A generalized nonlinear three-dimensional Hoek‒Brown failure criterion

To understand the strengths of rocks under complex stress states,a generalized nonlinear threedimensional(3D)Hoek‒Brown failure(NGHB)criterion was proposed in this study.This criterion shares the same parameters with the generalized HB(GHB)criterion and inherits the parameter advantages of GHB.Two new parameters,b,and n,were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression,respectively.The NGHB criterion can consider the influence of intermediate principal stress(IPS),where the deviatoric plane shape satisfies the smoothness requirements,while the HB criterion not.This criterion can degenerate into the two modified 3D HB criteria,the Priest criterion under triaxial compression condition and the HB criterion under triaxial compression and tension condition.This criterion was verified using true triaxial test data for different parameters,six types of rocks,and two kinds of in situ rock masses.For comparison,three existing 3D HB criteria were selected for performance comparison research.The result showed that the NGHB criterion gave better prediction performance than other criteria.The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions.

Estimating shear strength of high-level pillars supported with cemented backfilling using the HoekeBrown strength criterion

Deep metal mines are often mined using the high-level pillars with subsequent cementation backfilling(HLSCB)mining method.At the design stage,it is therefore important to have a reasonable method for determining the shear strength of the high-level pillars(i.e.cohesion and internal friction angle)when they are supported by cemented backfilling.In this study,a formula was derived for the upper limit of the confining pressure σ3max on a high-level pillar supported by cemented backfilling in a deep metal mine.A new method of estimating the shear strength of such pillars was then proposed based on the Hoek eBrown failure criterion.Our analysis indicates that the horizontal stress σhh acting on the cemented backfill pillar can be simplified by expressing it as a constant value.A reasonable and effective value for σ3max can then be determined.The value of s3max predicted using the proposed method is generally less than 3 MPa.Within this range,the shear strength of the high-level pillar is accurately calculated using the equivalent MohreCoulomb theory.The proposed method can effectively avoid the calculation of inaccurate shear strength values for the high-level pillars when the original HoekeBrown criterion is used in the presence of large confining pressures,i.e.the situation in which the cohesion value is too large and the friction angle is too small can effectively be avoided.The proposed method is applied to a deep metal mine in China that is being excavated using the HLSCB method.The shear strength parameters of the high-level pillars obtained using the proposed method were input in the numerical simulations.The numerical results show that the recommended level heights and sizes of the high-level pillars and rooms in the mine are rational.

Nonlinear empirical failure criterion for rocks under triaxial compression

Based on existing triaxial compression experimental data,a new empirical failure criterion with wide applicability was proposed considering hydrostatic pressure,second stress invariance,and maximum shear stress.Four fitting evaluation indicators were used to verify the consistency of the new failure criterion,and the differences with the other 6 failure criteria were discussed.The characteristics of the new failure criteria in the principal stress space were finally analyzed.The results indicate that(1)the new failure criterion exhibits strong predictive ability for triaxial experiments and has good applicability for both intact and jointed rocks;(2)the influence of hydrostatic pressure on the failure surface exhibits a non-linear trend,and different hydrostatic pressure also exhibits different distribution patterns on the deviatoric stress plane,with a distribution characteristic pattern of hexagonal snowflake-regular hexagon.The maximum shear stress has a torsional effect on the new criterion,in the three-dimensional failure surface.The parameters a and b of the rock have an impact on the failure surface morphology of the new criterion function on the offset surface.

Rockburst criterion and evaluation method for potential rockburst pit depth considering excavation damage effect

Excavation-induced disturbances in deep tunnels will lead to deterioration of rock properties and formation of excavation damaged zone(EDZ).This excavation damage effect may affect the potential rockburst pit depth.Taking two diversion tunnels of Jinping II hydropower station for example,the relationship between rockburst pit depth and excavation damage effect is first surveyed.The results indicate that the rockburst pit depth in tunnels with severe damage to rock masses is relatively large.Subsequently,the excavation-induced damage effect is characterized by disturbance factor D based on the Hoek-Brown criterion and wave velocity method.It is found that the EDZ could be further divided into a high-damage zone(HDZ)with D=1 and weak-damage zone(WDZ),and D decays from one to zero linearly.For this,a quantitative evaluation method for potential rockburst pit depth is established by presenting a three-element rockburst criterion considering rock strength,geostress and disturbance factor.The evaluation results obtained by this method match well with actual observations.In addition,the weakening of rock mass strength promotes the formation and expansion of potential rockburst pits.The potential rockburst pit depth is positively correlated with HDZ and WDZ depths,and the HDZ depth has a significant contribution to the potential rockburst pit depth.

