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.

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.

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.

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.

k-Bertrand判别法

正项级数的敛散性判别法中比较精细的有Raabe判别法、Gauss判别法和Bertrand判别法.在上述方法的基础上,给出了Raabe判别法、Gauss判别法和Bertrand判别法推广的统一形式,包括非极限形式、上、下极限形式以及极限形式,称之为k-Bertrand判别法.

A failure criterion for shale considering the anisotropy and hydration based on the shear slide failure model

A failure criterion fully considering the anisotropy and hydration of shale is essential for shale formation stability evaluation.Thus,a novel failure criterion for hydration shale is developed by using Jaeger’s shear failure criterion to describe the anisotropy and using the shear strength reduction caused by clay minerals hydration to evaluate the hydration.This failure criterion is defined with four parameters in Jaeger’s shear failure criterion(S_(1),S_(2),a andφ),three hydration parameters(k,ω_(sh)andσ_(s))and two material size parameters(d and l0).The physical meanings and determining procedures of these parameters are described.The accuracy and applicability of this failure criterion are examined using the published experimental data,showing a cohesive agreement between the predicted values and the testing results,R^(2)=0.916 and AAREP(average absolute relative error percentage)of 9.260%.The error(|D_(p)|)is then discussed considering the effects ofβ(angle between bedding plane versus axial loading),moisture content and confining pressure,presenting that|Dp|increases whenβis closer to 30°,and|D_(p)|decreases with decreasing moisture content and with increasing confining pressure.Moreover,|D_(p)|is demonstrated as being sensitive to S1and being steady with decrease in the data set whenβis 0°,30°,45°and 90°.

SSA-MLP模型在岩质边坡稳定性预测中的应用

岩质边坡的力学参数量化及稳定性分析对岩质边坡灾害的防治具有重要意义。Hoek-Brown(H B)准则是一种用于确定岩体力学参数的经典方法,能反映出边坡岩体变形和位移的非线性破坏特征。在此基础上,首先,提出一种麻雀搜索算法(Sparrow Search Algorithm,SSA)改进多层感知器(Multi-Layer Perceptron,MLP)的神经网络模型,并用于边坡稳定性预测、指标敏感性分析及参数反演。其次,将收集的1085组岩质边坡的几何参数和H B准则参数等作为输入变量,极限平衡理论Bishop法求解的安全系数作为输出变量,对SSA MLP模型进行训练学习和性能评估。最后,将该模型运用于25个边坡实例,验证模型的有效性。结果显示,该模型收敛速度快、精度高,为边坡稳定性分析和参数量化提供了一种新思路。

Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion.To provide an accurate prediction for the theoretical solution of the critical face pressure,this study adopts the piecewise linear method(PLM)to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule.The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem;it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables(m is the number of segments).Meanwhile,two classic linearized measures,the generalized tangential technique(GTT)and equivalent Mohr-Coulomb parameters method(EMM),are incorporated into the analysis for comparison.Surprisingly,the parametric study indicates a significant improvement in support pressure by up to 13%compared with the GTT,and as expected,the stability of the tunnel face is greatly influenced by the rock strength parameters.The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state.Although the limit analysis is incapable of calculating the true stress distribution in rock masses,a rough approximation of the stress vector on the rupture surface is permitted.In the end,sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.

基于Gram-Schmidt正交化和HSIC的核函数选择方法

核方法是一种解决非线性、异构数据的有效方法,核函数的选择问题是核方法中的一个重要课题,对于不同的应用问题,如何选择合适的核函数还没有足够的理论基础,不适当的核函数选取会降低核方法的性能。由此,提出了一种基于Gram-Schmidt正交化(GSO)和Hilbert-Schmidt独立准则的核选择方法(HSIC-GSO),该方法考虑了核函数选择过程中存在的不相关冗余信息。首先,利用GSO消除核函数之间的冗余信息;然后,使用HSIC度量核函数与理想核之间的相似性;最后,得到一组判别能力强、多样性大的基核函数。实验结果表明,HSIC-GSO方法选择的核函数泛化性好,并且提高了MKL的分类性能,验证了所提方法的有效性。

Numerical simulation study on shear resistance of anchorage joints considering tensile-shear fracture criterion of 2G-NPR bolt

