Artificial neural networks as a basis for new generation of rock failure criteria

Conventional methods for prediction of rock strength are based on using classical failure criteria. In this study, artificial neural networks were regarded as new tools for considering the strength of intact rock in a wide range of loading condition from uniaxial tension to triaxial compression. A comprehensive data set of the values of major and minor principal stresses at failure from 1638 laboratory tests on seven rock types was collected. For each rock type, data were randomly divided into two subsets, training and test sets. Neural networks were trained using training sets to predict the value of major principal stress at failure from uniaxial compressive stress and minor principal stress. Small architecture and regularization method were adopted to avoid over-fitting problems. The same training sets were used in determining the constants of two popular empirical failure criteria, namely Bieniawski–Yudhbir and Hoek–Brown. Then, the test sets were used to examine the accuracy and generalization of the models in predicting the strength in new situations. Comparison of the results of the neural network models with those of the empirical criteria showed that the former approach always lead to less root mean squared error and higher coefficient of determination. On average, for different rock types, using ANN models led to about 30% decrease in prediction error relative to best empirical models. These models also showed better flexibility in the prediction of major principal stress at failure in both brittle and ductile failure regimes.     

Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks

Triaxial or polyaxial strength of rocks is required while analysing many civil and mining engineering structures in rocks. Mohr–Coulomb criterion is the most widely used strength criterion in rock engineering problems. In its present form the criterion suffers from two major limitations. Firstly, it represents the strength of rock as a linear function of confining pressure. Secondly, the effect of intermediate principal stress is not considered by this criterion. In the present study, this criterion is modified to take into account the non-linearity and effect of intermediate principal stress on strength behaviour. Barton's [1] critical state concept for rocks has been employed for this purpose. The applicability of the proposed simple non-linear triaxial and polyaxial strength criteria has been verified by applying them to experimental results for the intact isotropic rock material available from literature and comparing the prediction with the other popular criteria in vogue. The agreement has been found to be excellent. The applicability of the concept to jointed rocks will be discussed in separate publication.     

复杂应力状态下岩体强度的各向异性研究

 岩体中存在着大量的节理裂隙等不连续面,这些不连续面对岩体的强度起着重要的作用,岩体可能会沿着这些不连续面发生破坏。在分析中间主应力对岩体强度影响的基础上,验证统一强度理论,并在此基础上,建立可以反映中间主应力变化的强度参数,同时采用试验对其进行验证。针对含有不连续面的岩体,分析不连续面上的应力分布,建立复杂应力条件下的岩体各向异性强度准则,并针对该强度的特殊情况作简化,分析适用条件。采用节理岩体的真三轴试验对其验证,结果表明所建立的各向异性强度准则可以恰当的反映岩体的强度。分析中间主应力,结构面倾角和走向对岩体强度的影响。     

Mine-by试验洞开挖过程中围岩应力路径与破坏模式分析

 地下洞室开挖过程中,围岩经历了复杂的应力路径,正确刻画围岩的应力路径及其影响是岩石地下工程中亟待解决的关键科学问题。基于起裂判据(CIC)、扰动应力比( )和Lode参数等力学表征指标,采用FLAC3D对Mine-by试验洞掌子面掘进过程中围岩的复杂应力路径和破坏模式进行探讨。研究表明：围岩应力场的扰动主要集中在掌子面前后一倍洞径范围内,围岩损伤受掌子面附近高度集中的偏应力和应力主轴旋转支配;随掌子面掘进,围岩顶部和底部偏应力集中程度加大,应力比n逐渐降低,逐步形成V型剥落,而隧洞边墙部位逐渐卸荷,损伤破裂转变为拉应力控制;原位岩体的应力路径涉及应力主轴旋转效应,远比实验室的单调加载路径复杂,Mine-by试验洞开挖过程中,在掌子面的顶部和底部,围岩大主应力方向几乎没有转动,而中主应力和小主应力旋转一定角度(35.2°)后回到初始方向,由于中主应力超过了岩体起裂强度(CIC＞1),其方向的旋转加剧了围岩的损伤程度。相关认识和结论具有一定的理论和工程意义。     

Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—Insight from numerical modeling