Enhanced Hoek-Brown(H-B)criterion for rocks exposed to chemical corrosion

Underground constructions often encounter water environments,where water–rock interaction can increase porosity,thereby weakening engineering rocks.Correspondingly,the failure criterion for chemically corroded rocks becomes essential in the stability analysis and design of such structures.This study enhances the applicability of the Hoek-Brown(H-B)criterion for engineering structures operating in chemically corrosive conditions by introducing a kinetic porosity-dependent instantaneous mi(KPIM).A multiscale experimental investigation,including nuclear magnetic resonance(NMR),X-ray diffraction(XRD),scanning electron microscopy(SEM),pH and ion chromatography analysis,and triaxial compression tests,is employed to quantify pore structural changes and their linkage with the strength responses of limestone under coupled chemical-mechanical(C-M)conditions.By employing ion chromatography and NMR analysis,along with incorporating the principles of free-face dissolution theory accounting for both congruent and incongruent dissolution,a kinetic chemical corrosion model is developed.This model aims to calculate the kinetic porosity alterations within rocks exposed to varying H+concentrations and durations.Subsequently,utilizing the generalized mixture rule(GMR),the kinetic porositydependent mi is formulated.Evaluation of the KPIM-enhanced H-B criterion using compression test data from 5 types of rocks demonstrated a high level of consistency between the criterion and the experimental results,with a coefficient of determination greater than 0.96,a mean absolute percentage error less than 4.84%,and a root-mean-square deviation less than 5.95 MPa.Finally,the physical significance of the porosity-dependent instantaneous mi is clarified:it serves as an indicator of a rock’s capacity to leverage the confining pressure effect.

Strength criterion for crystalline rocks considering grain size effect and tensile-compressive strength ratio

The macroscopic mechanical properties of rocks are significantly influenced by their microstructure.As a material bonded by mineral grains,the grain morphology of crystalline rock is the primary factor influencing the strength.However,most strength criteria neglect the strength variations caused by different grain characteristics in rocks.Furthermore,the traditional linear criteria tend to overestimate tensile strength and exhibit apex singularity.To address these shortcomings,a piecewise strength criterion that considers the grain size effect has been proposed.A part of an ellipse was employed to construct the envelope of the tensive-shear region on the meridian plane,to accurately reproduce the low tensile-compressive strength ratio.Based on the analysis of experimental data,both linear and exponential modification functions that account for grain size effects were integrated into the proposed criterion.The corresponding finite element algorithm has been implemented.The accuracy and applicability of the proposed criterion were validated by comparing with the experimental data.

Maximum Correntropy Criterion-Based UKF for Loosely Coupling INS and UWB in Indoor Localization

Indoor positioning is a key technology in today’s intelligent environments,and it plays a crucial role in many application areas.This paper proposed an unscented Kalman filter(UKF)based on the maximum correntropy criterion(MCC)instead of the minimummean square error criterion(MMSE).This innovative approach is applied to the loose coupling of the Inertial Navigation System(INS)and Ultra-Wideband(UWB).By introducing the maximum correntropy criterion,the MCCUKF algorithm dynamically adjusts the covariance matrices of the system noise and the measurement noise,thus enhancing its adaptability to diverse environmental localization requirements.Particularly in the presence of non-Gaussian noise,especially heavy-tailed noise,the MCCUKF exhibits superior accuracy and robustness compared to the traditional UKF.The method initially generates an estimate of the predicted state and covariance matrix through the unscented transform(UT)and then recharacterizes the measurement information using a nonlinear regression method at the cost of theMCC.Subsequently,the state and covariance matrices of the filter are updated by employing the unscented transformation on the measurement equations.Moreover,to mitigate the influence of non-line-of-sight(NLOS)errors positioning accuracy,this paper proposes a k-medoid clustering algorithm based on bisection k-means(Bikmeans).This algorithm preprocesses the UWB distance measurements to yield a more precise position estimation.Simulation results demonstrate that MCCUKF is robust to the uncertainty of UWB and realizes stable integration of INS and UWB systems.

