Barton-Bandis criterion-based system reliability analysis of rock slopes

Several potential failure modes generally exist in rock slopes because of the existence of massive structural planes in rock masses. A system reliability analyses method for rock slopes with multiple failure modes based on nonlinear Barton-Bandis failure criterion is proposed. The factors of safety associated with the sliding and overturning failure modes are derived, respectively. The validity of this method is verified through a planar rock slope with an inclined slope top and tension crack. Several sensitivity analyses are adopted to study the influences of structural-plane parameters, geometric parameters, anchoring parameters and fracture morphology on the rock slopes system reliability.

基于Barton-Bandis准则的岩体破坏模式快速识别方法

岩体由岩石和结构面网络组成,结构面强度模型对岩体稳定性分析起着决定性影响。本文研究详细探讨了Barton-Bandis准则在岩体结构破坏模式判断中的应用。首先,推导了当结构面服从Barton-Bandis准则时,结构面屈服时倾角的取值范围,提出了结构面屈服的判据,并采用数值模拟法验证了理论推导结果的正确性;基于理论推导的结果,并假定岩石服从Mohr-Coulomb准则,提出了一种岩体结构破坏模式的快速识别方法,将岩体结构破坏分为不发生破坏、沿结构面发生破坏、沿岩石发生破坏和同时沿岩石和结构面发生破坏4种模式,并验证了该识别方法的正确性。研究结果可以为工程实践的岩体结构破坏识别提供理论指导和技术支持。

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.

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.

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.

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Barton-Bandis准则的锚固边坡稳定性分析

结合岩石节理面非线性Barton-Bandis破坏准则,探讨了将Barton-Bandis破坏准则参数转化为线性Mohr-Coulomb破坏准则抗剪强度参数的两种常用方法,通过实例分析了各方法的优劣。推导了加锚单岩石节理面控制的平面滑动岩体边坡抗滑稳定性安全系数计算式,开展了锚固参数分析。研究表明:相对于采用等效线性拟合法或切线等效法获取Mohr-Coulomb抗剪强度参数而言,直接应用Barton-Bandis破坏准则计算节理面控制的岩石边坡稳定性更为直观和简便;随着结构面基本摩擦角、结构面粗糙度系数和结构面壁面有效抗压强度的增大,边坡安全系数逐步提高,且结构面基本摩擦角和粗糙度系数对边坡安全系数的影响程度更为显著;锚索锚固力越大,边坡抗滑稳定性越好,而锚索设置角度越大,边坡抗滑稳定性越低,锚索角度设置不当将明显减小锚固效应的有效性。

基于Barton-Bandis非线性破坏准则的岩体强度预测

为了采用Barton-Bandis模型描述岩体特征,并将其参数应用于数值计算中,探讨Barton-Bandis参数到Mohr-Coulomb准则参数的转换,研究Barton-Bandis参数对Mohr-Coulomb参数的影响。研究结果表明:Barton-Bandis参数到Mohr-Coulomb准则参数的转换方法方便有效;随着节理粗糙系数JRC和节理压缩强度JCS的增大,Mohr-Coulomb参数粘结力c和内摩擦角φ均呈现非线性增大,可通过指数方程对其关系进行拟合;JRC的变化对粘结力的影响大于其对内摩擦角的影响;JRC对岩体剪切强度的影响大于JCS对岩体剪切强度的影响。

基于Barton-Bandis准则下水力驱动型岩质边坡的稳定性分析

为了将水力作用下岩质边坡稳定性的评价方法与Barton-Bandis非线性破坏准则相结合,探讨了Barton-Bandis准则参数到Mohr-Coulomb准则参数转换的两种常用方法,并推导出了不同计算方法下边坡抗滑稳定性的表达式,然后进行算例分析。结果表明:直接利用J_(RC)-J_(CS)模型计算水力作用下边坡的稳定性是可行的;且在单因素影响下,边坡抗滑稳定性系数与裂隙水深h、坡高H和层面倾角α呈负相关,可分别用线性函数、幂函数来描述,而与J_(CS),J_(RC)和φ_b呈正相关,可分别用对数、指数方程来描述;对于裂隙水深h而言,其对等效c,φ值的影响恰好相反,但均可用线性函数拟合,而临界裂隙水深h_(cr)与J_(CS)和J_(RC)的关系分别符合对数、指数特征。

基于Barton-Bandis非线性破坏准则的边坡破坏概率分析

鉴于岩体结构面粗糙度和壁岩强度的影响使结构面抗剪强度呈现非线性特征,传统极限平衡分析法采用平均值来表征岩体物理力学指标使评价结论未能充分顾及到指标的离散性,提出了基于Barton-Bandis非线性破坏准则的边坡破坏概率分析方法。通过野外地质测量获得岩体结构面轮廓曲线及回弹值,经过处理计算后分别获得结构面粗糙度系数JRC,壁岩强度JCS、基本摩擦角φb等参数的多组样本数据,并验证了各参数样本数据的概率分布。基于Barton-Bandis准则建立了柏杨庙矿山边坡的稳定性分析模型,采用Morgenstern-Price法计算出该边坡的多组稳定性系数,通过蒙特卡罗法对其进行统计分析,确定了边坡的破坏概率,并与传统极限平衡分析法的计算结果进行了对比分析。研究表明:基于Barton-Bandis准则的边坡破坏概率分析方法在进行边坡稳定性分析时充分考虑了岩体结构面抗剪强度的非线性特征和抗剪强度参数的离散性,是岩质边坡稳定性分析的有效方法。

