剪胀对岩样全部变形特征的影响

采用FLAC内嵌语言FISH编制了计算平面应变压缩岩样轴向、侧向、体积应变及泊松比的FISH函数，研究了剪切扩容对剪切带图案及岩样全部变形特征的影响。在峰值强度之前及之后，岩石的本构模型分别取为线弹性及莫尔库仑剪破坏与拉破坏复合的应变软化模型。分析表明，增加剪胀角使岩样由单一向共轭剪切破坏转变，并使接近Arthur倾角的剪切带倾角增加。剪切带宽度随剪胀角增加，可由基于梯度塑性理论且考虑剪胀后的剪切带宽度公式进行解释。剪胀角增加导致峰值强度及对应的轴向、侧向及体积应变增加。在峰后，由于剪胀引起剪切带条数及宽度增加，因而，轴向应力-轴向及侧向应变曲线软化段都变平缓。剪胀角较高时，岩样可获得更大的侧向变形量及泊松比，甚至是负的体积应变；岩样失稳破坏的前兆更加明显。     

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．     

节理倾角对单节理岩样变形破坏影响的数值模拟

采用FLAC模拟了节理倾角对各向异性岩样峰值强度、力学行为及剪切带图案的影响。节理由实体单元模拟。对于节理之外的岩石,采用莫尔库仑与拉破坏复合的破坏准则,峰后本构关系选择线性应变软化模型;对于节理,采用理想弹塑性的莫尔库仑准则。结果表明,无节理密实岩石的峰值强度最高。节理岩样的剪切应变或集中在节理上,或集中在新剪切带上,峰值强度随节理倾角而改变。新剪切带启动于节理的端部,然后沿其固有方向传播。当节理倾角适中时,节理岩样的峰值强度较低,岩样的行为受控于节理。当节理倾角较高或较低时,可观测到应变软化行为。若节理倾角较低,新剪切带的长度随节理倾角的降低而增加,这导致了陡峭的峰后应力-应变曲线。若节理倾角较高,由于节理倾角对新剪切带的厚度和倾角几乎没有影响,因此,峰后斜率不依赖于节理倾角。     

初始内聚力及摩擦角对岩样全部变形特征的影响

目的研究初始内聚力及摩擦角对剪切带图案及岩样全部变形特征的影响.方法采用FLAC内嵌语言FISH编制了计算平面应变压缩岩样轴向、侧向、体积应变及泊松比的FISH函数.在峰值强度之前及之后,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.结果随着初始内聚力及摩擦角的增加,破坏模式由复杂向简单剪切破坏转变;发生破坏的单元数目降低;剪切带倾角增加;轴向应力的峰值强度及所对应的轴向、侧向应变的绝对值降低,岩样可以达到的最小体积增加.峰后的轴向应力-轴向应变曲线、轴向应力-侧向应变曲线、侧向应变-轴向应变曲线、泊松比-轴向应变曲线及体积应变-轴向应变曲线的斜率几乎不受初始内聚力及摩擦角的影响.但是,当初始内聚力及摩擦角最小时,5种峰后曲线略显平缓,这是由于发生破坏的单元数目最多及剪切带的倾角最低.结论剪切带倾角更接近Arthur倾角,说明了数值结果是可信的.岩样失稳破坏的前兆不随着初始内聚力及摩擦角的降低或增加而改变.     

双轴比例加载条件下岩石的应变局部化分析

采用梯度塑性理论对双轴比例加载条件下岩石变形局部化进行研究.应用应变梯度塑性增量本构关系,推导Mises屈服准则下岩石应变局部化带的带宽及其倾角的解析表达式.通过绘制定值泊松比和定值E/λ条件下的应变局部化带的带宽与倾角随双向荷载比值的变化曲线,分析应变局部化带宽度和倾角的变化范围及极值.结果表明:双轴比例加载条件下泊松比和E/λ对应变局部化带带宽和倾角的扩展作用效果相反,双向荷载比值在一定区间内的提高会促进应变局部化带的发展,区间具体大小与泊松比、E/λ有关.     

