Assessment on strength reduction schemes for geotechnical stability analysis involving the Drucker-Prager criterion

For geotechnical stability analysis involving the Drucker-Prager(DP)criterion,both the c-ϕreduction scheme and the M-K reduction scheme can be utilized.With the aid of the second-order cone programming optimized finite element method(FEM-SOCP),a comparison of the two strength reduction schemes for the stability analysis of a homogeneous slope and a multilayered slope is carried out.Numerical investigations disclose that the FoS results calculated by the c-ϕreduction scheme agree well with those calculated by the classical Morgenstern-Price solutions.However,the FoS results attained by the M-K reduction scheme may lead to conservative estimation of the geotechnical safety,particularly for the cases with large internal friction angles.In view of the possible big difference in stability analysis results caused by the M-K reduction scheme,the c-ϕreduction scheme is recommended for the geotechnical stability analyses involving the DP criterion.

一种扩展的Drucker-Prager准则及数值应用

已有Mohr-Coulomb(M-C)准则的匹配圆Drucker-Prager(D-P)准则只能在有限的应力点与M-C准则等效,且不具备应力角效应,在工程数值分析中受到限制.因此,对D-P准则设置了角隅函数来反映应力角效应,采用与M-C准则在π平面上面积等效的方法构建了等面积扩展D-P准则,进一步对等面积扩展D-P准则在中主应力影响下的强度特性进行了分析,最后通过三个算例比较了不同等效D-P强度准则在岩土工程分析中的适用性.结果表明:等面积扩展D-P准则相比其它D-P准则和M-C准则的强度离差更小,整体上在和M-C准则的等效性上表现更佳;数值模拟算例表明等面积扩展D-P准则能够适应各种应力状态,在数值模拟结果上和M-C准则具有更好的等效性,且在计算收敛性上还具有较好的表现,可作为M-C准则的替代.

基于Drucker-Prager屈服准则及加卸载判据的圆形隧道围岩-支护作用机制探讨

隧道围岩-支护相互作用机制是隧道力学中的基础理论,为了准确描述围岩与支护结构对隧道应力变形的影响,假定围岩本构模型为理想弹塑性模型,采用适用于岩土材料的Drucker-Prager屈服准则,考虑加卸载判据,证明了圆形隧道的开挖过程是一个加载过程,支护过程是卸载过程。通过大型有限元仿真软件Abaqus计算了平面应变情况下圆形隧道开挖与支护过程的弹塑性解。数值分析结果与理论公式结果相吻合,表明开挖的过程是解除内压、增大压差的加载过程,支护过程为施加内压、减小压差的卸载过程。支护后的围岩应力增量和位移增量符合弹性规律,且支护过后的应力等于开挖后的应力减去弹性应力。支护过程的卸载效应使得开挖过程产生的塑性区变成了残余变形区。研究结果可为工程应用提供参考。

基于改进Drucker-Prager准则的GFRP管约束高强混凝土短柱单轴压缩分析模型

针对玻璃纤维增强聚合物(glass fiber reinforced polymer, GFRP)管约束高强混凝土短柱的受力特点,及传统Drucker-Prager (D-P)准则存在拉剪区偏大的问题,提出了一种改进的D-P型塑性约束高强混凝土短柱单轴压缩分析模型,其考虑GFRP管约束效应相关的混凝土硬化/软化规律和非关联流动准则,以提高GFRP管约束高强混凝土短柱单轴压缩下轴向和环向应力-应变曲线的预测精度。该模型在ANSYS软件中实现了GFRP管约束高强混凝土短柱力学性能的计算模拟,并与试验结果的对比表明:两者的应力-应变曲线吻合较好,提出的分析模型合理可靠。此研究可为GFRP管约束高强混凝土的设计提供理论参考。

基于Drucker-Prager/Cap模型的Ti-30Cu粉末轧制过程模拟

对钛和铜质量比为7∶3的Ti-30Cu混合粉末进行单轴压缩、巴西圆盘和模压试验,获得该粉末Drucker-Prager/Cap本构参数与相对密度的关系;利用Abaqus软件建立粉末轧制模型,研究喂料高度对板料相对密度的影响,并进行了试验验证;采用该模型研究了辊缝宽度、轧速对Ti-30Cu合金板料相对密度的影响。结果表明:在辊缝宽度为1 mm、轧速为10 mm·s^(-1)条件下,随着喂料高度由150 mm增加到300 mm,板料的相对密度增大,模拟结果与试验结果基本吻合,最大相对误差为2.15%,验证了轧制模型的有效性;随着喂料高度的增加、辊缝宽度或轧速的减小,板料的相对密度增大。

FRP约束混凝土柱的修正Drucker-Prager模型

Drucker-Prager(DP)模型中,摩擦角和内聚力相关的参数决定屈服、硬化软化准则,与膨胀角相关的参数决定流动法则。通过对试验样本数据的分析,确定了摩擦角的影响因素,将摩擦角定义为塑性应变的函数;进而由DP模型的屈服准则更新了内聚力模型。通过计算侧向塑性应变与轴向塑性应变的比率,建立了考虑约束刚度比的膨胀角模型。基于ABAQUS中的USDFLD子程序对修正后DP模型参数实现自定义,结果表明提出的修正后的DP模型可以很好地预测FRP约束混凝土柱的应力-应变响应,具有一定的精度。

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.

