非线性Mohr-Coulomb准则适用范围及其改进研究

SINGH M为克服（Mohr-Coulomb M-C）准则只能线性表征岩石强度随围压变化这一局限性,在M-C准则的基础上添加一个修正项对其进行改进,提出非线性M-C准则。该准则认为,岩石在围压达到其单轴抗压强度时岩石就进入临界状态,此观点与部分岩石的试验结果有较大的出入,使得该准则的适用范围受到影响。为拓宽非线性M-C准则的适用范围,通过对其修正项的进一步改进,提出M-C准则修正一般表达式。应用11种岩石三轴试验数据对M-C准则修正一般表达式、非线性M-C准则和目前岩石力学界认为较好的双曲线型准则的精度进行比较,结果显示,M-C准则修正一般表达式对岩石三轴强度的拟合精度高于其他两种准则,且由岩石三轴试验强度的一致性更好。证明M-C准则修正一般表达式优于非线性M-C准则,且适用范围更广。     

临界状态围压在岩石强度准则改进中的应用

岩石强度准则一般是通过低围压岩石力学试验提出,这些准则在高围压下得到的岩石强度比实测强度偏大。为解决这一问题,提出岩石临界状态围压的概念,并推导得到当围压达到临界状态围压时,偏应力为常数,临界断裂角为45°,以广泛使用的Mohr-Coulomb和Hoek-Brown准则为例,将其应用到准则的改进中。通过完整岩石三轴试验数据对改进准则的准确性和适用性进行验证,分析结果表明：应用岩石临界状态围压改进的强度准则参数对围压变化的敏感度较低,其不仅保持了原准则在低围压时评估岩石强度的一致性、准确性,而且在高围压时其评估的强度与试验强度较一致,解决了高应力条件下原强度准则高估岩石强度的问题。     

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。     

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。     

锦屏大理岩卸荷本构模型与数值模拟研究

锦屏二级水电站深埋引水隧洞位于高地应力区,对取自隧洞内的大理岩进行常规三轴压缩试验、峰前卸围压试验。基于大理岩的峰前卸荷试验,研究峰前卸荷条件下岩石的变形、参数及破裂特征,建立峰前卸荷条件下岩石的幂函数型Mohr强度准则,给出数值仿真试验中大理岩的峰前卸载条件,利用有限差分程序FLAC3D建立了数值仿真模型,对模型进行了计算与分析,最后与室内试验结果对比,得到峰前卸荷状态下大理岩力学特性的相关规律。研究结果表明,幂函数型Mohr强度准则可较好地反映峰前卸荷条件下岩石的强度特性;卸围压初期,岩石试件呈现出明显的弹塑性特征;卸荷过程中岩石试件发生破坏时的峰值强度和围压降值随着围压增加而变大。研究结论揭示了锦屏大理岩卸载应力路径下的力学特性,具有一定的理论参考价值。     

不同应力路径下岩石三轴卸荷力学特性与强度准则研究EI北大核心CSCD

基于3种不同应力路径下花岗岩三轴卸荷试验,研究了岩石的应力-应变全过程曲线和变形特征及其强度准则。试验结果表明,卸围压过程中,侧向应变与围压先呈线性后呈非线性关系,且其增长速率约为轴向应变增长速率的3-5倍,表现出明显的侧向扩容,其扩容程度与卸载路径有关;从不同围压与体积应变曲线所围面积可以看出,卸荷前围压越大,卸荷释放的能量越大;变形模量随围压卸载而逐渐减小,且随初始围压增大,总体上呈负指数分布趋势,且同一种卸荷应力路径时,变形模量的减小量随初始围压增大有所增大,泊松比随围压降低而不断增大,两者之间呈现明显的非线性关系;岩石破坏特征以剪切破坏为主;采用幂函数型摩尔强度准则很好反应了岩石的强度特征。研究结果对地下金属矿深部开采具有一定的指导意义和参考价值。     

不同应力路径下岩石三轴卸荷力学特性与强度准则研究

基于3种不同应力路径下花岗岩三轴卸荷试验,研究了岩石的应力-应变全过程曲线和变形特征及其强度准则。试验结果表明,卸围压过程中,侧向应变与围压先呈线性后呈非线性关系,且其增长速率约为轴向应变增长速率的3～5倍,表现出明显的侧向扩容,其扩容程度与卸载路径有关;从不同围压与体积应变曲线所围面积可以看出,卸荷前围压越大,卸荷释放的能量越大;变形模量随围压卸载而逐渐减小,且随初始围压增大,总体上呈负指数分布趋势,且同一种卸荷应力路径时,变形模量的减小量随初始围压增大有所增大,泊松比随围压降低而不断增大,两者之间呈现明显的非线性关系;岩石破坏特征以剪切破坏为主;采用幂函数型摩尔强度准则很好反应了岩石的强度特征。研究结果对地下金属矿深部开采具有一定的指导意义和参考价值。     