三维岩样单轴压缩端面效应及破坏数值模拟

采用三维拉格朗日元法，对三维岩样在单轴压缩及不同端面约束条件下，试样端面上压应力的分布及演化规律、试样的破坏过程及空间局部化区域的形态进行数值模拟研究。在峰值强度之前及之后，岩石的本构模型分别取为线弹性及莫尔库仑剪破坏与拉破坏复合的应变软化模型。数值结果表明，对于粗糙端面，由于强烈的端面约束，试样的弹性区是以两端面为底面的锥体；锥体一旦形成，随着时间步的增加，其体积基本保持不变；压应力集中于端面的四个边上。对于光滑端面，弹性区被塑性区所包围，随着时间步的增加，弹性区逐渐缩小，直到消失；压应力集中于端面的中心。在平面应力状态下，未观测到明显的局部化剪切带图案。无论粗糙还是光滑端面，三维岩样都发生了明显的剪切破坏。三维岩样内部的剪切应变局部化带有主有次，占主导地位的剪切带尺寸较大，应变率集中程度较大。     

高应变率压缩载荷下钨合金变形与失效研究

本文借助于扫描电镜和光学显微镜，研究了９３Ｗ－Ｎｉ－Ｆｅ合金圆柱试样在高应变率压缩载荷下的变形与失效特征．研究表明，圆柱试样的变形过程经历了３个阶段：①均匀变形阶段；②对称不均匀变形阶段；③非对称不均匀变形阶段．其中不均匀变形是区域性的．绝热剪切带协调了上述不均匀变形区域的界面．失效时在拉应力最大的区域首先形成裂纹，这些裂纹扩展到一定深度后通过剪切带聚合     

缺陷岩样的变形局部化及剪切面的反射与折射

平面应变岩样在单方向施加栽荷条件下,采用拉格朗日元法(FLAC)模拟了端面约束对具有初始随机材料缺陷的岩样破坏过程及应力-应变曲线的影响.对于粗糙端面试样,可在试样中部观测到剪切带;靠近试样两端面的弹性区域的形状类似三角形,其高度随着轴向应变的增加而降低,直到达到常数.对于光滑端面情形,未观测到剪切带的停滞及折射现象,而反射现象较常见.对于粗糙端面试样,剪切带不能贯穿试样的两端面;很少观测到反射现象;可见到剪切带的停滞现象;剪切带的折射现象较常见;通常,一条较长的剪切带可以贯通试样;剪切带发生折射之后,其倾角有所降低.粗糙端面时的应力峰值比光滑端面时高.端面约束不同时的峰后刚度及应力峰值所对应的轴向应变没有明确的规律.不同端面条件下,试样中部剪切带花样既有一定的类似性(由于微弱的端面约束与相同的初始随机材料缺陷分布),又有不同的一面(端面约束的不同及两端面附近的剪切带传播至试样中部).     

韧性剪切带中S—C（C′）组构的成因及其运动学意义

韧性剪切带中常发育３种面理：呈Ｓ形平行变形矿物优选方位的Ｓ面理；平行剪切带边界的Ｃ面理；与剪切带边界斜交的Ｃ′面理．剪切条带（ＳｈｅａｒＢａｎｄ，简称ＳＢ），伸展折劈理（ＥｘｔｅｎｓｉｏｎａｌＣｒｅｎｕｌａｔｉｏｎＣｌｅａｖａｇｅ简称ＥＣＣ）及正滑动折劈理（ＮｏｒｍａｌＳｌｉｐＣｒｅｎｕｌａｔｉｏｎ，简称ＮＳＣ），均是不同学者给予Ｃ′面理的不同名称．Ｃ面理公认为平行剪切带的剪切流动面．Ｓ面理多数学者认为平行有限应变椭球的ＸＹ面．Ｃ′面理可用应变分解原理或补偿调整原理进行解释．在运动学上，Ｓ－Ｃ（Ｃ′）组构是极好的剪切指向判别标志，但是Ｓ－Ｃ（Ｃ′）组构不能用来准确地确定剪切方向．剪切方向一般是根据拉伸线理的测量来确定的．     

