An Optimized System of Random Forest Model by Global Harmony Search with Generalized Opposition-Based Learning for Forecasting TBM Advance Rate

As massive underground projects have become popular in dense urban cities,a problem has arisen:which model predicts the best for Tunnel Boring Machine(TBM)performance in these tunneling projects?However,performance level of TBMs in complex geological conditions is still a great challenge for practitioners and researchers.On the other hand,a reliable and accurate prediction of TBM performance is essential to planning an applicable tunnel construction schedule.The performance of TBM is very difficult to estimate due to various geotechnical and geological factors and machine specifications.The previously-proposed intelligent techniques in this field are mostly based on a single or base model with a low level of accuracy.Hence,this study aims to introduce a hybrid randomforest(RF)technique optimized by global harmony search with generalized oppositionbased learning(GOGHS)for forecasting TBM advance rate(AR).Optimizing the RF hyper-parameters in terms of,e.g.,tree number and maximum tree depth is the main objective of using the GOGHS-RF model.In the modelling of this study,a comprehensive databasewith themost influential parameters onTBMtogetherwithTBM AR were used as input and output variables,respectively.To examine the capability and power of the GOGHSRF model,three more hybrid models of particle swarm optimization-RF,genetic algorithm-RF and artificial bee colony-RF were also constructed to forecast TBM AR.Evaluation of the developed models was performed by calculating several performance indices,including determination coefficient(R2),root-mean-square-error(RMSE),and mean-absolute-percentage-error(MAPE).The results showed that theGOGHS-RF is a more accurate technique for estimatingTBMAR compared to the other applied models.The newly-developedGOGHS-RFmodel enjoyed R2=0.9937 and 0.9844,respectively,for train and test stages,which are higher than a pre-developed RF.Also,the importance of the input parameters was interpreted through the SHapley Additive exPlanations(SHAP)method,and it was found that thrust force per cutter is the most important variable on TBMAR.The GOGHS-RF model can be used in mechanized tunnel projects for predicting and checking performance.

Applications of Soft Computing Methods in Backbreak Assessment in Surface Mines: A Comprehensive Review

Geo-engineering problems are known for their complexity and high uncertainty levels,requiring precise defini-tions,past experiences,logical reasoning,mathematical analysis,and practical insight to address them effectively.Soft Computing(SC)methods have gained popularity in engineering disciplines such as mining and civil engineering due to computer hardware and machine learning advancements.Unlike traditional hard computing approaches,SC models use soft values and fuzzy sets to navigate uncertain environments.This study focuses on the application of SC methods to predict backbreak,a common issue in blasting operations within mining and civil projects.Backbreak,which refers to the unintended fracturing of rock beyond the desired blast perimeter,can significantly impact project timelines and costs.This study aims to explore how SC methods can be effectively employed to anticipate and mitigate the undesirable consequences of blasting operations,specifically focusing on backbreak prediction.The research explores the complexities of backbreak prediction and highlights the potential benefits of utilizing SC methods to address this challenging issue in geo-engineering projects.

Effects of data smoothing and recurrent neural network(RNN)algorithms for real-time forecasting of tunnel boring machine(TBM)performance

Tunnel boring machines(TBMs)have been widely utilised in tunnel construction due to their high efficiency and reliability.Accurately predicting TBM performance can improve project time management,cost control,and risk management.This study aims to use deep learning to develop real-time models for predicting the penetration rate(PR).The models are built using data from the Changsha metro project,and their performances are evaluated using unseen data from the Zhengzhou Metro project.In one-step forecast,the predicted penetration rate follows the trend of the measured penetration rate in both training and testing.The autoregressive integrated moving average(ARIMA)model is compared with the recurrent neural network(RNN)model.The results show that univariate models,which only consider historical penetration rate itself,perform better than multivariate models that take into account multiple geological and operational parameters(GEO and OP).Next,an RNN variant combining time series of penetration rate with the last-step geological and operational parameters is developed,and it performs better than other models.A sensitivity analysis shows that the penetration rate is the most important parameter,while other parameters have a smaller impact on time series forecasting.It is also found that smoothed data are easier to predict with high accuracy.Nevertheless,over-simplified data can lose real characteristics in time series.In conclusion,the RNN variant can accurately predict the next-step penetration rate,and data smoothing is crucial in time series forecasting.This study provides practical guidance for TBM performance forecasting in practical engineering.

