Prediction of unconfined compressive strength of rock surrounding a roadway using artificial neural network

The unconfined compressive strength (UCS) of rocks is an important design parameter in rock engineering and geotechnics, which is required and determined for rock mechanical studies in mining and civil projects. This parameter is usually determined through a laboratory UCS test. Since the preparation of high-quality samples is difficult, expensive and time consuming for laboratory tests, development of predictive models for determining the mechanical properties of rocks seems to be essential in rock engineering. In this study, an attempt was made to develop an artificial neural network (ANN) and multivariable regression analysis (MVRA) models in order to predict UCS of rock surrounding a roadway. For this, a database of laboratory tests was prepared, which includes rock type, Schmidt hardness, density and porosity as input parameters and UCS as output parameter. To make a database (including 93 datasets), different rock samples, ranging from weak to very strong types, are used. To compare the performance of developed models, determination coefficient (R ²), variance account for (VAF), mean absolute error (E _a) and mean relative error (E _r) indices between predicted and measured values were calculated. Based on this comparison, it was concluded that performance of the ANN model is considerably better than the MVRA model. Further, a sensitivity analysis shows that rock density and Schmidt hardness were recognized as the most effective parameters, whereas porosity was considered as the least effective input parameter on the ANN model output (UCS) in this study.     

Rock strength assessment based on regression tree technique

Uniaxial compressive strength (UCS) is one of the most important parameters for investigation of rock behaviour in civil and mining engineering applications. The direct method to determine UCS is time consuming and expensive in the laboratory. Therefore, indirect estimation of UCS values using other rock index tests is of interest. In this study, extensive laboratory tests including density test, Schmidt hammer test, point load strength test and UCS test were conducted on 106 samples of sandstone which were taken from three sites in Malaysia. Based on the laboratory results, some new equations with acceptable reliability were developed to predict UCS using simple regression analysis. Additionally, results of simple regression analysis show that there is a need to propose UCS predictive models by multiple inputs. Therefore, considering the same laboratory results, multiple regression (MR) and regression tree (RT) models were also performed. To evaluate performance prediction of the developed models, several performance indices, i.e. coefficient of determination (R ²), variance account for and root mean squared error were examined. The results indicated that the RT model can predict UCS with higher performance capacity compared to MR technique. R ² values of 0.857 and 0.801 for training and testing datasets, respectively, suggests the superiority of the RT model in predicting UCS, while these values are obtained as 0.754 and 0.770 for MR model, respectively.     

Uniaxial compressive strength prediction through a new technique based on gene expression programming

Proper estimation of rock strength is a critical task for evaluation and design of some geotechnical applications such as tunneling and excavation. Uniaxial compressive strength (UCS) test can be measured directly in the laboratory; nevertheless, the direct UCS determination is time-consuming and expensive. In this study, feasibility of gene expression programming (GEP) model in indirect determination of UCS values of sandstone rock samples is examined. In this regard, several laboratory tests including Brazilian test, density test, slake durability test and UCS test were conducted on 47 samples of sandstone which were collected from the Dengkil, Malaysia. Considering multiple inputs, several GEP models were constructed to estimate UCS of the rock and finally, the best GEP model was selected. In order to indicate capability of the proposed GEP model, linear multiple regression (LMR) was also performed. It was found that the GEP model is superior to LMR one in terms of applied performance indices. Based on coefficient of determination (R ²) of testing datasets, by proposing GEP model, it can be improved from 0.930 (which was obtained by LMR model) to 0.965. As a result, it is concluded that the proposed models in this study, could be utilized to estimate UCS of similar rock type in practice.

     

Rock strength estimation: a PSO-based BP approach

Application of back-propagation (BP) artificial neural network (ANN) as an accurate, practical and quick tool in indirect estimation of uniaxial compressive strength (UCS) of rocks has recently been highlighted in the literature. This is mainly due to difficulty in direct determination of UCS in laboratory as preparing the core samples for this test is troublesome and time-consuming. However, ANN technique has some limitations such as getting trapped in local minima. These limitations can be minimized by combining the ANNs with robust optimization algorithms like particle swarm optimization (PSO). This paper gives insight into development of a hybrid PSO–BP predictive model of UCS. For this reason, dataset comprising the results of 228 laboratory tests including dry density, moisture content, P wave velocity, point load index test, slake durability index and UCS was prepared. These tests were conducted on 38 sandstone samples which were taken from two excavation sites in Malaysia. Findings showed that PSO–BP model performs well in predicting UCS. Nevertheless, to compare the prediction performance of the PSO–BP model, the UCS is predicted using ANN-based PSO and BP models. The correlation coefficient, R, values equal to 0.988 and 0.999 for training and testing datasets, respectively, suggest that the PSO–BP model outperforms the other predictive models.