The influence of the intermediate principal stress on rock fracturing and strength near excavation boundaries is studied using a FEM/DEM combined numerical tool. A loading condition of σ₃=0 and σ₁≠0, and σ₂≠0 exists at the tunnel boundary, where σ₁, σ₂, and σ₃, are the maximum, intermediate, and minimum principal stress components, respectively. The numerical study is based on sample loading testing that follows this type of boundary stress condition. It is seen from the simulation results that the generation of tunnel surface parallel fractures and microcracks is attributed to material heterogeneity and the existence of relatively high intermediate principal stress (σ₂), as well as zero to low minimum principal stress (σ₃) confinement. A high intermediate principal stress confines the rock in such a way that microcracks and fractures can only be developed in the direction parallel to σ₁ and σ₂. Stress-induced fracturing and microcracking in this fashion can lead to onion-skin fractures, spalling, and slabbing in shallow ground near the opening and surface parallel microcracks further away from the opening, leading to anisotropic behavior of the rock. Hence, consideration of the effect of the intermediate principal stress on rock behavior should focus on the stress-induced anisotropic strength and deformation behavior of the rocks. It is also found that the intermediate principal stress has limited influence on the peak strength of the rock near the excavation boundary.     

基于改进双剪统一强度理论的围岩松动圈分析

为了研究岩石应变软化、剪胀性质、中间主应力和拉压不等特性对围岩松动圈的影响,基于改进双剪统一强度理论,得到了隧道围岩松动圈半径、围岩应力及洞壁位移的解析表达式。通过与已有方法计算结果的对比,验证了该方法的可行性,并进一步分析了中间主应力大小以及软化程度对结果的影响。研究结果表明:(1)随着软化模量的降低,隧道围岩塑性区、松动区(圈)半径以及洞壁位移均逐渐减小;(2)中间主应力大小对隧道围岩弹塑性行为具有一定的影响,随着中间主应力系数b的增大,围岩的切向应力在塑性软化区、破碎区内变大,而在弹性区内减小,围岩的径向应力在3个区域内均增大;(3)隧道洞壁位移随着中间主应力系数b的增大而减小;(4)考虑中间主应力的影响以及围岩软化的程度,能够充分发挥围岩的强度潜能,合理指导隧道布置、支护设计与施工。该结果为隧道围岩松动破裂分析提供了理论依据,具有一定的工程参考价值。     

岩石指数型强度准则在主应力空间的特征

 指数型强度准则利用显式函数表示最小主应力和中间主应力对强度的影响,强度准则参数具有明确的力学含义;常规三轴压缩强度表明,随着正应力增大,剪切强度趋于常数,而破裂角趋于45°;但Mohr应力圆与外包络线在切点附近差异较小,且岩石并非均匀各向同性材料,实际破裂角与理论破裂不会完全一致。真三轴试验数据的离散性较大,强度准则参数对拟合偏差的影响并不显著,而以最小拟合偏差确定的参数未必体现岩石的真实力学性质。在研究强度准则在主应力空间内的力学特征之后,建议依据应力趋于无限时中间主应力与最小主应力对强度的影响系数在s2 = s3处相等来确定强度准则参数,由此得到的拟合误差并未显著增大。     

基于统一强度理论的软岩损伤统计本构模型研究

基于统一强度理论，在考虑洛德参数的基础上，得到随洛德参数和中间主应力系数变化的材料统一强度参数，建立可以考虑中间主应力的统一强度理论平面形式的强度准则。假定软岩微元强度分布统计概率，定义软岩的统计损伤变量，依据统一强度理论建立三轴应力状态下软岩的损伤统计本构模型。通过软岩的常规三轴试验结果对其进行验证，对偏应力-应变的理论结果与试验结果进行比较。研究结果表明，该本构模型能够较好地反映软岩的偏应力-应变关系，尤其是应变软化特性。而且依据统一强度理论和统一强度内摩擦角的发挥，进一步分析表明洛德参数以及中间主应力系数b对偏应力一应变关系有影响，软岩的偏应力-应变曲线先随洛德参数的增大而上升到一定值，而后随洛德参数的增大而降低；随中间主应力系数b的增大而不断增加。     

