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.

Selecting proper sites for underground dam construction using Multi-Attribute Utility Theory in arid and semi-arid regions

Although the construction of underground dams is one of the best methods to conserve water resources in arid and semi-arid regions,applying efficient methods for the selection of suitable sites for subsurface dam construction remains a challenge.Due to the costly and time-consuming methods of site selection for underground dam construction,this study aimed to present a new method using geographic information systems techniques and decision-making processes.The exclusionary criteria including fault,slope,hypsometry,land use,soil,stream,geology,and chemical properties of groundwater were selected for site selection of dam construction and inappropriate regions were omitted by integration and scoring layers in ArcGIS based on the Boolean logic.Finally,appropriate sites were prioritized using the Multi-Attribute Utility Theory.According to the results of the utility coefficient,seven sites were selected as the region for underground dam construction based on all criteria and experts’opinions.The site of Nazarabad dam was the best location for underground dam construction with a utility coefficient of 0.7137 followed by sites of Akhavan with a utility coefficient of 0.4633 and Mirshamsi with a utility coefficient of 0.4083.This study proposed a new approach for the construction of the subsurface dam at the proper site and help managers and decision-makers achieve sustainable water resources with limited facilities and capital and avoid wasting national capital.

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.

Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle uncertain information,Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making(MADM)problems.This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership,non-membership,and priority are considered simultaneously.Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators,this paper proposes the Fermatean hesitant fuzzy Heronian mean(FHFHM)operator and the Fermatean hesitant fuzzyweighted Heronian mean(FHFWHM)operator.Then,considering the priority relationship between attributes is often easier to obtain than the weight of attributes,this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator(FHFPHM),and discusses its elegant properties such as idempotency,boundedness and monotonicity in detail.Later,for problems with unknown weights and the Fermatean hesitant fuzzy information,aMADM approach based on prioritized attributes is proposed,which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results.Finally,a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.

A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Probabilistic linguistic term sets(PLTSs)are an effective tool for expressing subjective human cognition that offer advantages in the field ofmulti-attribute decision-making(MADM).However,studies have found that PLTSs have lost their ability to accurately capture the views of decision-makers(DMs)in certain circumstances,such as when the DM hesitates between multiple linguistic terms or the decision information is incomplete,thus affecting their role in the decision-making process.Belief function theory is a leading streamof thought in uncertainty processing that is suitable for dealing with the limitations of PLTS.Therefore,the purpose of this study is to extend PLTS to incorporate belief function theory.First,we provide the basic concepts of the extended PLTS(i.e.,belief-based PLTS)through case analyses.Second,the aggregation operator of belief-based PLTS is defined with the ordered weighted average(OWA)-based soft likelihood function,which is improved by considering the reliability of the information source.Third,to measure the magnitude of different belief-based PLTSs,the belief interval of singleton is calculated,and the comparison method of belief-based PLTS is constructed based on probabilities.On the basis of the preceding discussion,we further develop an emergency decision framework that includes several novel techniques,such as attribute weight determination and decision information aggregation.Finally,the usefulness of the framework is demonstrated through a case study,and its effectiveness is illustrated through a series of comparisons.

Two-Sided Matching Decision Making with Multi-Attribute Probabilistic Hesitant Fuzzy Sets

In previous research on two-sided matching(TSM)decision,agents’preferences were often given in the form of exact values of ordinal numbers and linguistic phrase term sets.Nowdays,the matching agent cannot perform the exact evaluation in the TSM situations due to the great fuzziness of human thought and the complexity of reality.Probability hesitant fuzzy sets,however,have grown in popularity due to their advantages in communicating complex information.Therefore,this paper develops a TSM decision-making approach with multi-attribute probability hesitant fuzzy sets and unknown attribute weight information.The agent attribute weight vector should be obtained by using the maximum deviation method and Hamming distance.The probabilistic hesitancy fuzzy information matrix of each agent is then arranged to determine the comprehensive evaluation of two matching agent sets.The agent satisfaction degree is calculated using the technique for order preference by similarity to ideal solution(TOPSIS).Additionally,the multi-object programming technique is used to establish a TSM method with the objective of maximizing the agent satisfaction of two-sided agents,and the matching schemes are then established by solving the built model.The study concludes by providing a real-world supply-demand scenario to illustrate the effectiveness of the proposed method.The proposed method is more flexible than prior research since it expresses evaluation information using probability hesitating fuzzy sets and can be used in scenarios when attribute weight information is unclear.

