岩石试样的破坏过程及对应力一应变曲线的影响。利用FISH函数于试样内部规定初始缺陷。密实的岩石服从莫尔库仑剪破坏与拉破坏复合的破坏准则，破坏之后呈现应变软化一理想塑性行为。缺陷在破坏之后经历理想塑性行为。扩容角较高时试样内部最终发生破坏的单元数目较多。随着扩容角的增加，剪切带变得粗壮和陡峭。扩容角对应力一轴向应变曲线影响不大。扩容角增加时，在应变软化阶段，应力一侧向应变曲线变平缓，根据作者过去提出的理论公式，这是由于剪切带宽度增加的贡献超过剪切带倾角增加的贡献所致。当扩容角较高时，应力峰值时试样内部的最大剪切应变增量较高，因而试样破坏的前兆比较明显。剪切带倾角的数值结果与Arthur倾角比较接近，未能超过Coulomb倾角。扩容角越大，剪切带最终可以获得越来越高的剪切应变和体积应变。     

分区破裂相似材料分层观测试验研究

以沙土作为相似材料,观测了圆桶模型内部裂纹的分布规律及沿轴向的变化规律。研究表明:在若干沙土层间预制界面,然后将各层沙土依次从铁桶中压出的实验方法可以更深入地观测硐室围岩裂纹沿轴向的变化规律。巴西圆盘模型不能解释分区破裂现象,而用空间共轭剪切带解释则更加合理。支护对分区破裂有一定的影响。     

考虑应变梯度效应的三点弯梁模型解析研究--第一部分:局部化带的传播

为分析应变软化和由此带来的应变局部化问题,将梯度塑性理论引入裂纹带模型。以拉应变局部化区域代替裂纹带,在三点弯梁裂纹带(具有一定尺寸的带宽由特征长度确定)内部存在着不均匀分布的拉应变,这与实验结果相符。对拉应变进行积分,得到了拉应变局部化区域的张拉位移的理论表达式,结果表明:该位移与拉应力成线性规律,拉应变局部化区域的宽度越大,弹性模量越小或降模量越小,则该位移越大。此外,采用应力平衡条件、应变软化的本构关系及平截面假定,还得到了拉应变局部化区域的扩展规律,结果表明:下降模量越大、三点弯梁高度越小及弹性模量越小,则在相同的拉应力的情况下,拉应变局部化区扩展的长度越小;抗拉强度对拉应变局部化区扩展长度的最大值没有影响。此外,还研究了梁中部横截面内中性轴到具有最大承载能力的点的距离的变化规律。     

辽宁工程技术大学，辽宁 阜新 123000

提出了利用梯度塑性理论计算Ti-6Al-4V绝热剪切带的局部剪切应变新方法.绝热剪切带的最大局部塑性剪切应变依赖于临界塑性剪切应变、试样的标定长度、绝热剪切带总厚度、绝热剪切带的平均塑性剪切应变.计算表明,随着绝热剪切带总厚度的增加,绝热剪切带的最大局部塑性剪切应变以非线性方式下降.当绝热剪切带总厚度的取值接近1 mm时,尽管确定临界塑性剪切应变的方法不同,但是,绝热剪切带的最大局部塑性剪切应变的计算值差别很小.当绝热剪切带总厚度取值在0.335～1 mm之间时,绝热剪切带的最大局部塑性剪切应变的计算值位于Liao及Duffy(1998)实验结果的下限(75%)和上限(350%)之间.