2G-NPR bolt (the 2nd generation Negative Poisson’s Ratio bolt) is a new type of bolt with high strength, high toughness and no yield platform. It has signifcant efects on improving the shear strength of jointed rock mass and controlling the stability of surrounding rock. To achieve an accurate simulation of bolted joint shear tests, we have studied a numerical simulation method that takes into account the 2G-NPR bolt's tensile–shear fracture criterion. Firstly, the indoor experimental study on the tensile–shear mechanical properties of 2G-NPR bolt is carried out to explore its mechanical properties under diferent tensile–shear angles, and the fracture criterion of 2G-NPR bolt considering the tensile–shear angle is established. Then, a three-dimensional numerical simulation method considering the tensile–shear mechanical constitutive and fracture criterion of 2G-NPR bolt, the elastoplastic mechanical behavior of surrounding rock and the damage and deterioration of grouting body is proposed. The feasibility and accuracy of the method are verifed by comparing with the indoor shear test results of 2G-NPR bolt anchorage joints. Finally, based on the numerical simulation results, the deformation and stress of the bolt, the distribution of the plastic zone of the rock mass, the stress distribution and the damage of the grouting body are analyzed in detail. The research results can provide a good reference value for the practical engineering application and shear mechanical performance analysis of 2G-NPR bolt.

Correction of dynamic Brazilian disc tensile strength of rocks under preloading conditions considering the overload phenomenon and invoking the Griffith criterion

Dynamic tensile failure is a common phenomenon in deep rock practices,and thus accurately evaluating the dynamic tensile responses of rocks under triaxial pressures is of great significance.The Brazilian disc(BD)test is the suggested method by the International Society for Rock Mechanics and Rock Engineering(ISRM)for measuring both the static and dynamic tensile strengths of rock-like materials.However,due to the overload phenomenon and the complex preloading conditions,the dynamic tensile strengths of rocks measured by the BD tests tend to be overestimated.To address this issue,the dynamic BD tensile strength(BTS)of Fangshan marble(FM)under different preloading conditions were measured through a triaxial split Hopkinson pressure bar(SHPB).The fracture onset in BD specimen was captured through a strain gage around the disc center.The discrepancy between the traditional tensile strength(TTS,determined by the peak load P_(f) of the BD specimen)and the nominal tensile strength(NTS,obtained from the load P_(i) when the diametral fracture commences in the tested BD specimen)was applied to quantitatively evaluating the overload phenomenon.The Griffith criterion was used to rectify the calculation of the tensile stress at the disc center under triaxial stress states.The results demonstrate that the overload ratio(s)increases with the loading rate(σ)and decreases with the hydrostatic pressure(σ_(s)).The TTS corrected by the Griffith criterion is independent of theσ_(s)due to the overload phenomenon,while the NTS corrected by the Griffith criterion is sensitive to both the andσ.Therefore,it is essential to modify the tensile stress in dynamic confined BD tests using both the overload correction and the Griffith criterion rectification to obtain the accurate dynamic BTS of rocks.

基于ALARP准则的继电保护设备拒动风险评估方法

常规的继电保护设备拒动风险评估结构多为独立形式,评估效率较低,导致风险评估差值增加,为此提出基于ALARP准则的继电保护设备拒动风险评估方法。根据当前测试需求,提取拒动风险特征,采用多层级的方式,设计多阶拒动风险评估结构;在ALARP准则下,构建继电保护设备拒动风险评估模型,采用连锁故障辅助标定的方式,完善风险评估结果。测试结果表明:该方法的风险评估差值均控制在1.2以下,说明此次在ALARP准则的辅助与分析下,所设计方法更加高效、细化,针对性较强,具有实际的应用价值。

ZL114A铝合金本构关系与失效准则参数的确定

针对航空发动机机匣材料ZL114A铝合金,构建描述该材料在较大温度范围下大变形及失效行为的材料模型。通过万能试验机及分离式霍普金森压杆试验装置测试ZL114A铝合金在常温准静态、高温和高应变率下的力学性能,分析温度和应变率对材料流动应力的影响。采用有限元程序和优化算法反求25~375℃内材料的硬化参数,结合高应变率(1310~5964 s^(-1))下材料的动态行为关系,构建包含塑性应变、温度及应变率的经验型本构模型。开展缺口拉伸、缺口压缩等试验并建立相对应的有限元模型,获取材料在不同应力三轴度下的失效应变,标定分段形式的Johnson-Cook(J-C)失效准则参数。通过不同温度下的平板侵彻试验和数值模拟验证失效准则及其参数的有效性。结果表明,ZL114A铝合金具有明显的应变硬化、温度软化及高应变率强化特性;具有应力饱和特征的Hockett-Sherby(HS)硬化模型较为准确地描述材料大变形下的力学行为;构建的材料本构关系可以描述ZL114A铝合金在大应变、宽温度、高应变率下的力学行为;分段形式的失效准则具有预测不同温度下材料失效行为的能力。

