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1.
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.  相似文献   

2.
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.  相似文献   

3.
The capacity of energy absorption by fault bands after rock burst was calculated quantitatively according to shear stressshear deformation curves considering the interactions and interplaying among microstructures due to the heterogeneity of strain softening rock materials. The post~peak stiffness of rock specimens subjected to direct shear was derived strictly based on gradientdependent plasticity, which can not be obtained from the classical elastoplastic theory. Analytical solutions for the dissipated energy of rock burst were proposed whether the slope of the post-peak shear stress-shear deformation curve is positive or not. The analytical solutions show that shear stress level, confining pressure, shear strength, brittleness, strain rate and heterogeneity of rock materials have important influence on the dissipated energy. The larger value of the dissipated energy means that the capacity of energy dissipation in the form of shear bands is superior and a lower magnitude of rock burst is expected under the condition of the same work done by external shear force. The possibility of rock burst is reduced for a lower softening modulus or a larger thickness of shear bands.  相似文献   

4.
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.  相似文献   

5.
Shear-box test with strain measurement was used to study time-dependent stress and strain of in-plane shear(Mode Ⅱ) fracture process of rock and to reveal the mechanism of Mode Ⅱ fracture.Numerical results show that the maximum shear stress τmax at the crack tip is much larger than the maximum tensile stress σ1 and the ratio of τmax/σ1 is about 5,which favors Mode Ⅱ fracture of rock.Test results indicate that the strain—time curve comprises three stages:the linear deformation stage,the micro-cracking stage ...  相似文献   

6.
According to the tensile failure of rock bolt in weakly cemented soft rock, this paper presents a new segmented anchoring style in order to weaken the cumulative effect of anchoring force associated with the large deformation. Firstly, a segmented mechanical model was established in which free and anchoring section of rock bolt were respectively arranged in different deformation zones. Then, stress and displacement in elastic non-anchoring zone, elastic anchoring zone, elastic sticking zone, softening sticking zone and broken zone were derived respectively based on neural theory and tri-linear strain softening constitutive model of soft rock. Results show that the anchoring effect can be characterized by a supporting parameter b. With its increase, the peak value of tangential stress gradually moves to the roadway wall, and the radial stress significantly increases, which means the decrease of equivalent plastic zone and improvement of confining effect provided by anchorage body. When b increases to 0.72, the equivalent plastic zone disappears, and stresses tend to be the elastic solutions. In addition, the anchoring effect on the displacement of surrounding rock can be quantified by a normalization factor δ.  相似文献   

7.
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.  相似文献   

8.
Numerical study on deformation and failure of reinforced sand   总被引:1,自引:0,他引:1  
In order to investigate the deformation and failure of reinforced sand, and the reinforcing mechanism of flexible and rigid reinforcement, a set of plane strain compression tests of dense Toyoura reinforced sand with planar reinforcement of a wide range of stiffness were analysed by a nonlinear finite element method. The analysis was incorporated into an energy-based elasto-plastic constitutive model for sand to develop a stress path-independent workhardening parameter based on the modified plastic strain energy concept. Numerical results indicate that the global stress-strain relations of sand specimens are reinforced by using relatively flexible and rigid reinforcement, and an unreinforced sand specimen can be reasonably simulated by the current finite element method. It is also found that the reinforcing mechanism and progressive failure with a development of shear bands in reinforced sand can be reasonably examined by the finite element method.  相似文献   