考虑应变率效应的广义Hoek-Brown动态强度准则

岩石强度特性具有明显的围压效应和应变率效应,研究复杂应力状态下动态强度准则对于岩石动力学分析至关重要。利用10~(-5)~10~(2.32) s~(-1)应变率范围内砂岩静动态间接拉伸和单、三轴压缩强度试验数据,进行了广义Hoek-Brown强度准则预测砂岩动态强度的适用性研究,分析了材料参数的应变率效应。结果表明,广义Hoek-Brown强度准则能够较好地描述同一应变率下较低拉应力区到较高压应力区砂岩强度规律,低应变率区单轴抗压强度c_s和参数a变化不大,高应变率区随应变率的增加非线性增大,而参数m几乎不受应变率影响。基于分析建立了单轴抗压强度c_s和参数a的应变率效应函数关系,提出了由低应变率到高应变率下的广义Hoek-Brown动态强度准则统一表达式,进一步探讨了岩石强度依赖应变率效应和围压效应的物理机制。     

不同破坏准则下水合物沉积物的统计损伤模型

利用连续介质损伤力学理论与概率统计方法,假设水合物沉积物微元强度服从Weibull分布,在现有室内三轴和直剪试验数据的基础上,考虑水合物饱和度的影响,分别建立了基于修正Mohr-Coulomb强度准则和修正Lade-Duncan强度准则的水合物沉积物统计损伤本构模型,并将理论模型预测结果与室内试验进行对比,验证了模型的有效性。结果显示：基于Lade-Duncan强度准则的损伤本构模型能够较准确地反映水合物沉积物峰前的应力?应变规律,而基于修正Mohr-Coulomb强度准则的损伤本构模型则对于模拟峰后的应变软化特征有较好的适用性。对于在低有效围压、不同水合物饱和度条件下的水合物沉积物,基于修正Mohr-Coulomb强度准则的损伤本构模型的模拟精确性要优于基于修正Lade-Duncan准则的损伤模型;而在同一饱和度、不同有效围压条件下,基于修正Lade-Duncan强度准则的损伤本构模型的模拟结果则要优于基于修正Mohr-Coulomb强度准则的损伤本构模型。     

基于Hoek-Brown的岩石横观各向同性屈服准则研究

为了描述岩石强度的各向异性特征,通过引入材料的微结构张量,考虑单轴抗压强度σ_cβ随层理倾角β而变化,提出了基于微结构张量的修正Hoek-Brown屈服准则。开展不同层理倾角(0°、15°、30°、45°、60°、75°和90°)的页岩试样不同围压(0、5、10、15和20 MPa)下的三轴压缩试验,结果显示,页岩峰值强度与层理倾角β呈"U"形曲线关系,在围压较低时呈"肩"形曲线关系,弹性模量E_t和泊松比ν对围压不敏感,其平均值随层理倾角β的变化关系分别呈倒"U"形、"肩"形。页岩的微观和宏观破坏图像表明,其破坏模式受围压和层理倾角双重控制。试验值与模型预测值的对比表明,修正的Hoek-Brown屈服准则可较好地对页岩强度的各向异性进行模拟。同时,采用Koteshwar千枚岩、Koteshwar板岩、绿泥石片岩等层状结构岩石的单轴和三轴压缩试验数据,进一步验证了提出的修正Hoek-Brown屈服准则对多数具有层理结构的横观各向同性岩石峰值强度模拟具有普遍适用性,并对屈服准则在试验数据较多和较少情况下的峰值强度模拟效果进行了评价。     

Application of the Christensen Failure Criterion to Intact Rock

The Christensen criterion, originally introduced in materials science, has a simple mathematical form and uniaxial tensile and compressive strength as the only parameters, making it an attractive candidate for rock engineering purposes. In this study, the applicability of the criterion to rock materials is examined. Explicit equations for application of the criterion under biaxial, triaxial compression, triaxial extension, and polyaxial states of stresses are derived. A comprehensive strength data set including the results of tests on synthetic rock, chert dyke, Carrara marble and Westerly granite is utilized to examine the accuracy of the Christensen criterion to the failure of rock material. The two surprising findings about the Christensen criterion are the zero values of tensile strength and the very low slopes of the failure envelope obtained from fitting analyses for chert dyke and Westerly granite. It is shown that the two problems are interrelated and the values of tensile strength tend to zero to produce higher slopes. It is then mathematically proven that the maximum initial slope of the Christensen failure envelope is limited to 4 in triaxial compression and 2.5 in triaxial extension which is considerably lower than the slope of experimental data. The accuracy of the Christensen criterion was found to be significantly lower than the well-established Hoek–Brown criterion. The circular π-plane representations and brittle-to-ductile transition limits from the Christensen criterion are also inconsistent with the observed behavior of rocks.     

A Simplified Failure Criterion for Intact Rocks Based on Rock Type and Uniaxial Compressive Strength

The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available.     