Introduction to the Special Issue on Computational Intelligent Systems for Solving Complex Engineering Problems: Principles and Applications

Computational Intelligent(CI)systems represent a pivotal intersection of cutting-edge technologies and complex engineering challenges aimed at solving real-world problems.This comprehensive body of work delves into the realm of CI,which is designed to tackle intricate and multifaceted engineering problems through advanced computational techniques.The history of CI systems is a fascinating journey that spans several decades and has its roots in the development of artificial intelligence and machine learning techniques.Through a wide array of practical examples and case studies,this special issue bridges the gap between theoretical concepts and practical implementation,shedding light on how CI systems can optimize processes,design solutions,and inform decisions in complex engineering landscapes.This compilation stands as an essential resource for both novice learners and seasoned practitioners,offering a holistic perspective on the potential of CI in reshaping the future of engineering problem-solving.

Novel Hybrid X GBoost Model to Forecast Soil Shear Strength Based on Some Soil Index Tests

When building geotechnical constructions like retaining walls and dams is of interest,one of the most important factors to consider is the soil’s shear strength parameters.This study makes an effort to propose a novel predictive model of shear strength.The study implements an extreme gradient boosting(XGBoost)technique coupled with a powerful optimization algorithm,the salp swarm algorithm(SSA),to predict the shear strength of various soils.To do this,a database consisting of 152 sets of data is prepared where the shear strength(τ)of the soil is considered as the model output and some soil index tests(e.g.,dry unit weight,water content,and plasticity index)are set as model inputs.Themodel is designed and tuned using both effective parameters of XGBoost and SSA,and themost accuratemodel is introduced in this study.Thepredictionperformanceof theSSA-XGBoostmodel is assessedbased on the coefficient of determination(R2)and variance account for(VAF).Overall,the obtained values of R^(2) and VAF(0.977 and 0.849)and(97.714%and 84.936%)for training and testing sets,respectively,confirm the workability of the developed model in forecasting the soil shear strength.To investigate the model generalization,the prediction performance of the model is tested for another 30 sets of data(validation data).The validation results(e.g.,R^(2) of 0.805)suggest the workability of the proposed model.Overall,findings suggest that when the shear strength of the soil cannot be determined directly,the proposed hybrid XGBoost-SSA model can be utilized to assess this parameter.

Introduction to the Special Issue on Soft Computing Techniques in Materials Science and Engineering

Soft computing(SC)refers to the ability of a digital computer or robot to perform functions that are normally associated with intelligent individuals,such as reasoning and problem-solving.An example of this would be a project aimed at creating systems capable of reasoning,discovering meaning,generalising,or learning from past experience.Science and engineering problems that are both non-linear and complex can be solved using these methodologies.It has been proven that these algorithms can be used to solve numerous real-world problems.The techniques outlined can be used to increase the accuracy of existing models/equations,or they can be used to propose a newmodel that can address the problem.

Rockburst prediction in hard rock mines developing bagging and boosting tree-based ensemble techniques

Rockburst prediction is of vital significance to the design and construction of underground hard rock mines.A rockburst database consisting of 102 case histories,i.e.,1998−2011 period data from 14 hard rock mines was examined for rockburst prediction in burst-prone mines by three tree-based ensemble methods.The dataset was examined with six widely accepted indices which are:the maximum tangential stress around the excavation boundary(MTS),uniaxial compressive strength(UCS)and uniaxial tensile strength(UTS)of the intact rock,stress concentration factor(SCF),rock brittleness index(BI),and strain energy storage index(EEI).Two boosting(AdaBoost.M1,SAMME)and bagging algorithms with classification trees as baseline classifier on ability to learn rockburst were evaluated.The available dataset was randomly divided into training set(2/3 of whole datasets)and testing set(the remaining datasets).Repeated 10-fold cross validation(CV)was applied as the validation method for tuning the hyper-parameters.The margin analysis and the variable relative importance were employed to analyze some characteristics of the ensembles.According to 10-fold CV,the accuracy analysis of rockburst dataset demonstrated that the best prediction method for the potential of rockburst is bagging when compared to AdaBoost.M1,SAMME algorithms and empirical criteria methods.