基于Mogi-Coulomb强度准则的隧道围岩理想弹塑性解答

合理选择岩石强度准则对隧道应力及位移预测和支护设计都具有重要意义,基于MogiCoulomb强度准则和理想弹塑性模型,通过中间主应力系数反映中间主应力的影响,推导了圆形隧道围岩应力和位移的解析解,并对所得结果进行比较与验证,得到了中间主应力和围岩抗剪强度参数的影响特性。研究表明:具有广泛的适用性和较好的可比性,Mohr-Coulomb强度准则解答和Matsuoka-Nakai准则解答均为其特例;结果关于中间主应力系数b=0.5对称,较好地反映了岩石强度的中间主应力效应及其区间性;粘聚力及内摩擦角对围岩塑性区半径和隧道洞壁位移的影响显著,应充分考虑中间主应力影响及围岩抗剪强度参数变化对隧道设计与施工的影响。     

统一强度理论的试验数据拟合及评价

 基于中间主应力对岩石强度影响,统一强度理论可作为Coulomb准则的推广,并已得到广泛的研究和使用。利用已有的8种岩石真三轴试验结果,研究强度准则参数的确定方法以及相应的拟合误差。依据常规三轴压缩强度与围压的关系确定Q和K,再依据真三轴的强度确定参数b,统一强度理论所给出的双折线难以描述强度变化的整体趋势,对部分岩石试验数据的拟合误差超过Coulomb准则;如果以最小拟合误差为目标,对参数Q,K和b进行协同搜索,那么统一强度理论可以有较小的拟合误差,但其给出的部分岩石常规三轴压缩强度明显偏离实际结果。此外,统一强度理论认为岩石三轴伸长强度与常规三轴压缩强度相同,在最小主应力恒定时中间主应力引起的强度最大增加值随最小主应力线性增加,且强度关于中间主应力的一阶导数在峰值点是不连续的,这些都与试验结果不能完全协调。由于真三轴压缩试验结果还较少,中间主应力的试验范围也较小,而数据的离散性又较大,以最小拟合误差确定的强度准则能否适用于实际工程的分析计算,需要更深入的研究。     

Peak shear strength prediction for discontinuities between two different rock types using a neural network approach

The peak shear strength of discontinuities between two different rock types is essential to evaluate the stability of a rock slope with interlayered rocks. However, current research has paid little attention to shear strength parameters of discontinuities with different joint wall compressive strength (DDJCS). In this paper, a neural network methodology was used to predict the peak shear strength of DDJCS considering the effect of joint wall strength combination, normal stress and joint roughness. The database was developed by laboratory direct shear tests on artificial joint specimens with seven different joint wall strength combinations, four designed joint surface topographies and six types of normal stresses. A part of the experimental data was used to train a back-propagation neural network model with a single-hidden layer. The remaining experimental data was used to validate the trained neural network model. The best geometry of the neural network model was determined by the trial-and-error method. For the same data, multivariate regression analysis was also conducted to predict the peak shear strength of DDJCS. Prediction precision of the neural network model and multivariate regression model was evaluated by comparing the predicted peak shear strength of DDJCS with experimental data. The results showed that the capability of the developed neural network model was strong and better than the multivariate regression model. Finally, the established neural network model was applied in the stability evaluation of a typical rock slope with DDJCS as the critical surface in the Badong formation of China.

     

三维地应力BWSRM测量新方法及其测井机器人在重大工程中的应用

地壳上层岩体的应力状态是地壳最重要的性质之一,获取岩体应力状态最直接、可靠的手段是原位地应力测量.首先简要回顾地应力测量的研究历程及其发展现状,分析岩石力学与工程中常用的几种地应力测量方法和技术.重点介绍钻孔局部壁面应力解除法(BWSRM)这一新的三维地应力测量方法的原理,以及基于BWSRM的地应力测井机器人研制过程和...     

