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．     

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）.     

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。     

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.     

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。     

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.     

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。     

Constitutive equations and finite element implementation of strain localization in sand deformation

A recently proposed model coupling with the solid-fluid of the saturated sand was utilized to study the deformation band. Based on the critical state plasticity model by Borja and Andrade, the hydraulic conductivity tensor was naturally treated as a function of the spatial discretization matrix about the displacement and the stress field, allowing a more realistic representation of the physical phenomenon. The fully Lagrangian form of the Darcy law was resolved by Piola algorithm, and then the flow law was gained, leading to the implementation of a modified model of the saturated sand. Then the criterion for the onset of localization was derived and utilized to detect instability. The constitutive model was implemented in a finite element program coded by FORTRAN, which was used to predict the formation and development of shear bands in plane strain compression of saturated sand. At last, the formation mechanism of the shear band was discussed. It is shown that the model works well, and the simulation sample bifurcates at 1.18% axial strain, which is in a good qualitative agreement with the experiment. The pore pressure greatly affects the onset and development of the deformation band, and it obviously increases around the localization-prone regions with the direction toward the outer side of the normal of the shear band, while the pore stress flows nearly horizontally and is distributed equally far away the shear band region. Foundation item: Project(2006G007-C) supported by the Foundation of the Science and Technology Section of Ministry of Railway of China; Project(77206) supported by the Excellent PhD Thesis Innovation Foundation of Central South University, China     

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.     

Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity

A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An instability criterion is derived analytically based on the energy principle using a known size of localization band according to gradientdependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.     

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.     

Effect of Relative Stress on Post-Peak Uniaxial Compression Fracture Energy of Concrete

1　IntroductionItisrealizedthatthelinearelasticfracturemechan icsisnownotapplicabletofractureinordinaryconcretestructures .Todescribethesofteningbehaviorofconcrete ,differentmodelsbasedonnon linearfracturemechanicalideaswereproposed ,suchasthefictitiouscrackmodel[1](FCM )byHillerborgetal.(1976 ) ,thecrackbandmodel[2 ] byBazant (1983) ,andthetwo parameterfrac turemodel[3 ] byJenqandShah (1985 ) .ThedifficultywithFCMliesindeterminingtheval uesofthethreeparametersbyexperiments .Toobtaintheval…     

温度对深部岩石力学性质的影响

处于地温环境中的深部岩石,其力学特性与地表岩石有极大差异.温度对岩石力学性质的影响机理包括:矿物颗粒热膨胀;含水性及比例;岩石孔 隙结构;矿物结构及成分.随温度增加,岩石变形特征从脆性向塑性变化,峰值强度降低,弹性模量降低,压密阶段应变变长,线弹性阶段的应变降低,峰后阶段的应变增加,抗压强度降低,弹性模量降低.     

线性软化土体中球孔扩张问题的解析解

采用三折线线性软化模型描述了土体应力－应变关系，以Mohr-Coulomb为屈服准则，同时考虑塑性区弹性变形、土体剪胀以及土体软化的特性，推导了孔扩张后孔周各个区域的应力、应变及位移解析解，讨论了剪胀角、应变软化系数、是否考虑塑性区弹性变形对解答结果的影响.结果表明，最终扩张压力、塑性区半径都随剪胀角的增大而增大；软化系数对塑性区半径影响很小，但对最终扩张压力影响较大，随着软化系数的增大，最终扩张压力增大；考虑塑性区弹性变形对扩张问题解答的影响随扩张半径的增大越趋明显；考虑塑性区的弹性变形，最终扩孔压力偏小.     

双材料界面剪切应力分析

在传统弹塑性理论的基本框架内,考虑应变梯度效应,分析了钢与混凝土粘结界面处混凝土局部滑移带内部塑性剪应变的规律,推导了剪应力与剪切滑动位移的关系及剪切滑移切向速度表达式.混凝土粘结滑移层内部应变集中程度随剪应力降增加而加剧,在应变软化阶段,剪切滑移切向速度与剪应力卸载率成正比.应用虚功率原理和塑性极限分析上限定理,分析了钢与混凝土双材料界面的剪切滑移强度,认为起主要作用的是混凝土的抗拉强度、与型钢表面状况有关的粘聚力、机械咬合力和混凝土对型钢的横向约束力等.     