Structural Damage Identification Using Ensemble Deep Convolutional Neural Network Models

The existing strategy for evaluating the damage condition of structures mostly focuses on feedback supplied by traditional visualmethods,which may result in an unreliable damage characterization due to inspector subjectivity or insufficient level of expertise.As a result,a robust,reliable,and repeatable method of damage identification is required.Ensemble learning algorithms for identifying structural damage are evaluated in this article,which use deep convolutional neural networks,including simple averaging,integrated stacking,separate stacking,and hybridweighted averaging ensemble and differential evolution(WAE-DE)ensemblemodels.Damage identification is carried out on three types of damage.The proposed algorithms are used to analyze the damage of 4585 structural images.The effectiveness of the ensemble learning techniques is evaluated using the confusion matrix.For the testing dataset,the confusion matrix achieved an accuracy of 94 percent and a minimum recall of 92 percent for the best model(WAE-DE)in distinguishing damage types as flexural,shear,combined,or undamaged.

Application of several optimization techniques for estimating TBM advance rate in granitic rocks

This study aims to develop several optimization techniques for predicting advance rate of tunnel boring machine(TBM)in different weathered zones of granite.For this purpose,extensive field and laboratory studies have been conducted along the 12,649 m of the Pahang-Selangor raw water transfer tunnel in Malaysia.Rock properties consisting of uniaxial compressive strength(UCS),Brazilian tensile strength(BTS),rock mass rating(RMR),rock quality designation(RQD),quartz content(q)and weathered zone as well as machine specifications including thrust force and revolution per minute(RPM)were measured to establish comprehensive datasets for optimization.Accordingly,to estimate the advance rate of TBM,two new hybrid optimization techniques,i.e.an artificial neural network(ANN)combined with both imperialist competitive algorithm(ICA)and particle swarm optimization(PSO),were developed for mechanical tunneling in granitic rocks.Further,the new hybrid optimization techniques were compared and the best one was chosen among them to be used for practice.To evaluate the accuracy of the proposed models for both testing and training datasets,various statistical indices including coefficient of determination(R^2),root mean square error(RMSE)and variance account for(VAF)were utilized herein.The values of R^2,RMSE,and VAF ranged in 0.939-0.961,0.022-0.036,and 93.899-96.145,respectively,with the PSO-ANN hybrid technique demonstrating the best performance.It is concluded that both the optimization techniques,i.e.PSO-ANN and ICA-ANN,could be utilized for predicting the advance rate of TBMs;however,the PSO-ANN technique is superior.

Predicting TBM penetration rate in hard rock condition:A comparative study among six XGB-based metaheuristic techniques

A reliable and accurate prediction of the tunnel boring machine(TBM)performance can assist in minimizing the relevant risks of high capital costs and in scheduling tunneling projects.This research aims to develop six hybrid models of extreme gradient boosting(XGB)which are optimized by gray wolf optimization(GWO),particle swarm optimization(PSO),social spider optimization(SSO),sine cosine algorithm(SCA),multi verse optimization(MVO)and moth flame optimization(MFO),for estimation of the TBM penetration rate(PR).To do this,a comprehensive database with 1286 data samples was established where seven parameters including the rock quality designation,the rock mass rating,Brazilian tensile strength(BTS),rock mass weathering,the uniaxial compressive strength(UCS),revolution per minute and trust force per cutter(TFC),were set as inputs and TBM PR was selected as model output.Together with the mentioned six hybrid models,four single models i.e.,artificial neural network,random forest regression,XGB and support vector regression were also built to estimate TBM PR for comparison purposes.These models were designed conducting several parametric studies on their most important parameters and then,their performance capacities were assessed through the use of root mean square error,coefficient of determination,mean absolute percentage error,and a10-index.Results of this study confirmed that the best predictive model of PR goes to the PSO-XGB technique with system error of(0.1453,and 0.1325),R^(2) of(0.951,and 0.951),mean absolute percentage error(4.0689,and 3.8115),and a10-index of(0.9348,and 0.9496)in training and testing phases,respectively.The developed hybrid PSO-XGB can be introduced as an accurate,powerful and applicable technique in the field of TBM performance prediction.By conducting sensitivity analysis,it was found that UCS,BTS and TFC have the deepest impacts on the TBM PR.