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.

Multi-attribute decision-making based on subjective and objective integrated eigenvector method

An integrated approach is proposed to investigate the fuzzy multi-attribute decision-making （MADM） problems, where subjective preferences are expressed by a pairwise comparison matrix on the relative weights of attributes and objective information is expressed by a decision matrix. An eigenvector method integrated the subjective fuzzy preference matrix and objective information is proposed. Two linear programming models based on subjective and objective information are introduced to assess the relative importance weights of attributes in an MADM problem. The simple additive weighting method is utilized to aggregate the decision information, and then all the alternatives are ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the method. The result shows that it is easier than other methods of integrating subjective and objective information.

APPROACH FOR FUZZY MULTI-ATTRIBUTE DECISION-MAKING WITH FUZZY COMPLEMENTARY PREFERENCE RELATION ON ALTERNATIVES

In presented fuzzy multi-attribute decision-making （FMADM） problems, the information about attribute weights is interval numbers and the decision maker （DM） has fuzzy complementary preference relation on alternatives. Firstly, the decision-making information based on the subjective preference information in the form of the fuzzy complementary judgment matrix is uniform by using a translation function. Then an objective programming model is established. Attribute weights are obtained by solving the model, thus the fuzzy overall values of alternatives are derived by using the additive weighting method. Secondly, the ranking approach of alternatives is proposed based on the degree of similarity between the fuzzy positive ideal solution of alternatives （FPISA） and the fuzzy overall values. The method can sufficiently utilize the objective information of alternatives and meet the subjective requirements of the DM as much as possible. It is easy to be operated and implemented on a computer. Finally, the proposed method is applied to the project evaluation in the venture investment.

Multi-attribute Decision Making Method Based on the Attribute Difference Degree and Its Application in Rice Breeding

[Objective]The aim was to establish a multi-attribute decision making method and introduce its application in rice breeding.[Method]Based on the defined closeness degree among attributes,the difference degrees among attributes were discussed.Furthermore,the weights of attributes were determined based on the difference degrees among the attributes.[Result]A multi-attribute decision making method based on difference degrees among attributes was established,the feasibility of applying it in rice breeding was also analyzed.[Conclusion]This study enriched the methods to determine attribute weights in multi-attribute decision making and provided the necessary theoretical support for selecting rice varieties scientifically and rationally.

Two-phase TOPSIS of uncertain multi-attribute group decision-making

To solve the uncertain multi-attribute group decision-making of unknown attribute weights,three optimal models are built to decide the corresponding ideal solution weights,standard deviation weights and mean deviation weights.The comprehensive attribute weights are gotten through the product of the above three kinds of weights.And each decision maker＇s weighted decision matrices are also received by using the integrated attribute weights.The closeness degrees are also gotten by use of technique for order preference by similarity to ideal solution（TOPSIS） through dealing with the weighted decision matrices.At the same time the group decision matrix and weighted group decision matrix are gotten by using each decision-maker＇s closeness degree to every project.Then the vertical TOPSIS method is used to calculate the closeness degree of each project.So these projects can be ranked according to their values of the closeness degree.The process of the method is also given step by step.Finally,a numerical example demonstrates the feasibility and effectiveness of the approach.

An Improved Method Based on TODIM and TOPSIS for Multi-Attribute Decision-Making with Multi-Valued Neutrosophic Sets

Due to the complexity of decision-making problems and the subjectivity of decision-makers in practical application,it is necessary to adopt different forms of information expression according to the actual situation of specific decision-making problems and choose the best method to solve them.Multi-valued neutrosophic set,as an extension of neutrosophic set,can more effectively and accurately describe incomplete,uncertain or inconsistent information.TODIM and TOPSIS methods are two commonly used multi-attribute decision-making methods,each of which has its advantages and disadvantages.This paper proposes a new method based on TODIM and TOPSIS to solve multi-attribute decision-making problems under multi-valued neutrosophic environment.After introducing the related theory of multi-valued neutrosophic set and the traditional TODIM and TOPSIS methods,the new method based on a combination of TODIM and TOPSIS methods is described.And then,two illustrative examples proved the feasibility and validity of the proposed method.Finally,the result has been compared with some existing methods under the same examples and the proposed method’s superiority has been proved.This paper studies this kind of decision-making problem from algorithm idea,algorithm steps and decision-making influencing factors.

Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making

To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.