9.
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.  相似文献   

10.
The rheological behavior of aluminum alloy and its influencing factors in physical simulation of continuous roll casting process were studied by using a Gleeble-1500 thermal-mechanical simulation tester with a set of special clamp system. The relationships between the flow stress and the strain rate in the deformation process of simulating roll casting experiment were obtained. The results show that four different characteristic stages exist in the temperature range of the whole rheological process. The first occurs when the temperature is higher than 600℃, which belongs to the creep deformation stage; the second occurs when the temperature lies in the range of 500 - 600℃, and it can be regarded as the high temperature and low stress level deformation stage; the third occurs when the temperature decreases to the range of 300 - 500℃, it is considered to be the middle stress level deformation stage; the last occurs when the temperature is less than 300℃ and the strain rate is less than 1.00 s^-1 , it belongs to middle stress level deformation stage. But when the strain rate is larger than 1.00 s^-1, it belongs to the high stress level deformation stage. And the relative constitutive models suitable for the four different stages of continuous roll casting process were established through multivariate linear regression analysis of the experimental data.  相似文献   

11.
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.  相似文献   

12.
三维岩样单轴压缩端面效应及破坏数值模拟   总被引:6,自引:0,他引:6  
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。  相似文献   

13.
条带开采中条带煤柱塑性区宽度分析   总被引:10,自引:0,他引:10  
根据煤的变形破坏特点,对煤变形采用弹塑性应变软化模型,根据条带开采的特殊性,用三维受力单元模型来分析。通过数学运算推导出条带煤柱塑性区应力及宽度的表达式。最后,对影响塑性区宽度的几个主要因素作了分析。  相似文献   

14.
应变软化及剪胀性土体中考虑大应变的孔扩张问题解析   总被引:2,自引:1,他引:2  
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.  相似文献   

15.
土工合成材料界面应变软化特性的一种本构新模型   总被引:2,自引:0,他引:2  
在土工合成材料工程的数值研究中,根据土工合成材料界面的力学特性,构建合理有效的本构模型是提高数值计算可靠性的关键.针对部分土工合成材料界面存在的应变软化特性,提出了一种新的本构模型.以剪应力峰值为分界点,将剪应力剪切位移曲线前后两部分分别进行模拟.剪应力峰值前,采用Clough和Duncan双曲线模型进行模拟;剪应力峰值后的应变软化阶段,以剪应力峰值为原点,用另外一条倒置的双曲线进行模拟.通过系统的公式推导描述了模型的构建过程,给出了应变软化阶段界面剪切刚度计算表达式.通过对界面直剪试验结果的模拟初步验证了模型的拟合能力.  相似文献   

16.
Estimation of compaction grouting pressure in strain softening soils   总被引:3,自引:2,他引:1  
A new method was proposed to predict the limited compaction grouting pressure for the soft soils. Theoretical basis of the method considered the conical shear failure above the grout bulb. Using the Mohr-Coulomb yield criterion as the initial yield function, the limited compaction grouting pressure was determined, according to the softening elastic-plastic model based on the conventional triaxial compression tests to simulate the strain softening soils. The small strain in the elastic zone and large stain in the plastic zone and the rational yield function for the strain softening phase stage, the analytical solutions to the compaction grouting pressure were presented. The results indicate reasonable agreement and show a good potential of the proposed method for rationally optimizing the design of compaction grouting operations. Foundation item: Project (200550) supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China; Project (09JJ1008) supported by Hunan Provincial Natural Science Foundation of China  相似文献   

17.
高水材料广泛应用于地下采空区充填支护,其形状和尺寸对力学性质影响显著。为了研究不同形状和尺寸改性高水材料的力学性质,借助四川大学ETM力学试验系统,通过对不同尺寸和形状下的改性高水材料的破坏过程、抗压强度和变形特性等性质的测试,系统研究了改性高水材料的尺寸和形状效应。结果表明:改性高水材料是一种弹塑性材料,其变形破坏过程可以分为弹性阶段、屈服阶段、塑形阶段和破坏阶段四个过程;改性高水材料的尺寸仅影响其应力—应变曲线峰值强度,而形状对应力—应变曲线的峰值强度和形状均有较大影响;在一定范围内,随着材料尺寸的增加,圆柱体和立方体试件的抗压强度、弹性模量和变形模量均在一定范围内逐渐减小;在相同条件下,圆柱体试件的抗压强度、弹性模量大于立方体试件,变形模量小于立方体试件。  相似文献   

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