Prediction of flyrock distance induced by mine blasting using a novel Harris Hawks optimization-based multi-layer perceptron neural network

In mining or construction projects,for exploitation of hard rock with high strength properties,blasting is frequently applied to breaking or moving them using high explosive energy.However,use of explosives may lead to the flyrock phenomenon.Flyrock can damage structures or nearby equipment in the surrounding areas and inflict harm to humans,especially workers in the working sites.Thus,prediction of flyrock is of high importance.In this investigation,examination and estimation/forecast of flyrock distance induced by blasting through the application of five artificial intelligent algorithms were carried out.One hundred and fifty-two blasting events in three open-pit granite mines in Johor,Malaysia,were monitored to collect field data.The collected data include blasting parameters and rock mass properties.Site-specific weathering index(WI),geological strength index(GSI) and rock quality designation(RQD)are rock mass properties.Multi-layer perceptron(MLP),random forest(RF),support vector machine(SVM),and hybrid models including Harris Hawks optimization-based MLP(known as HHO-MLP) and whale optimization algorithm-based MLP(known as WOA-MLP) were developed.The performance of various models was assessed through various performance indices,including a10-index,coefficient of determination(R^(2)),root mean squared error(RMSE),mean absolute percentage error(MAPE),variance accounted for(VAF),and root squared error(RSE).The a10-index values for MLP,RF,SVM,HHO-MLP and WOA-MLP are 0.953,0.933,0.937,0.991 and 0.972,respectively.R^(2) of HHO-MLP is 0.998,which achieved the best performance among all five machine learning(ML) models.

Optimized functional linked neural network for predicting diaphragm wall deflection induced by braced excavations in clays

Deep excavation during the construction of underground systems can cause movement on the ground,especially in soft clay layers.At high levels,excessive ground movements can lead to severe damage to adjacent structures.In this study,finite element analyses(FEM)and the hardening small strain(HSS)model were performed to investigate the deflection of the diaphragm wall in the soft clay layer induced by braced excavations.Different geometric and mechanical properties of the wall were investigated to study the deflection behavior of the wall in soft clays.Accordingly,1090 hypothetical cases were surveyed and simulated based on the HSS model and FEM to evaluate the wall deflection behavior.The results were then used to develop an intelligent model for predicting wall deflection using the functional linked neural network(FLNN)with different functional expansions and activation functions.Although the FLNN is a novel approach to predict wall deflection;however,in order to improve the accuracy of the FLNN model in predicting wall deflection,three swarm-based optimization algorithms,such as artificial bee colony(ABC),Harris’s hawk’s optimization(HHO),and hunger games search(HGS),were hybridized to the FLNN model to generate three novel intelligent models,namely ABC-FLNN,HHO-FLNN,HGS-FLNN.The results of the hybrid models were then compared with the basic FLNN and MLP models.They revealed that FLNN is a good solution for predicting wall deflection,and the application of different functional expansions and activation functions has a significant effect on the outcome predictions of the wall deflection.It is remarkably interesting that the performance of the FLNN model was better than the MLP model with a mean absolute error(MAE)of 19.971,root-mean-squared error(RMSE)of 24.574,and determination coefficient(R^(2))of 0.878.Meanwhile,the performance of the MLP model only obtained an MAE of 20.321,RMSE of 27.091,and R^(2)of 0.851.Furthermore,the results also indicated that the proposed hybrid models,i.e.,ABC-FLNN,HHO-FLNN,HGS-FLNN,yielded more superior performances than those of the FLNN and MLP models in terms of the prediction of deflection behavior of diaphragm walls with an MAE in the range of 11.877 to 12.239,RMSE in the range of 15.821 to 16.045,and R^(2)in the range of 0.949 to 0.951.They can be used as an alternative tool to simulate diaphragm wall deflections under different conditions with a high degree of accuracy.

An evolutionary adaptive neuro-fuzzy inference system for estimating field penetration index of tunnel boring machine in rock mass

Field penetration index(FPI) is one of the representative key parameters to examine the tunnel boring machine(TBM) performance.Lack of accurate FPI prediction can be responsible for numerous disastrous incidents associated with rock mechanics and engineering.This study aims to predict TBM performance(i.e.FPI) by an efficient and improved adaptive neuro-fuzzy inference system(ANFIS) model.This was done using an evolutionary algorithm,i.e.artificial bee colony(ABC) algorithm mixed with the ANFIS model.The role of ABC algorithm in this system is to find the optimum membership functions(MFs) of ANFIS model to achieve a higher degree of accuracy.The procedure and modeling were conducted on a tunnelling database comprising of more than 150 data samples where brittleness index(BI),fracture spacing,α angle between the plane of weakness and the TBM driven direction,and field single cutter load were assigned as model inputs to approximate FPI values.According to the results obtained by performance indices,the proposed ANFISABC model was able to receive the highest accuracy level in predicting FPI values compared with ANFIS model.In terms of coefficient of determination(R^(2)),the values of 0.951 and 0.901 were obtained for training and testing stages of the proposed ANFISABC model,respectively,which confirm its power and capability in solving TBM performance problem.The proposed model can be used in the other areas of rock mechanics and underground space technologies with similar conditions.

