基于脆剪分析的岩体非线性强度特性在统一强度理论中的实现

针对统一强度理论（UST）拟合非线性强度的局限和岩土材料强度特点,提出拟合岩土非线性强度特征的脆性剪切分析方法,建立了过渡式双线性强度分解公式。以脆断、剪切双重破坏机制,解释Hoek-Brown准则的非线性特征机制,并推导出体现岩石、岩体类材料非线性强度特征的脆剪强度公式。Mine-by隧道和北山花岗岩强度数据分析显示,在岩体折减强度、试验数据直接拟合实例分析中,脆剪强度与Hoek-Brown强度相关性系数均在0.98以上,在该基础上建立岩体非线性强度脆剪分析的双线性过渡式,并提出对应的统一强度理论形式,实现统一强度理论在拟合岩土非线性强度准则中的扩展。     

岩石材料的一种非线性三参数强度准则及应用

为了更好地描述岩石材料在多种复杂应力作用下的强度状态,在已提出的双T~2强度理论基础上,建立了一种新的非线性三参数强度准则。通过与Westerly花岗岩等5种岩石材料试验数据的比较,对准则在σ_1=σ_2σ_3,σ_1σ_2=σ_3,σ_3=0、σ_10、σ_20,σ_30和σ-τ 5种复杂应力状态下的合理性和适用性进行了讨论。研究表明:待定系数A、B、C可通过简单的试验确定且具有明确的物理意义;不同岩石材料的极限应力比α和β对应不同的强度理论;非线性三参数强度准则的π平面迹线介于单剪强度理论和Mises准则、双剪强度理论之间,符合各向同性材料屈服面三轴对称和外凸的公设;理论预测曲线可反映岩石材料中主应力效应的区间性与静水压力效应,并与多种岩石材料在复杂应力状态下的强度变化趋势基本吻合。     

岩土类软化材料的柱形孔扩张统一解问题

用应力一次跌落应变软化模型来模拟岩土软化材料特性，采用双剪统一强度理论的屈眼函数形式，推导了柱形孔扩张问题应力场及位移场的统一计算公式，分析了不同模型、不同软化程度对柱形孔扩张时应力、位移及塑性区开展规律的影响。     

高地应力下硬岩的本构模型研究

传统的本构模型在模拟高地应力下硬岩破坏的范围和深度方面并不理想。针对高应力下的拉西瓦花岗岩,通过真三轴压缩试验模拟了开挖时应力路径的演化。在摩尔-库仑强度准则、格里菲斯强度准则、德鲁克-普拉格准则、双剪统一强度理论和霍克-布朗强度准则的基础上,考虑十二面单元体主剪面上主剪应力、正应力和静水压力的共同作用,提出了一个有关高应力下硬岩的三剪强度准则。根据试验结果,利用遗传算法全局寻优的功能,搜索出了三剪强度准则的参数。预测样本和与摩尔-库仑强度准则、德鲁克-普拉格准则、双剪统一强度理论的比较表明,该三剪强度准则与试验结果吻合,适用于高地应力下的硬岩。根据试验得到的应力-应变关系曲线,建立了基于三剪强度准则和应变软化的弹-脆-塑性本构模型,并用FLAC3D提供的基于C++的用户自定义模型工具UDM,创建了用户自定义模型的动态链接库,嵌入了FLAC3D软件。采用遗传算法-FLAC方法,搜索得到了基于岩石试样和岩体的本构模型参数。计算结果与实测情况吻合,表明建立的本构模型适用于高地应力下的硬岩,为高地应力下硬岩地下工程的安全性和稳定性分析奠定了基础。     

广义双剪屈服准则在岩石力学中的应用

本文就适合于岩石力学的广义双剪屈服准则、双剪帽子模型、双剪角隅模型以及与洛德(Lods)参数对应的双剪参数t_τ,利用有限元法结合实际工程中的算例进行了全面研究。初次用某高地应力区花岗岩进行的真三轴试验和计算结果表明,岩石强度符合广义双剪准则。双剪强度理论具有概念清晰,考虑了应力状态的各个分量,能够反映中间主应力效应等特点,并且可以节省大量工程投资,具有较大的经济价值。     