基于ARIMA模型的矿井灾害预测方法研究

矿井灾害频发是影响我国煤炭产业发展的重要问题之一,灾前预警技术是目前应对这一问题的主要方法。为进一步提升矿井灾害监测预警能力,提出了基于ARIMA模型的矿井灾害预测方法研究。通过确立灾害风险监测指标构建了安全态势评估指标体系,基于时序预测法建立了灾害预测评估模型,经模型定阶及训练等过程确定最佳ARIMA预测模型参数。通过研究模型残差的正态性分布从而得到预测模型可靠度,将ARIMA(10,0,0)模型与时间序列拟合后进行自相关图和偏自相关图分析,得到了风险灾害未来短期预测结果;提出了“红橙黄蓝绿”5级灾害预警等级和准则,并进行了现场应用试验,结果证明,ARIMA模型对未来值的预测具有较高准确性,系统能及时对灾害进行预测和分级响应,可实现对矿井灾害的风险判别和预测预警。

Investigation of anisotropic strength criteria for layered rock mass

Layered rock mass is a type of engineering rock mass with sound mechanical anisotropy,which is generally unfavorable to the stability of underground works.To investigate the strength anisotropy of layered rock,the Mohr-Coulomb and Hoek-Brown criteria are introduced to establish the two transverse isotropic strength criteria based on Jaeger's single weak plane theory and maximum axial strain theory,and parameter determination methods.Furthermore,the sensitivity of strength parameters(K 1,K 2,and K 3)that are used to characterize the anisotropy strength of non-sliding failure involved in the strength criteria and confining pressure are investigated.The results demonstrate that strength parameters K 1 and K 2 affect the strength of layered rock samples at all bedding angles except for the bedding angle of 90°and the angle range that can cause the shear sliding failure along the bedding plane.The strength of samples at any bedding angle decreases with increasing K 1,whereas the opposite is for K 2.Except for bedding angles of 0°and 90°and the bedding angle range that can cause the shear sliding along the bedding plane,K 3 has an impact on the strength of rock samples with other bedding angles that the specimens'strength increases with increase of K 3.In addition,the strength of the rock sample increases as confining pressure rises.Furthermore,the uniaxial and triaxial tests of chlorite schist samples were carried out to verify and evaluate the strength criteria proposed in the paper.It shows that the predicted strength is in good agreement with the experimental results.To test the applicability of the strength criterion,the strength data of several types of rock in the literature are compared.Finally,a comparison is made between the fitting effects of the two strength criteria and other available criteria for layered rocks.

Health diagnosis of ultrahigh arch dam performance using heterogeneous spatial panel vector model

Currently,more than ten ultrahigh arch dams have been constructed or are being constructed in China.Safety control is essential to long-term operation of these dams.This study employed the flexibility coefficient and plastic complementary energy norm to assess the structural safety of arch dams.A comprehensive analysis was conducted,focusing on differences among conventional methods in characterizing the structural behavior of the Xiaowan arch dam in China.Subsequently,the spatiotemporal characteristics of the measured performance of the Xiaowan dam were explored,including periodicity,convergence,and time-effect characteristics.These findings revealed the governing mechanism of main factors.Furthermore,a heterogeneous spatial panel vector model was developed,considering both common factors and specific factors affecting the safety and performance of arch dams.This model aims to comprehensively illustrate spatial heterogeneity between the entire structure and local regions,introducing a specific effect quantity to characterize local deformation differences.Ultimately,the proposed model was applied to the Xiaowan arch dam,accurately quantifying the spatiotemporal heterogeneity of dam performance.Additionally,the spatiotemporal distri-bution characteristics of environmental load effects on different parts of the dam were reasonably interpreted.Validation of the model prediction enhances its credibility,leading to the formulation of health diagnosis criteria for future long-term operation of the Xiaowan dam.The findings not only enhance the predictive ability and timely control of ultrahigh arch dams'performance but also provide a crucial basis for assessing the effectiveness of engineering treatment measures.