     

An application of adaptive neuro fuzzy inference system for estimating the uniaxial compressive strength of certain granitic rocks from their mineral contents

The uniaxial compressive strength (UCS) of rocks is an important intact rock parameter, and it is commonly used for various engineering applications. This parameter is mainly controlled by the mineralogical and textural characteristics of rocks. In this study, a soft computing method, an adaptive neuro-fuzzy inference system (ANFIS), was employed to estimate UCS from the mineral contents of certain granitic rocks selected from Turkey; nonlinear multiple regression analysis was then employed to validate these estimations. Five nonlinear multiple regressions and ANFIS models were constructed with three inputs: quartz, orthoclase and plagioclase. To determine the optimal model, various performance indices (R, values account for and root mean square error) were determined, and the model obtained from dataset #3 was selected as the optimal model. The coefficients of correlation for the nonlinear multiple regression and ANFIS models were 0.87 and 0.91, respectively. Thus, both models yielded acceptable results, and the ANFIS is a suitable method for estimating the UCS of rocks.     

Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances

Uniaxial compressive strength (UCS) of rock is crucial for any type of projects constructed in/on rock mass. The test that is conducted to measure the UCS of rock is expensive, time consuming and having sample restriction. For this reason, the UCS of rock may be estimated using simple rock tests such as point load index (I _s(50)), Schmidt hammer (R _n) and p-wave velocity (V _p) tests. To estimate the UCS of granitic rock as a function of relevant rock properties like R _n, p-wave and I _s(50), the rock cores were collected from the face of the Pahang–Selangor fresh water tunnel in Malaysia. Afterwards, 124 samples are prepared and tested in accordance with relevant standards and the dataset is obtained. Further an established dataset is used for estimating the UCS of rock via three-nonlinear prediction tools, namely non-linear multiple regression (NLMR), artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). After conducting the mentioned models, considering several performance indices including coefficient of determination (R ²), variance account for and root mean squared error and also using simple ranking procedure, the models were examined and the best prediction model was selected. It is concluded that the R ² equal to 0.951 for testing dataset suggests the superiority of the ANFIS model, while these values are 0.651 and 0.886 for NLMR and ANN techniques, respectively. The results pointed out that the ANFIS model can be used for predicting UCS of rocks with higher capacity in comparison with others. However, the developed model may be useful at a preliminary stage of design; it should be used with caution and only for the specified rock types.     

Estimating the uniaxial compressive strength of some clay-bearing rocks selected from Turkey by nonlinear multivariable regression and rule-based fuzzy models

Abstract: Although the use of predictive models in rock engineering and engineering geology is an important issue, some simple and multivariate regression techniques traditionally employed in these areas have recently been challenged by the use of fuzzy inference systems and artificial neural networks. The purpose of this study was to construct some predictive models to estimate the uniaxial compressive strength of some clay-bearing rocks, depending on examination of their slake durability indices and clay contents. For this purpose, the simple and nonlinear multivariable regression techniques and the Mamdani fuzzy algorithm are compared in terms of their accuracy. To increase the accuracy of the Mamdani fuzzy inference system, the weighted if–then rules are extracted. To compare the predictive performances of the models, the statistical performance indices (root mean square error and variance account for) are calculated and the results are discussed. The indices reveal that the fuzzy inference system has a slightly higher prediction capacity than the regression models. The basic reason for the higher performance of the fuzzy inference system is the flexibility of the fuzzy approach.     

Constitutive models describing the influence of the geometry of partially-spanning joints on jointed rock mass strength: Regression and fuzzy logic analysis of experimental data

Using existing experimental data from Uniaxial Compressive Strength (UCS) testing, constitutive models were produced to describe the influence of joint geometry (joint location, trace length and orientation) on the UCS of rock containing partially-spanning joints. Separate approaches were used to develop two models: a multivariable regression model, and a fuzzy inference system model. Comparison of model predictions to the experimental data demonstrates that both models are capable of accurately describing the UCS of jointed rock with partially-spanning joints using information relating to joint geometry. However, according to the statistical evaluation methods used for performance evaluation, the multivariable regression model was significantly more accurate. Analysis of predictions made by the fuzzy inference system model showed that it was capable of resolving certain peculiarities in the influence of partially-spanning joint orientation on the compressive strength of rock that, from rock mechanics and fracture mechanics theory, should be expected. The multivariable regression model, whilst more accurate, did not recognise these peculiarities. Due to the additional insight that can be gleaned from the fuzzy inference system modelling, we recommend the use of the fuzzy inference system constitutive model in combination with the multivariable regression model.     