主应力对洞室围岩失稳破坏行为的影响研究

 针对复杂应力环境三向应力状态下地下洞室围岩破坏条件和破裂机制,采用统计损伤理论和数值模拟方法,建立三维非均匀性地质模型,考虑应力的三维效应,引入强度折减法,一方面在保持模型边界条件的同时实现洞室围岩的逐步破坏,另一方面以此定量评价不同应力场中洞室安全稳定状况,探讨不同侧压力系数和轴向应力条件下洞室围岩破坏模式,探究中间主应力对洞室稳定性的影响以及深部岩体分区破裂化现象产生条件和破裂规律等。结果表明,侧压力系数影响洞室围岩初始破裂形成部位和发展趋势;不同的轴向应力使得洞室围岩破裂区域和范围显著不同,在不同的侧压力系数条件下,轴向应力影响洞室稳定的规律存在差异;不同方向中间主应力对洞室围岩安全稳定状况的影响是不同的;当洞室轴线方向与最大水平应力方向平行时,较大的轴向应力会使洞室围岩产生分区破裂化现象,围岩破坏的区域也是拉应变集中的区域等。这些结果对进一步揭示地下洞室围岩非线性变形破坏行为,评价岩土工程安全稳定性,采取合理的支护措施等均具有重要意义。     

Effect of principal stress axis rotation on cyclic plastic deformation characteristics of unsaturated base course material

It is generally observed that the stress state induced through traffic loads inside the substructure of pavements cannot be exactly reproduced in laboratory element tests. Moreover, there are not sufficient studies that examine the behavior of granular material under unsaturated conditions, although such conditions are very prevalent in pavement structures. In this research, an attempt is made to determine the cyclic plastic deformation characteristics of unsaturated granular base course material, and to examine the effect of the rotation of the principal stress axis (experienced by pavement elements under traffic loads) on the mechanical behavior of unsaturated granular base course material by applying various loading methods. A series of laboratory element tests using a multi-ring shear apparatus, which can take into account the rotation of the principal stress axis, were carried out on granular base course material under different moisture contents. The experimental results show that the moisture content has an obvious effect on both the shear behavior and the cyclic plastic deformation of granular base course material. However, the moisture content for the maximum deformation of granular base course material varies according to the loading method. It is also explained that cyclic plastic deformation considerably increases due to the rotation of the principal stress axis under repeated axial and shear loading tests. Therefore, the principal stress axis rotation has a significant influence on the cyclic plastic deformation of unsaturated granular base course material.     

真三轴应力条件下层状复合岩石破坏准则

 为探究层状复合岩石的强度特性,利用均质化理论方法,将层状复合岩石虚拟为一种等效的均质岩石,建立了真三轴应力条件下基于MLC准则的层状复合岩石破坏准则,该准则由层状复合岩石各组分的强度参数以及几何参数来确定;同时,利用自行研制的多功能真三轴流固耦合试验系统,进行细砂岩、粉砂岩、板岩和层状复合岩石在三向不等应力条件(体应力不变,改变应力罗德角、等中主应力系数等?3)下的真三轴试验,研究层状复合岩石的强度特性以及中间主应力和中主应力系数对复合岩石强度的影响。真三轴试验结果表明,所建立的准则能较好的描述层状复合岩石的强度特征,可为解决层状岩石工程结构的强度及稳定性问题提供了理论参考和依据。     

多轴应力对深埋硬岩破裂行为的影响研究

 针对深埋硬岩在多轴应力条件下的破坏特征,在笔者所在课题组工作的基础上,提出能够反映岩石在多轴应力作用下力学参数随塑性内变量的演化关系以及中间主应力和最小主应力对深埋硬岩脆延转换行为影响的岩体局部劣化模型(rock mass local deterioration model,RLDM),该模型考虑真实岩体应力状态对岩体力学行为的控制作用,并嵌入到自行开发的三维弹塑性细胞自动机软件系统中,而基于局部作用原理的细胞自动机方法能够方便地考虑岩石破坏过程中局部力学参数的动态更新。实验室尺度岩样的破坏过程模拟,较好地反映了随着围压的升高,岩石由脆性向延性转化的试验现象;工程尺度的锦屏二级水电站引水隧洞破坏行为模拟,获得的隧洞破裂模式较好地反映现场实际破坏现象,从而验证模型和模拟方法的正确性和合理性。在此基础上,以深埋硬岩为研究对象,分别考虑不同侧压力系数、不同中间主应力大小和方向,分析多轴应力对深埋硬岩破裂行为的影响,解释造成深埋硬岩隧洞复杂破裂模式的原因。结果表明,最小主应力升高使深埋隧洞的稳定性增强;深埋隧洞围岩的稳定性具有中间主应力效应及其区间性的特征。     