中等应变速率对砂岩破坏形态和力学性质的影响

以砂岩为研究对象,根据砂岩的颗粒分析试验、抗压强度、抗拉强度和强度试验结果,在颗粒流程序下,通过fish语言编程,虚拟实现了砂岩数值试件和单轴压缩试验,设计10-3、5×10-3、10-2、2×10-2、5×10-2、10-1、2×10-1s-1这7个应变率下的单轴压缩试验.分析应变率对砂岩破裂形态、裂纹数量和扩展、应力-应变曲线和能量转换的影响.结果发现:应变率的增加破坏了优势剪切带的发展,使得剪切带等速发展,材料由剪切破坏向锥形破坏发展;材料的力学性能表现出极大的伪增强,应力-应变曲线上扬、斜率提高、峰值提高,峰后曲线震荡剧烈;裂缝数量增多,其中拉裂缝减少,剪切裂缝增多;边界输入能量增加,造成加载过程中材料的摩擦能、动能和应变能单调增大,摩擦能增大说明剪切裂缝增多,动能增大说明破坏剧烈,应变能增大说明更容易产生岩爆现象.     

Entire deformational characteristics and strain localization of jointed rock specimen in plane strain compression

Shear band （SB）, axial, lateral and volumetric strains as well as Poisson＇s ratio of anisotropic jointed rock specimen （JRS） were modeled by Fast Lagrangian Analysis of Continua （FLAC）. Failure criterion of rock was a composited Mohr-Coulomb criterion with tension cut-off. An inclined joint was treated as square elements of ideal plastic material beyond the peak strength. Several FISH functions were written to automatically find the addresses of elements in the joint and to calculate the entire deformational characteristics of plane strain JRS. The results show that for moderate joint inclination （JI） , strain is only concentrated into the joint governing the behavior of JRS, leading to ideal plastic responses in axial and lateral directions. For higher JI, the post-peak stress-axial and lateral strain curves become steeper as JI increases owing to the increase of new SB＇s length. Lateral expansion and precursor to the unstable failure are the most apparent, resulting in the highest Poisson＇s ratio and even negative volumetric strain. For lower JI, the entire post-peak deformational characteristics are independent of JI. The lowest lateral expansion occurs, leading to the lowest Poisson＇s ratio and positive volumetric strain all along. The present prediction on anisotropic strength in plane strain compression qualitatively agrees with the results in triaxial tests of rocks. The JI calculated by Jaeger＇s formula overestimates that related to the minimum strength. Advantages of the present numerical model over the Jaeger＇s model are pointed out.     

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）.     

Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion

Fault rockburst is treated as a strain localization problem under dynamic loading condition considering strain gradient and strain rate. As a kind of dynamic fracture phenomena, rockburst has characteristics of strain localization, which is considered as a one-dimensional shear problem subjected to normal compressive stress and tangential shear stress. The constitutive relation of rock material is bilinear (elastic and strain softening) and sensitive to shear strain rate. The solutions proposed based on gradientdependent plasticity show that intense plastic strain is concentrated in fault band and the thickness of the band depends on the characteristic length of rock material. The post-peak stiffness of the fault band was determined according to the constitutive parameters of rock material and shear strain rate. Fault band undergoing strain softening and elastic rock mass outside the band constitute a system and the instability criterion of the system was proposed based on energy theory. The criterion depends on the constitutive relation of rock material, the structural size and the strain rate. The static result regardless of the strain rate is the special case of the present analytical solution. High strain rate can lead to instability of the system.     