Experimental research on mechanical characteristics and strength criterion of rock of triaxial unloading tests under different stress pathsEI北大核心CSCD

By carrying out triaxial unloading test under different stress paths on rock, the complete stress-strain curves, deformation characteristics and its strength criterion are studied. The test results show that the relation between lateral strain and confining pressure firstly is linear, and then is nonlinear in the total stage of unloading confining pressure. And its growth rate is about 3 to 5 times the growth rate of the axial strain. It shows obvious lateral dilatancy, and the degree of dilatancy is related to the unloading path. According to the area that is enclosed by confining pressure and volumetric strain curve, it can be seen that the greater the confining pressure is before unloading, the more the energy releases. Deformation modulus decreases gradually with the unloading confining pressure, and increases with the initial confining pressure; the relation between deformation modulus and confining pressure shows negative exponential distribution overall. At the same unloading paths, the reduction of the deformation modulus increases with the increase of initial confining pressure. The Poisson's ratio rises up continually, and the variation law with the confining pressure can be well described by nonlinear. Failure characteristics of rock are mainly shear failure. The strength characteristics of rock can be well characterized by using the Mohr strength criterion of power function. These conclusions provide reliable theoretical reference and guiding significance for the deep mining of the underground metal mine.     

砂岩试验强度与强度准则预测结果对比分析

对山西大同煤峪口矿巷道砂岩进行了巴西劈裂、单轴和常规三轴试验,分析了其变形和强度特性,以整体平方根误差最小为依据拟合确定了5种强度准则参数,比较各准则的整体拟合效果以及抗拉强度和抗压强度预测值与试验值之间的差异。结果表明:砂岩单轴和低围压下的脆性特征显著,随着围压增大屈服段明显增加,逐渐由脆性向延性转变;对试验数据的整体拟合效果,Mohr-Coulomb准则最不理想,指数强度准则最好,Hoek-Brown准则和Bieniawski准则相接近;对抗拉强度的预测,Mohr-Coulomb准则明显高估了砂岩的抗拉强度,不适合预测抗拉强度,指数强度准则最为理想,Bieniawski准则不能反映岩石抗拉特性;单轴和不同围压下砂岩强度,直线型Mohr-Coulomb准则偏离了大多数试验数据点,特别是高围压下偏离显著结果失真,Hoek-Brown准则和Bieniawski准则预测结果几乎一致,Sheorey准则高围压下预测结果稍有偏高,指数强度准则接近大多数试验数据,预测效果最佳。      

冻结粉土强度准则探讨

冻土的强度随围压的增加呈先增大后减小的趋势,通过修正子午面内q-p曲线的斜率M*来探讨冻土强度变化规律。基于摩尔圆和包络线定理,推导了冻土内摩擦角随平均正应力的变化规律。假定偏应力的大小采用Mohr-Coulomb和Von-Mises强度准则的组合形式表示,将内摩擦角引入到偏平面中获得了偏平面内的强度准则。在不同温度（-6、-10、-15 ℃）和0.3～15.0 MPa围压下对冻结粉土进行了一系列低温三轴压缩试验,根据试验结果确定了子午面和偏平面的相关强度参数。结果表明：（1）子午面内的强度准则能较好模拟冻土在低围压下的强化效应和高围压下的弱化效应;（2）内摩擦角随平均正应力增大呈先增大后减小的趋势;（3）随控制参数s的增加,在偏平面内偏应力由Mohr-Coulomb包络线逐渐向Von-Mises包络线转化,其形状大小与极限强度值呈一一对应关系。最后通过试验结果与已有的强度准则对比表明：修正的强度准则具有一定的适用性。     

Experimental Investigation on the Strength, Deformability, Failure Behavior and Acoustic Emission Locations of Red Sandstone Under Triaxial Compression

Conventional triaxial compression and “reducing confining pressure” experiments were carried out for red sandstone by an MTS815 Flex Test GT rock mechanics experimental system. Our results show that the post-peak axial deformation characteristics of red sandstone changed as the confining pressure was increased from 5 to 65?MPa. Young’s modulus of red sandstone increased nonlinearly with increasing confining pressure, but Poisson’s ratio remained unaffected. Using our new data, the compactive and dilatant behavior, strength and failure characteristics of sandstone under triaxial compression are further discussed. For our data, the nonlinear Hoek-Brown criterion better reflects the peak strength properties than the linear Mohr-Coulomb criterion. However, the residual strength shows a clear linear relationship with confining pressure, which can be best described using the linear Mohr-Coulomb criterion. The peak and residual strengths were not directly related to the two different loading paths. The onset of dilatancy (C′), the switch from compaction-dominated to dilatant-dominated behavior (D′) and the stress at zero volumetric strain all increased linearly with the confining pressure. In our conventional triaxial compression experiments, the failure mode changed from mixed tension and shear fracture (single shear fracture) to shear fracture with double slippage planes with increasing confining pressure. However, the failure mode in our “reducing confining pressure” experiments was more complicated and results mainly from the unstable failure characteristics of the rock during the reduction in confining pressure. Finally, based on our acoustic emission (AE) locations, at a confining pressure of 35?MPa, a detailed analysis of the evolutionary process of internal cracks is presented for the entire loading process.