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity(UPC)of anchor cables in most previous research.This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass.The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method.The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory,which more accurately reflects the failure state of the anchor cable,as opposed to that being assumed in advance.The results reveal that relying solely on a single failure mode for UPC calculations has limitations,as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.

基于K-L变换的红外图像弱小目标检测与分析

针对红外图像中的目标对比度低、尺寸小及背景复杂等特点 ,利用正交变换的去相关特性 ,提出了一种改进的 K - L变换和广义 K- L变换的红外弱小目标检测与描述方法 ,从而实现低信噪比条件下红外弱小目标的检测 .

高斯混合分布之间K-L散度的近似计算

高斯混合分布之间的K-L散度没有闭式解,通常采用其上界来近似.对于具有相同高斯数的混合分布,基于相对熵链规则推导其K-L散度上界,提出一种更紧上界的计算方法.为计算具有不同高斯数的混合分布之间的K-L散度上界,提出基于最佳高斯分量复制的方法.在中文声韵母声学模型上的实验结果显示,所提出方法可更好地近似等高斯数的混合分布之间的K-L散度,并能有效处理具有不同高斯数的混合分布.

基于压缩感知的K-L分解语音稀疏表示算法

为克服稀疏基在KLT域不便传输的不足,提出一种基于Karhunen-Loeve(K-L)正交分解的语音稀疏表示算法。结合压缩感知理论,建立语音自相关模型并求解Fredholm积分方程,采用二分法估计出可实时传输的模型参数,构造非相干字典;然后用随机矩阵对语音在字典上的稀疏投影系数进行观测获得低维观测值。重构结果表明:相比已有的稀疏表示算法,本文算法的字典匹配性更好,且具有较好的语音质量。

Formation mechanism and criterion of linear segregation in ZL205A alloy

The experiments and numerical simulation were conducted for ZL205A aluminum alloy cylindrical shell casting. The formation mechanism of the linear segregation produced by the low pressure die casting (LPDC) process was investigated. And the heat transfer of the casting during solidification process was analyzed by simulation technique, resulting from the information of linear segregation obtained by plenty of experiments. The new linear segregation criterion was proposed through the simulation and experimental results. It was found that the melting metal with high Cu contents was feeding the crack shrinkage formed by the tearing under the effect of feeding pressure during the later solidification, which led to the formation of linear segregation. The control methods for the linear segregation were suggested based on the proposed mechanism. Finally, the criterion of linear segregation was confirmed by the production of the actual castings.

巴氏距离和K-L变换结合的特征选择

该文提出巴氏距离(BhattacharyyaDistance)和K-L(Karhunen-Loeve)变换结合的特征选择。采用巴氏距离特征选择眼3,5演的迭代算法,可以获得最小错误率上界。当特征维数高时,为了减少巴氏距离特征选择计算时间,对样本先进行K-L变换,将特征降低到中间维数。然后进行巴氏距离特征选择,降低到结果的维数。用基于MNIST手写体数字库的试验表明,该文方法比单纯用巴氏距离特征选择计算时间大大减少,并比主分量方法(即单纯使用K-L变换)特征选择的错误率小得多。

基于K-L变换与LS-SVM的玉米品种识别方法

为实现外观相似的不同玉米品种的有效识别,提出了K-L变换与最小二乘支持向量机相结合的籽粒品种鉴别方法。采用标记算法及多尺度小波分析方法获得玉米单籽粒图像,应用K-L变换技术提取籽粒图像的特征数据,设计了二叉树型多类LS-SVM分类器,实现了对特征数据的有效分类。通过试验分析,确定了较为合理的状态空间维数(L=3),正确识别率可达95.3%。