Triaxial extension and tension tests on lime-cement-improved clay

This paper presents the results of a series of undrained and drained isotropic consolidated triaxial extension, tension and compression laboratory tests on lime-cement-improved very soft clay. The main objective of these tests was to investigate the material strength and stiffness properties for stress conditions similar to those expected on the passive side of excavations where a retaining structure is supported by Deep Mixing columns. The different stress paths to failure were obtained by varying the directions of the major and minor principal stresses in a conventional triaxial test cell. The undrained tests conducted at low consolidation stresses, corresponding to depths of approximately 0–10 m below the ground surface, revealed significant differences in undrained strength depending on the directions of the major and minor principal stresses, indicating anisotropic material behavior. Based on the undrained triaxial test results, the relationship among the undrained strength, the effective consolidation stress and the over-consolidation ratio (OCR) is presented for different stress paths to failure.The experimental data from the drained tests show that a failure surface comprised of a shear failure function based on the Mohr-Coulomb failure criterion and a tensile failure function based on the tensile strength and the confining stress can be applied for lime-cement-stabilized clay.     

高地应力下岩石的真三轴试验研究

通过真三轴试验模拟高地应力条件下地下工程开挖引起的复杂的应力路径的演化。在设定的加载方式下，针对拉西瓦新鲜花岗岩的试验结果表明：当卸载最小主应力时，岩石发生回弹变形，声发射计数率比卸载前显著增加，增加的幅度随中间主应力的增加而逐渐提高。岩石的应力一应变关系为弹脆性，峰值强度随中间主应力的增加有所提高，峰值强度的提高值与中间主应力的比值随中间主应力的提高逐渐减小。声发射计数率峰值与应力水平有关，峰值的次数与破坏后主裂缝的条数相对应。最后，分析了岩石的破坏机制。     

Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution

Tensile strength of rock is among the most important parameters influencing rock deformability, rock crushing and blasting results. To calculate the tensile strength from the indirect tensile (Brazilian) test, one must know the principal tensile stress, in particular at the rock disc center, where a crack initiates. This stress can be assessed by an analytical solution. A study of this solution for anisotropic (transversely isotropic) rock is presented.

The solution is given explicitly. The key expansion coefficients are obtained from a complex-valued 2×2 matrix equation. The convergence of the solution is greatly improved by a new procedure. It is shown that the dimensionless stress field depends only on two intrinsic parameters, E′/E and b. The stress at the center of the disc is given in charts as a function of these parameters (and the angle θ_b between the direction of applied force and the plane of transverse isotropy). Furthermore, a new, reasonably accurate, approximate formula for the principal tension at the disc center, (0,0), is derived from the analytical solution:

where

The elastic parameters of rock in two perpendicular directions were measured in the laboratory. The result of the stress analysis was applied in calculating the indirect tensile strength of gneiss, which has a well-defined foliation plane (transversely isotropic). When the results were compared with the tensile strength of rock obtained by using a conventional formula that assumes isotropic material, there was a significant difference. Moreover, good agreement was observed for the tensile strength calculated from the stress charts and the proposed formula, when compared with other published stress charts.     

考虑中间主应力的横观各向同性深埋圆隧弹塑性解

平面应变条件下的深埋圆形交通隧道问题一般忽略中间主应力影响,但塑性区围岩的变形与实际情况会产生较大差异。岩土与地下工程中多遇到层状岩体,常将其处理为横观各向同性固体材料。充分考虑中间主应力对深埋圆形隧道的影响,基于平面应变假设得出了与横观各向同性材料相适应的Drucker-Prager准则并将其与Mohr-Coulomb准则精确匹配,在此基础上推导了考虑剪胀特性的横观各向同性理想弹塑性材料在塑性阶段的中间主应力表达式;根据所得的中间主应力表达式,推导出横观各向同性深埋圆形隧道围岩塑性区应力位移解析式;结合实际算例,分析了横观各向同性参数与围岩剪胀角对横观各向同性深埋圆形公路隧道围岩塑性区位移的影响规律。为深埋圆形交通隧道的计算和设计提供更为合理的理论基础。