高应力区岩石统计损伤本构模型研究

为了反映高应力区岩石变形破坏全过程,通过引入双参数抛物线型Mohr强度准则,建立适用于高应力区岩体的微元强度度量方式,并假定由该度量方式得到的微元强度服从幂函数概率密度分布,结合连续损伤理论,考虑损伤变量修正,建立一个新的适用于高应力区岩体的统计损伤本构模型。以高应力区英安岩为验证对象,进行常规三轴压缩试验,依据岩石应力-应变曲线特征,给出模型参数确定方法。引用基于线性Mohr强度准则而建适用于浅部低应力水平岩体的相关统计损伤模型,利用该模型和所建模型对高应力区英安岩和相关文献中的高应力区砂岩、花岗岩试验数据进行验证,对比试验曲线和理论曲线,证明所建模型的可行性和适用性,并对英安岩累积损伤的扩展过程进行分析。     

空心圆柱砂岩真三轴试验研究

利用岩石空心圆柱扭剪试验系统针对灰砂岩进行真三轴试验研究,分别开展控制（σ2-σ3）（σ2为中间主应力,σ3为最小主应力）条件压缩试验和恒σ3、变σ2条件压缩试验,对灰砂岩的应力-应变规律、强度特性及破坏特征进行详细分析,并进一步探讨了中间主应力效应,最小主应力效应,应力洛德角效应以及强度准则的适用性。研究结果表明：岩石空心圆柱扭剪试验系统能够实现真三轴应力状态的模拟,相较于常规的实现方式,该方法可避免端部摩擦的影响;内外围压的压差对岩石强度有很大影响,尤其是在高围压下,较大的压差使得岩石强度迅速弱化导致剧烈破坏;中间主应力对岩石强度影响显著且具有区间效应,最小主应力对岩石强度有强化作用,该特点对于实际工程开挖岩体的高效及时支护具有重要的指导意义;进一步地,根据所获试验结果对现阶段用于描述岩石力学特性的强度准则进行分析,认为采用指数强度准则能合理反映岩石真三轴应力状态,具有较好的适用性,可用来评价实际工程中岩石的强度特征。     

基于统一强度理论的柱形孔扩张问题研究

考虑了岩土材料的软化和剪胀特性,利用空间轴对称问题的统一强度理论分析了柱形孔扩张问题,求出了岩土材料在柱形孔扩张时的应力场、应变场、位移场和最终扩张压力的统一解表达式。对蒋明镜-沈珠江扩孔公式从不同的方面作了论述。通过算例分析了岩土材料的软化和剪胀特性以及统一强度理论参数对应力场、位移场和扩张压力的影响。已有的关于该问题的Tresca解和Mohr-Coulomb解均为本文的一个特例。     

红砂岩长期强度特性的试验研究

岩石的流变特性是岩石的重要力学特性之一,其中岩石的长期强度是绝大多数岩土工程所必须引起重视的力学特性,然而就目前研究现状而言,与蠕变特性相比较是极不对称的。由岩石蠕变试验确定岩石的长期强度是现有最常用的方法,具有重要的现实意义。通过对完整红砂岩在CSS－2950岩石双轴流变试验机上进行的单轴压缩蠕变试验,利用过渡蠕变法、等时曲线法探讨了这些方法确定岩石长期强度在理论上的正确性和试验方法的可操作性,同时,将蠕变曲线与应力-应变曲线结合,提出了确定岩石长期强度的新方法,预测了岩石在荷载作用下可能破坏的时间。分析结果表明,将蠕变曲线与应力-应变曲线结合确定岩石长期强度对岩土工程设计具有重要的指导意义     

几种岩石强度准则的对比分析

采用常规三轴试验数据,以最小平均拟合差为评价指标定量地对比分析5种强度准则描述岩石非线性强度特征的适用性。结果表明：直线型Mohr-Coulomb准则不能描述岩石强度的非线性特征;抛物线型Mohr-Coulomb虽能描述岩石强度的非线性特征,但拟合误差较大,计算所得强度参数与事实不符,不宜使用;对于中低围压（ ）下岩石强度的非线性特征,单参数Bieniawski准则拟合精度与Hoek-Brown准则相当或稍好,拟合精度接近于指数强度准则,均优于双参数Bieniawski准则;在高围压下岩石强度非线性特征较为显著,应用单参数Bieniawski 准则或Hoek-Brown准则描述误差较大,三参数Bieniawski准则和指数强度准则拟合误差较小,可用于评价深部或特深部高应力状态下岩石的强度特征。     