Rock Strength Estimation Using Several Tree-Based ML Techniques

The uniaxial compressive strength(UCS)of rock is an essential property of rock material in different relevant applications,such as rock slope,tunnel construction,and foundation.It takes enormous time and effort to obtain the UCS values directly in the laboratory.Accordingly,an indirect determination of UCS through conducting several rock index tests that are easy and fast to carry out is of interest and importance.This study presents powerful boosting trees evaluation framework,i.e.,adaptive boosting machine,extreme gradient boosting machine(XGBoost),and category gradient boosting machine,for estimating the UCS of sandstone.Schmidt hammer rebound number,P-wave velocity,and point load index were chosen as considered factors to forecast UCS values of sandstone samples.Taylor diagrams and five regression metrics,including coefficient of determination(R2),root mean square error,mean absolute error,variance account for,and A-20 index,were used to evaluate and compare the performance of these boosting trees.The results showed that the proposed boosting trees are able to provide a high level of prediction capacity for the prepared database.In particular,itwas worth noting that XGBoost is the best model to predict sandstone strength and it achieved 0.999 training R^(2) and 0.958 testing R^(2).The proposed model had more outstanding capability than neural network with optimization techniques during training and testing phases.The performed variable importance analysis reveals that the point load index has a significant influence on predicting UCS of sandstone.

A stacked multiple kernel support vector machine for blast inducedflyrock prediction

As a widely used rock excavation method in civil and mining construction works, the blasting operations and theinduced side effects are always investigated by the existing studies. The occurrence of flyrock is regarded as one ofthe most important issues induced by blasting operations, since the accurate prediction of which is crucial fordelineating safety zone. For this purpose, this study developed a flyrock prediction model based on 234 sets ofblasting data collected from Sugun Copper Mine site. A stacked multiple kernel support vector machine (stackedMK-SVM) model was proposed for flyrock prediction. The proposed stacked structure can effectively improve themodel performance by addressing the importance level of different features. For comparison purpose, 6 othermachine learning models were developed, including SVM, MK-SVM, Lagragian Twin SVM (LTSVM), ArtificialNeural Network (ANN), Random Forest (RF) and M5 Tree. This study implemented a 5-fold cross validationprocess for hyperparameters tuning purpose. According to the evaluation results, the proposed stacked MK-SVMmodel achieved the best overall performance, with RMSE of 1.73 and 1.74, MAE of 0.58 and 1.08, VAF of 98.95and 99.25 in training and testing phase, respectively.

Tree-Based Solution Frameworks for Predicting Tunnel Boring Machine Performance Using Rock Mass and Material Properties

Tunnel Boring Machines(TBMs)are vital for tunnel and underground construction due to their high safety and efficiency.Accurately predicting TBM operational parameters based on the surrounding environment is crucial for planning schedules and managing costs.This study investigates the effectiveness of tree-based machine learning models,including Random Forest,Extremely Randomized Trees,Adaptive Boosting Machine,Gradient Boosting Machine,Extreme Gradient Boosting Machine(XGBoost),Light Gradient Boosting Machine,and CatBoost,in predicting the Penetration Rate(PR)of TBMs by considering rock mass and material characteristics.These techniques are able to provide a good relationship between input(s)and output parameters;hence,obtaining a high level of accuracy.To do that,a comprehensive database comprising various rock mass and material parameters,including Rock Mass Rating,Brazilian Tensile Strength,and Weathering Zone,was utilized for model development.The practical application of these models was assessed with a new dataset representing diverse rock mass and material properties.To evaluate model performance,ranking systems and Taylor diagrams were employed.CatBoost emerged as the most accurate model during training and testing,with R2 scores of 0.927 and 0.861,respectively.However,during validation,XGBoost demonstrated superior performance with an R2 of 0.713.Despite these variations,all tree-based models showed promising accuracy in predicting TBM performance,providing valuable insights for similar projects in the future.