基于K-L变换和灰度共生矩阵下的桂西—滇东南地质构造遥感信息提取方法研究

桂西—滇东南是植被高覆盖区域,地质遥感信息相对于地表覆盖(植被)信息而言相对较弱。有效消除地表覆盖信息、突出地质遥感信息是遥感地质专题信息提取的瓶颈之一。本文运用K-L变换提取代表地质构造信息的成分波段,有效滤去地表覆盖信息;利用灰度共生矩阵、定向检测和环形滤波检测相结合的方法,并通过阈值设置,提取地质构造的遥感专题信息,从而达到实现计算机自动提取地质构造信息的目的。经过野外实地验证,结果表明:地质构造信息提取精度较高,特别是一些小的地质构造信息也能有效提取;但是环形地质构造信息没有有效提取,地表覆盖类型对地质构造信息的提取仍有较小影响。

基于K-L展开式的车牌倾斜校正方法

在车牌识别系统中,为提高后续字符分割和识别的效果,需要对定位后的车牌图像进行倾斜校正。本文提出了一种基于Karhunen-Loeve展开式的车牌倾斜校正方法。首先对车牌图像进行垂直边缘检测;然后利用K-L展开式推导出垂直边缘点在最小均方误差意义下的特征直线,由此确定车牌的倾斜角度;最后通过双线性插值方法校正车牌。文中给出了实验结果,并与车牌倾斜校正的Hough变换法、旋转投影法进行了精确度、算法复杂度及运算时间的比较,结果表明,本文提出的方法精确度高、复杂性低、鲁棒性好、实时性强。

Evaluation of varying ductile fracture criterion for 7075 aluminum alloy

As one of the principal failures,ductile fracturing restricts metal forming process.Cockcroft-Latham type fracture criterion is suited for ductile fracture in bulk metal-forming simulation.Finding a way to evaluate the ductile fracture criterion（DFC） and identify the relationship between DFC and deformation conditions for a strain-softening material,7075 aluminum alloy;however,it is a non-trivial issue that still needs to be addressed in a greater depth.An innovative approach is brought forth that the compression tests and numerical simulations provide mutual support to evaluate the ductile damage cumulating process and determine the DFC diagram.One of the results shows that for a fixed temperature,the maximum cumulated damage decreases regularly with increasing strain rate.The most important result shows that DFC of 7075 aluminum alloy at temperatures of 573-723 K and strain rates of 0.01-10 s-1 is not a constant but a change in a range of 0.255-0.453,thus it has been defined with varying ductile fracture criterion（VDFC） and characterized by a function of strain rate and temperature.According to VDFC diagram,the exact fracture moment and position during various forming processes will be predicted conveniently,in addition to which,the deformation domains with lower fracture risk corresponding to higher VDFC can be identified.

K-L变换在地震资料去噪声的应用

介绍了K-L变换衰减噪声的基本原理,并将其用于实际地震资料的处理中.针对不同类型的干扰波,利用实例对K-L变换进行了讨论.结果表明,K-L变换可压制噪声提高信噪比,去噪的效果与所选取的特征值的个数有关.利用K-L变换对浅层多次波、折射波、直达波的压制,可避免手工切除对浅层有效信息和干扰信息一刀切的弊端,保存了浅层有效信息.

结合K-L散度和互信息的无监督波段选择算法

波段选择是重要的高光谱图像降维手段。为了达到降维的目的,提出结合K-L散度和互信息的无监督波段选择算法,并进行了理论分析和实验验证。首先选出信息熵最大的波段作为初始波段,然后将散度与互信息量的比值定义为联合散度互信息(KLMI)准则,选择KLMI值大且信息量也大的波段加入波段子集中,选出信息量大且相似度低的波段集合,最终利用k最近邻分类算法实现了基于最大方差主成分分析算法、聚类算法、互信息算法和本文中方法的真实高光谱数据分类实验。结果表明,本文中的算法总体分类精度和κ系数均达到0.8以上,高于其它算法;大多数地物的分类精度均得到提升,具有较好的分类性能。该算法是一种实用的高光谱图像降维算法。

K-L子空间法在风机振动故障诊断中的应用

提出用基于 K- L 变换的多子空间模式识别方法解决旋转机械的多类故障诊断问题。通过 K- L 变换 ,能有效降低特征空间的维数 ,形成各类别对应的特征子空间 ,然后分别计算待分类模式与各子空间的距离实现模式分类。实验室离心风机几种常见机械故障的实例诊断结果表明 ,该方法能有效解决多类故障的诊断问题。