广义非线性强度理论体系

广义非线性强度理论用一个表达式统一描述各种材料在 平面及子午面上的非线性强度特性,形成了一个全新的非线性强度理论系统,使非线性强度理论从适用于某一类特定材料的单一非线性强度理论发展到可以适用于众多不同材料的广义非线性强度理论,完善了强度理论体系。广义非线性强度理论包含了一系列现有的和可能有的单一非线性强度理论,如Mises准则、SMP准则等。利用土、岩石和混凝土强度试验结果验证了广义非线性强度理论适用于多种材料的优越性。     

统一强度理论在边坡稳定性分析中的应用

基于统一强度理论,以某高速公路路基边坡的典型断面为例,运用刚体极限平衡理论中的毕肖普简化法进行计算,得到不同的统一强度理论参数、不同的双剪应力状态参数与边坡稳定系数之间的关系。在此基础上,讨论了边坡问题的强度理论效应。通过分析可知,中间主应力在边坡稳定性分析中不容忽视。实际工程中,应根据具体边坡的岩土特征及应力状态确定统一强度理论参数和双剪应力状态参数,确切地反映岩土强度特性,界定稳定系数的上下限范围,有效地发挥材料的强度潜能,节约工程费用。      

The effect of the intermediate principal stress on the ultimate bearing capacity of a foundation on rock masses

In this paper, the strength envelope of rock masses is considered to follow a non-linear unified strength criterion that considers the effect of the intermediate principal stress. A unified slip line method for resolving the differential equation system that governs the stress field is established to research the ultimate bearing capacity, which can be adapted for a wide variety of rock masses. Through this new theory, a suitable characteristic method for rock masses of interest can be obtained, and the relationships between different types of characteristic methods are revealed. The characteristic methods are based on different strength criteria, such as the Hoek–Brown criterion, modified Hoek–Brown criterion, or non-linear twin-shear strength criterion; each of these criteria is a special case of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. In terms of the proposed theory, the ultimate bearing capacity with the Hoek–Brown criterion forms the lower bound; the ultimate bearing capacity with a non-linear twin-shear strength criterion forms the upper bound; and a series of the ultimate bearing capacities ranging between these two bounds may be derived from a non-linear unified strength criterion. A comparison is made between existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. It is shown that the present results are in good agreement with existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion.     

Effects of confining pressure and loading path on deformation and strength of cohesive granular materials: a three-dimensional DEM analysis

This paper is devoted to numerical analysis of strength and deformation of cohesive granular materials. The emphasis is put on the study of effects of confining pressure and loading path. To this end, the three-dimensional discrete element method is used. A nonlinear failure criterion for inter-granular interface bonding is proposed, and it is able to account for both tensile and shear failure for a large range of normal stress. This criterion is implemented in the particles flow code. The proposed failure model is calibrated from triaxial compression tests performed on representative sandstone. Numerical results are in good agreement with experimental data. In particular, the effect of confining pressure on compressive strength and failure pattern is well described by the proposed model. Furthermore, numerical predictions are studied, respectively, for compression and extension tests with a constant mean stress. It is shown that the failure strength and deformation process are clearly affected by loading path. Finally, a series of numerical simulations are performed on cubic samples with three independent principal stresses. It is found that the strength and failure mode are strongly influenced by the intermediate principal stress.

     

基于灰色理论的脆性岩石抗压强度尺寸效应试验研究

采用相同直径不同高度的圆柱形白色大理岩及灰岩试样进行单轴压缩试验研究,验证了脆性岩石抗压强度在一定范围内随高径比的增大而减小的规律。依据岩石单轴压缩试验结果,基于灰色预测GM（1,1）模型建立了脆性岩石的单轴抗压强度与试件高径比之间的非线形关系式,该经验公式对脆性岩石具有统一的形式,同时通过式中参数a值反映了由于岩性、试验条件等不同而引起的强度差异。利用该关系式可以很方便地在相关岩土工程中为相似岩石估算其强度值提供参考、借鉴。     