Nonlinear shear behavior of rock joints using a linearized implementation of the Barton-Bandis model

Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing,inducing dilation and resulting in nonlinear joint shear strength and shear stress vs.shear displacement behaviors.The Barton-Bandis(B-B) joint model provides the most realistic prediction for the nonlinear shear behavior of rock joints.The B-B model accounts for asperity roughness and strength through the joint roughness coefficient(JRC) and joint wall compressive strength(JCS) parameters.Nevertheless,many computer codes for rock engineering analysis still use the constant shear strength parameters from the linear Mohr-Coulomb(M-C) model,which is only appropriate for smooth and non-dilatant joints.This limitation prevents fractured rock models from capturing the nonlinearity of joint shear behavior.To bridge the B-B and the M C models,this paper aims to provide a linearized implementation of the B-B model using a tangential technique to obtain the equivalent M-C parameters that can satisfy the nonlinear shear behavior of rock joints.These equivalent parameters,namely the equivalent peak cohesion,friction angle,and dilation angle,are then converted into their mobilized forms to account for the mobilization and degradation of JRC under shearing.The conversion is done by expressing JRC in the equivalent peak parameters as functions of joint shear displacement using proposed hyperbolic and logarithmic functions at the pre-and post-peak regions of shear displacement,respectively.Likewise,the pre-and post-peak joint shear stiffnesses are derived so that a complete shear stress-shear displacement relationship can be established.Verifications of the linearized implementation of the B-B model show that the shear stress-shear displacement curves,the dilation behavior,and the shear strength envelopes of rock joints are consistent with available experimental and numerical results.

基于Barton-Bandis节理模型的重力坝坝基节理加卸载变形规律研究

鉴于离散单元法在处理富含节理面的岩体方面比常规有限元有明显优势,首先分析Barton-Bandis(B-B)节理模型加卸载时的应力应变关系和剪胀规律,然后建立基于B-B节理模型的重力坝加(卸)载模型,通过记录监测点位移历程,探讨坝体及坝基软弱结构面在加卸载作用下的位移变化规律,并提出强度转换公式,将B-B节理模型强度转换成等效M-C模型的粘聚力和摩擦角,发现随着加卸载次数的增多,转换后的节理强度逐渐减小。

基于非线性Barton-Bandis准则节理软岩边坡锚杆加固研究

采用Barton-Bandis准则可简便获取岩体的力学参数并能较好地反映节理岩体力学性质的非线性。通过回弹法量化Barton-Bandis准则参数以及得到等效的Mohr-Coulomb准则参数,并基于极限平衡条分法推导出Barton-Bandis准则下的节理岩质边坡的稳定性分析及锚固设计。通过采用内含Barton-Bandis准则计算程序的软件SLIDE对某节理软岩边坡的稳定性分析及锚固设计,验证了采用Barton-Bandis准则进行节理岩坡分析的可行性与正确性。

基于Barton-Bandis准则的双滑块平面岩质边坡系统稳定性拟动力分析

基于非线性Barton-Bandis(B-B)节理剪切强度经验准则,采用极限平衡拟动力方法,考虑潜在失稳滑块间的相互作用力,推导双滑块平面岩质边坡系统的安全系数计算公式,分析岩性参数及边坡几何形态对边坡系统安全系数的影响。该方法可以有效分析拟动力条件下双滑块平面岩质边坡的系统稳定性,判断边坡系统稳定状态及失稳模式。研究结果表明:边坡几何形状参数,结构面粗糙系数JRC,水平地震力系数kh,结构面有效抗压强度JCS和结构面基本摩擦角φb等对边坡稳定性均有较大影响,而地震力放大系数fs和竖向地震力系数kv影响相对较小。

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°.

基于Barton-Bandis准则的边坡稳定性极限平衡分析方法

针对传递系数法中抗剪强度参数的取值无法适应潜在滑移面的实际受力情况,本文提出了基于Barton-Bandis准则的边坡稳定性极限平衡分析方法。通过切线等效法将Barton-Bandis准则抗剪强度参数转化为Mohr-Coulomb准则抗剪强度参数,在边坡滑体每一条块采用不同抗剪强度参数的前提下,基于隐式解法实现边坡的稳定性分析,并与传统传递系数法的计算结果对比分析。案例分析表明,基于Barton-Bandis准则的边坡稳定性极限平衡分析方法在边坡稳定性分析时考虑到了岩体结构面所处的实际应力环境,是岩质边坡稳定性分析的有效方法。