Estimation of the TBM advance rate under hard rock conditions using XGBoost and Bayesian optimization

The advance rate(AR)of a tunnel boring machine(TBM)under hard rock conditions is a key parameter in the successful implementation of tunneling engineering.In this study,we improved the accuracy of prediction models by employing a hybrid model of extreme gradient boosting(XGBoost)with Bayesian optimization(BO)to model the TBM AR.To develop the proposed models,1286 sets of data were collected from the Peng Selangor Raw Water Transfer tunnel project in Malaysia.The database consists of rock mass and intact rock features,including rock mass rating,rock quality designation,weathered zone,uniaxial compressive strength,and Brazilian tensile strength.Machine specifications,including revolution per minute and thrust force,were considered to predict the TBM AR.The accuracies of the predictive models were examined using the root mean squares error(RMSE)and the coefficient of determination(R^(2))between the observed and predicted yield by employing a five-fold cross-validation procedure.Results showed that the BO algorithm can capture better hyper-parameters for the XGBoost prediction model than can the default XGBoost model.The robustness and generalization of the BO-XGBoost model yielded prominent results with RMSE and R^(2) values of 0.0967 and 0.9806(for the testing phase),respectively.The results demonstrated the merits of the proposed BO-XGBoost model.In addition,variable importance through mutual information tests was applied to interpret the XGBoost model and demonstrated that machine parameters have the greatest impact as compared to rock mass and material properties.

Intelligent rockburst prediction model with sample category balance using feedforward neural network and Bayesian optimization

The rockburst prediction becomes more and more challenging due to the development of deep underground projects and constructions.Increasing numbers of intelligent algorithms are used to predict and prevent rockburst.This paper investigated the drawbacks of neural networks in rockburst prediction,and aimed at these shortcomings,Bayesian optimization and the synthetic minority oversampling technique+Tomek Link(SMOTETomek)were applied to efficiently develop the feedforward neural network(FNN)model for rockburst prediction.In this regard,314 real rockburst cases were collected to establish a database for modeling.The database was divided into a training set(80%)and a test set(20%).The maximum tangential stress,uniaxial compressive strength,tensile strength,stress ratio,brittleness ratio,and elastic strain energy were selected as input parameters.Bayesian optimization was implemented to find the optimal hyperparameters in FNN.To eliminate the effects of imbalanced category,SMOTETomek was adopted to process the training set to obtain a balanced training set.The FNN developed by the balanced training set received 90.48% accuracy in the test set,and the accuracy improved 12.7% compared to the imbalanced training set.For interpreting the FNN model,the permutation importance algorithm was introduced to analyze the relative importance of input variables.The elastic strain energy was the most essential variable,and some measures were proposed to prevent rockburst.To validate the practicability,the FNN developed by the balanced training set was utilized to predict rockburst in Sanshandao Gold Mine,China,and it had outstanding performance(accuracy 100%).

Stability analysis of underground mine hard rock pillars via combination of finite difference methods,neural networks,and Monte Carlo simulation techniques

Pillar stability is always evaluated using the safety factor(SF),which is defined as the ratio of pillar strength to pillar stress.However,most researchers have estimated pillar stress using the pillar shape ratio(w/h),uniaxial compressive strength(UCS)of the intact rock mass,and pillar depth(H).In this study,the geological strength index(GSI)of hard rock pillars was considered as a new variable for predictive purposes.This index was developed by combining numerical simulation software(i.e.,FLAC3D)and a backpropagation neural network(BPNN).A hard rock pillar stability analysis,based on three methods including deterministic method,sensitivity analysis,and Monte Carlo simulation(MCS),was performed.A new formula was proposed to estimate the SF values based on the predicted stress,considering the GSI variable in the deterministic method.The sensitivity analysis indicated that the variables impacting the SF from high to low are UCS,GSI,w/h,and H.In this study,pillar stability was analyzed mainly using the GSI and MCS techniques.The MCS results revealed that the GSI is also a major factor in pillar stability and has a greater effect on weak pillars than on strong ones.Furthermore,a pillar is more likely to be unstable when both the GSI and the UCS are decreased.This study provides several references and procedures for improving the design of stable pillars considering the GSI as an important factor.