Finite Element Implementation of the Exponential Drucker-Prager Plasticity Model for Adhesive Joints

This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer.The developed user subroutine UMAT,which utilizes an associated plastic flow during a plastic deformation,can provide a good agreement between the simulations and the experimental data.Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used.

Cause of Errors Associated with Application of Drucker-Prager Yield Criterion in MSC/NASTRAN Program

When the Drucker Prager yield criterion is used, the MSC/NASTRAN program frequently predicts noticeable errors. The relevant part of NASTRAN Handbook was checked and some errors in the elasto plastics theory used in NASTRAN were detected in this paper. The procurement to prove these errors was verified by numerical calculation.

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.

Drucker-Prager准则参数特性分析

Drucker-Prager准则在数值计算中得到广泛运用。但如果该准则的参数选取不当,可能导致预测与试验结果之间不一致。通过分析函数基本特性,考察该准则反映中主应力对强度参数影响的能力,探讨导致预测与试验结果之间不一致的可能原因。进而对目前常用的参数表达式进行详细的分析,并考察平面应变情况下Drucker-Prager准则的参数特性。分析表明:Drucker-Prager准则不能合理地反映中主应力对强度参数的影响,且在平面应变情况下会得出中主应力系数小于0的结论。

基于Drucker-Prager准则的深部巷道破裂围岩弹塑性分析

基于Drucker-Prager屈服准则和非关联流动法则,考虑中间主应力、塑性区弹性应变及岩体剪胀性的影响,推导了深部圆形巷道围岩应力、变形及塑性区半径的封闭解析解。结合工程实例,对比分析了不同屈服准则和围岩参数对围岩状态变化的影响,研究结果表明:中间主应力对围岩破裂范围和表面位移均具有重要影响,且表现出明显的区间效应;剪胀角越大,扩容系数越大,围岩破裂范围与表面位移也就越大;围岩参数(残余黏聚力、残余内摩擦角、初始黏聚力)和支护阻力越大,围岩塑性区及破裂区范围均越小;D-P准则解分别与统一强度准则解、双剪强度准则解和M-C准则解相比,围岩破裂范围及表面位移均偏大,但与M-C准则解最为接近;在满足相同围岩变形条件下,D-P准则解所需支护阻力较其他3种准则解均较大,更偏向于刚性支护形式,分析结果可为巷道围岩稳定性评价与支护设计提供重要理论依据。

基于Drucker-Prager准则的边坡安全系数定义及其转换

探讨了基于D-P(Drucker-Prager)准则的边坡稳定安全系数定义形式,提出了各D-P准则之间的安全系数转换关系,并据此建立了基于D-P准则的边坡稳定安全系数与传统莫尔–库仑准则条件下安全系数的关系表达式。目前,ANSYS有限元软件采用的岩土材料屈服准则为莫尔–库仑六边形外接圆D-P准则,在利用有限元强度折减法计算边坡稳定安全系数时,可以先求出外接圆D-P准则条件下的安全系数,然后利用所提出的安全系数转换公式就可直接计算出各D-P准则条件下的安全系数。对于平面应变条件下的强度问题,平面应变莫尔–库仑匹配D-P准则(分关联和非关联两种情况)与莫尔–库仑准则等效,因此,通过转换就可以在ANSYS程序中实现莫尔–库仑准则,而不需要进行二次开发。这样就解决了基于D-P准则的有限元强度折减安全系数与传统工程中采用的安全系数(基于莫尔–库仑准则)间的接轨问题。大量算例结果表明:在平面应变条件下采用平面应变莫尔–库仑匹配D-P准则求得的安全系数与传统极限平衡条分法中用Spencer法求得的安全系数非常接近,且误差在1%～2%,已经具有相当高的计算精度,也同时证明所提出的方法是可行的。

一种修正的Drucker-Prager屈服准则

Drucker-Prager(以下简称D-P)屈服准则因其形式简单、物理意义明确而得到广泛的应用,然而经过多年的应用和研究,其缺点逐渐显现出来,如拉剪区偏大、不具有应力角效应等,针对这些不足,提出了修正的D-P屈服准则。在拉剪区用圆球面和横截面的组合方式代替原来的圆锥面,从而不改变D-P屈服准则压剪区的形式,在考虑岩石实际的拉伸强度的同时,也满足该屈服准则经过单轴抗拉强度点的条件;为考虑岩石在三轴压缩和三轴拉伸状态下不同的强度特性,即应力角效应,引入了一种角隅模型;为保证屈服准则始终通过岩石的单轴抗压强度点,建议了一种材料参数k值的取值方法。为验证屈服准则修正后的适用性和正确性,将修正屈服准则与真三轴试验结果进行了拟合,同时与Mohr-Coulomb(以下简称M-C)准则进行对比,结果表明,修正屈服准则可以很好地描述试验现象,且比M-C准则更接近真实结果。