颗粒形态对离散介质剪切强度的影响

自然条件下,颗粒介质大多以非规则单元形态存在。非规则几何形态对颗粒介质的宏观力学性能有很大影响。针对颗粒单元的不同几何形态,采用团颗粒单元对离散介质的直剪试验过程进行了离散元数值计算,详细地讨论了颗粒形态对离散介质剪切强度的影响。该非规则颗粒由不同形态、不同数目、镶嵌尺寸、组合方位和颗粒大小的球形颗粒进行随机构造,其在局部与整体坐标之间的转动、力矩和方位关系通过4元素方法进行确定,基本球体颗粒之间的作用力采用具有Mohr-Coulomb摩擦定侓的Hertz-Mindlin非线性接触模型,并考虑了非线性法向粘滞力的影响。通过构造7种具有相同的质量概率分布的不同形态的团颗粒,在不同法向应力下,对团颗粒的直剪试验进行了离散元模拟,分析了不同形态颗粒的剪切强度。通过对不同形态颗粒介质剪切强度的数值分析,进一步揭示了非规则颗粒间的咬合互锁效应,为分析非规则颗粒的宏观动力特性提供了依据。     

一种岩石统计损伤本构模型的研究

基于岩石的非均质性,假设岩石微元粘聚力服从Weibull分布,微元破坏后其粘聚力降为0,结合统计理论和岩石剪切面上剪力平衡方程,建立了岩石发生剪切破坏时的损伤演化方程。该损伤演化方程考虑了破坏微元的抗压和抗剪能力,能够反映岩石峰后强度逐步丧失过程和残余强度。将该模型编入有限元程序,数值计算了不同围压下岩石应力-应变全过程曲线,与试验曲线比较取得了很好的一致性。     

Effects of particle size on crushing and deformation behaviors of rockfill materials

Strength and deformation behaviors of rockfill materials,key factors for determining the stability of dams,pertain strongly to the grain crushing characteristics.In this study,single-particle crushing tests were carried out on rockfill materials with nominal particle diameters of 2.5 mm,5 mm and 10 mm to investigate the particle size effect on the single-particle strength and the relationship between the characteristic stress and probability of non-failure.Test data were found to be described by the Weibull distribution with the Weibull modulus of 3.24.Assemblies with uniform nominal grains were then subjected to one-dimensional compression tests at eight levels of vertical stress with a maximum of 100 MPa.The yield stress in one-dimensional compression tests increased with decreasing the particle size,which could be estimated from the single-particle crushing tests.The void ratio-vertical stress curve could be predicted by an exponential function.The particle size distribution curve increased obviously with applied stresses less than 16 MPa and gradually reached the ultimate fractal grading.The relative breakage index became constant with stress up to 64 MPa and was obtained from the ultimate grading at the fractal dimension(a?2:7).A hyperbolical function was also found useful for describing the relationship between the relative breakage index and input work during one-dimensional compression tests.     

A bonded-particle model for cemented sand

We propose an extension of the Discrete Element Method for the numerical simulation of cemented sands, in which spherical particles are bonded together by elastic beams connecting the centers of the spheres. The parameters of this model are the strengths and stiffnesses of the bonds and particles. For small strains, the elasticity of the bond element is equal to the well-known linear finite-element Timoshenko beam element with reduced integration. The finite rotations are represented by unit quaternions. An efficient way to compute relative rotations and to decompose them into their components is presented.The results of triaxial compression tests on artificially cemented sands are used to verify that the model can capture the macroscopic behavior of such materials. The results show that peak stress mainly depends on the strength of the bonds and the number of initially bonded particles in the material. Results of triaxial tests with different cement contents are reproduced by the analysis. An important parameter of the model is the strength difference between tension and compression of the bond element. This property controls the influence of the confining pressure on peak strength. In the future, the model could be adapted to other types of bonded materials like asphalt or rock.     

中主应力对砂土抗剪强度影响的分析

土的抗剪强度参数一般通过三轴压缩试验确定。而三轴压缩试验中土的应力状态是轴对称的,这往往与实际工程中土体的受力情况不相同。因此,探讨一般应力条件下与三轴应力条件下强度指标之间的相互关系是至关重要的。基于砂土的空间滑动面强度准则即SMP准则,针对不同中主应力系数,通过数值分析探讨了中主应力系数对砂土抗剪强度指标的影响。分析结果表明,中主应力对土的抗剪强度指标具有显著的影响,一般地在平面应变条件下这种影响最大。