平面应变含缺陷岩样变形破坏全过程数值模拟

采用拉格朗日元法(FLAC)研究了左边界有缺陷的压缩岩样剪切带的启动及演变规律，峰后本构关系采用线性应变软化模型．计算结果表明，在应力一时步曲线峰值之前，剪切带首先出现在缺陷附近，直到贯通试样右边界；在剪切带传播过程中，塑性区沿切向及法线向外扩展；剪切带内部单元的剪切应变率一时步曲线经历了稳定、线性上升和非线性上升3个阶段．然而，剪切应变增量随时步持续增加．剪切带倾角接近于Arthur倾角，表明数值计算结果是可信的。     

卸围压条件下砂岩变形破坏特性试验研究

从可释放弹性应变能角度对岩石卸围压条件下破坏特性进行研究,利用MTS815电液压伺服可控制刚性试验机进行保持轴向变形不变的卸围压试验,根据卸围压试验数据,分析了该砂岩卸围压过程中变形、强度、弹性模量及能量变化特征。结果表明:随着围压逐渐降低,岩样发生侧向不断扩容;轴向应力逐渐降低,呈现出非线性特征;弹性模量在初始阶段几乎不变化,越过破坏点之后大幅降低;可释放的弹性应变能在初始阶段增大比较缓慢,当围压降低至一定程度时急剧增大;推导出基于可释放弹性应变能的卸荷岩石的整体破坏准则Ue0。     

不同受力状态下岩石破坏过程次声信号特征

采用室内试验方法,分别开展了岩石在压缩、剪切和拉伸状态下的破坏试验,利用高灵敏度的次声信号采集设备同步采集岩石破坏过程中的次声信号,对不同受力状态下岩石次声信号的特征差异进行了研究。结果表明:在压缩状态下,岩石次声信号发射主要在弹性和塑性变形阶段,次声信号的峰值频率在7 Hz左右,在岩石临近破坏前,次声信号振幅和频率范围均有所增加;在剪切状态下,次声信号主要集中在峰值后应力逐步下降的阶段,信号功率分布集中程度较压缩试件略低,峰值频率在8 Hz左右;在拉伸状态下,试件加载初始阶段便有次声信号发生,次声信号频率通常存在高、低两个中心,其中低频与压缩试件接近,高频则高出3 Hz,拉伸试件内部裂隙的萌生和发展较压缩和剪切状态下更为迅速、有序,随着试件内部裂隙的发展,次声信号频率逐渐升高。以上特征的发现为不同受力状态下次声信号的识别以及岩体灾变预测提供了依据。     

饱和土体中衬砌隧道在移动荷载下的动力响应

为了研究移动点荷载作用下饱和土体全空间中圆形衬砌隧道的三维动力响应,采用解析方法进行求解.用无限长圆柱壳模拟衬砌,用Biot饱和多孔介质模型模拟土体.引入两类势函数表示土骨架和孔隙水的位移,在不同环向模态下利用修正Bessel方程求解各势函数.结合边界条件,得到频率-波数域内衬砌和土骨架位移、孔隙水压力的解答.对各模态下的解答求和,并进行双重Fourier逆变换得到时间-空间域内的动力响应.通过算例分析荷载速度、土体渗透性等对位移及土体孔压的影响.结果表明：饱和土体中衬砌隧道系统存在临界速度,该速度与土体剪切波波速很接近;位移场和孔压场分布受荷载速度、土体渗透性影响较大;随着土体渗透性增大,土体孔压减小;高速荷载时的位移响应频谱与低速荷载时的差别很大．     

高地应力下砂岩力学参数和波速变化规律试验研究

基于波动方程,提出一种砂岩的纵波波速与静水围压关系的数学模型。在岩石常规三轴试验的基础上得到不同静水围压下砂岩的静弹性模量、静泊松比和纵波波速,并分别拟合得到静弹性模量-静水围压和静泊松比-静水围压关系的拟合曲线和拟合公式。试验结果表明,砂岩的静弹性模量和静泊松比随静水围压的增大而增加,且静弹性模量增加速率缓慢减少。基于波动方程求解得到纵波波速-静水围压关系的数学模型,利用数学模型计算得到的纵波波速可知,砂岩的纵波波速随静水围压的增大而增大,且增加速率逐渐变缓。计算得到的纵波波速与试验测得的纵波波速进行对比验证,误差范围为7.0%~8.3%,故基于波动方程求解的砂岩纵波波速-静水围压关系的数学模型可靠性和准确性较高,对高地应力下岩石的物理力学参数和波速变化规律的分析判定具有指导意义。