Effect of pore pressure on deformation and unstable snap-back for shear band and elastic rock system

Fast Lagrangian analysis of continua（FLAC） was used to study the influence of pore pressure on the mechanical behavior of rock specimen in plane strain direct shear, the distribution of yielded elements, the distribution of displacement and velocity across shear band as well as the snap-back （elastic rebound） instability. The effective stress law was used to represent the weakening of rock containing pore fluid under pressure. Numerical results show that rock specimen becomes soft （lower strength and hardening modulus） as pore pressure increases, leading to higher displacement skip across shear band. Higher pore pressure results in larger area of plastic zone, higher concentration of shear strain, more apparent precursor to snap-back （unstable failure） and slower snap-back. For higher pore pressure, the formation of shear band-elastic body system and the snap-back are earlier; the distance of snap-back decreases; the capacity of snap-back decreases, leading to lower elastic strain energy liberated beyond the instability and lower earthquake or rockburst magnitude. In the process of snap-back, the velocity skip across shear band is lower for rock specimen at higher pore pressure, showing the slower velocity of snap-back.     

Volume Change of Heterogeneous Quasi-brittle Materials in Uniaxial Compression

The volumetric strain was categorized into elastic and plastic parts. The farmer camposed of axial and lateral strains is uniform and determined by Hooke＇s law ; however, the latter consisting of axial and lateral strains is a fuaction af thickness af shear band determined by grndieat-dependeat plasticity by cansidering the heterngeneity of quasi- brittle materials. The non- uniform lateral strain due to the fact that shear band was farmed in the middle of specimen was averaged within specimen to precisely assess the volumetric strain. Then, the analytical expression for volumetric strain was verified by comparison with two earlier experimental results for concrete and rack. Finally, a detailed parametric study was carried out to investigate effects of constitutive parameters （ shear band thickness, elastic and softening rnoduli ） and geometrical size of specimen（ height and width of specimen ） on the volume dilatancy.     

Adiabatic shear localization evolution for steel based on the Johnson-Cook model and gradient-dependent plasticity

Gradient-dependent plasticity is introduced into the phenomenological Johnson-Cook model to study the effects of strainhardening, strain rate sensitivity, thermal-softening, and microstructure. The microstructural effect （interactions and interplay among microstructures） due to heterogeneity of texture plays an important role in the process of development or evolution of an adiabatic shear band with a certain thickness depending on the grain diameter. The distributed plastic shear strain and deformation in the shear band are derived and depend on the critical plastic shear strain corresponding to the peak flow shear stress, the coordinate or position, the internal length parameter, and the average plastic shear strain or the flow shear stress. The critical plastic shear strain, the distributed plastic shear strain, and deformation in the shear band are numerically predicted for a kind of steel deformed at a constant shear strain rate. Beyond the peak shear stress, the local plastic shear strain in the shear band is highly nonuniform and the local plastic shear deformation in the band is highly nonlinear. Shear localization is more apparent with the increase of the average plastic shear strain. The calculated distributions of the local plastic shear strain and deformation agree with the previous numerical and experimental results.     

Unified analytical stress- strain curve for quasibrittle geomaterial in uniaxial tension, direct shear and uniaxial compression

Considering strain localization in the form of a narrow band initiated just at peak stress, three analytical expressions for stress - strain curves of quasibrittle geomaterial （such as rock and concrete） in uniaxial tension, direct shear and uniaxial compression were presented, respectively. The three derived stress - strain curves were generalized as a unified formula. Beyond the onset of strain localization, a linear strain-softening constitutive relation for localized band was assigned. The size of the band was controlled by internal or characteristic length according to gradient-dependent plasticity. Elastic strain within the entire specimen was assumed to be uniform and decreased with the increase of plastic strain in localized band. Total strain of the specimen was decomposed into elastic and plastic parts. Plastic strain of the specimen was the average value of plastic strains in localized band over the entire specimen. For different heights, the predicted softening branches of the relative stress- strain curves in uniaxial compression are consistent with the previously experimental results for normal concrete specimens. The present expressions for the post-peak stress - deformation curves in uniaxial tension and direct shear agree with the previously numerical results based on gradient-dependent plasticity.