Developing a new uncertain rule-based fuzzy approach for evaluating the blast-induced backbreak

This study proposes a new uncertain rule-based fuzzy approach for the evaluation of blast-induced backbreak. The proposed approach is based on rock engineering systems (RES) updated by the fuzzy system. Additionally, a genetic algorithm (GA) and imperialist competitive algorithm (ICA) were employed for the prediction aim. The most key step in modeling of fuzzy RES is the coding of the interaction matrix. This matrix is responsible for analyzing the interrelationships among the parameters influencing the rock engineering activities. The codes of the interaction matrix are not unique; thus, probabilistic coding can be done non-deterministically, which allows the uncertainties to be considered in the RES analysis. To achieve the objective of this research, 62 blasts in Shur River dam region, located in south of Iran, were investigated and the required datasets were measured. The performance of the proposed models was then evaluated in accordance with the statistical criteria such as coefficient of determination (R²). The results signify the effectiveness of the proposed GA- and ICA-based models in the simulating process. R² of 0.963 and 0.934 obtained from ICA- and GA-based models, respectively, revealed that both models were capable of predicting the backbreak. Further, the fuzzy RES was introduced as a powerful uncertain approach to evaluate and predict the backbreak.

     

An application of fuzzy sets to the Geological Strength Index (GSI) system used in rock engineering

Characterization of rock masses is one of the fundamental aspects of rock engineering. Particularly, as a rock mass characteristic, determination of the strength of closely jointed rock masses is difficult since the size of representative specimens including discontinuities is too large for laboratory testing. This difficulty can be overcome by using the Hoek–Brown empirical failure criterion in conjunction with the Geological Strength Index (GSI) Classification System. However, characterization of rock masses and determination of their strength may involve some uncertainties due to their complex nature. The fuzzy set theory is one of the tools to handle such uncertainties. This paper describes the application of fuzzy set theory to the GSI System by incorporating judgement and experience of practising engineers. For the purpose, the original GSI System and its modified form were defined by fuzzy sets, and Mamdani fuzzy algorithm was constructed using 22 “if–then” rules for evaluating discontinuity parameters and their ratings considered in the GSI System. In addition, slope instabilities in heavily jointed rock masses selected from two open pit mines in Turkey were back analysed and the results were evaluated to demonstrate and to check the performance of this approach.     

Design and implementation of a new tuned hybrid intelligent model to predict the uniaxial compressive strength of the rock using SFS-ANFIS

This study proposes a novel design to systematically optimize the parameters for the adaptive neuro-fuzzy inference system (ANFIS) model using stochastic fractal search (SFS) algorithm. To affirm the efficiency of the proposed SFS-ANFIS model, the predicting results were compared with ANFIS and three hybrid methodologies based on ANFIS combined with genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO). Accurate prediction of uniaxial compressive strength (UCS) is of great significance for all geotechnical projects such as tunnels and dams. Hence, this study proposes the use of SFS-ANFIS, GA-ANFIS, DE-ANFIS, PSO-ANFIS, and ANFIS models to predict UCS. In this regard, the fresh water tunnel of Pahang–Selangor located in Malaysia was considered and the requirement data samples were collected. Different statistical metrics such as coefficient of determination (R²) and mean absolute error were used to evaluate the models. Referring to the efficiency results of SFS-ANFIS, it can be found that the SFS-ANFIS (with the R² of 0.981) has higher ability than PSO-ANFIS, DE-ANFIS, GA-ANFIS, and ANFIS models in predicting the UCS.

     

Application of improved support vector regression model for prediction of deformation modulus of a rock mass

Deformation modulus of a rock mass is one of the crucial parameters used in the design of surface and underground rock engineering structures. Determination of this parameter by testing cylindrical core samples is almost impossible due to the presence of discontinuities. Due to the problems in determining the deformability of jointed rock masses at the laboratory-scale, various in situ test methods such as plate loading tests, dilatometer etc. have been developed. Although these methods are currently the best techniques, they are expensive and time-consuming, and present operational problems. To overcome this difficulty, in this paper, presents the results of the application of hybrid support vector regression (SVR) with harmony search algorithm , differential evolution algorithm and particle swarm optimization algorithm (PSO). The optimized models were applied to available data given in open source literature and the performance of optimization algorithm was assessed by virtue of statistical criteria. In these models, rock mass rating (RMR), depth, uniaxial compressive strength of intact rock (UCS) and elastic modulus of intact rock (E _i) were utilized as the input parameters, while the deformation modulus of a rock mass was the output parameter. The comparative results revealed that hybrid of PSO and SVR yield robust model which outperform other models in term of higher squared correlation coefficient (R ²) and variance account for (VAF) and lower mean square error (MSE), root mean squared error (RMSE) and mean absolute percentage error (MAPE).     

Estimation of elastic constant of rocks using an ANFIS approach

The engineering properties of the rocks have the most vital role in planning of rock excavation and construction for optimum utilization of earth resources with greater safety and least damage to surroundings. The design and construction of structure is influenced by physico-mechanical properties of rock mass. Young's modulus provides insight about the magnitude and characteristic of the rock mass deformation due to change in stress field. The determination of the Young's modulus in laboratory is very time consuming and costly. Therefore, basic rock properties like point load, density and water absorption have been used to predict the Young's modulus. Point load, density and water absorption can be easily determined in field as well as laboratory and are pertinent properties to characterize a rock mass. The artificial neural network (ANN), fuzzy inference system (FIS) and neuro fuzzy are promising techniques which have proven to be very reliable in recent years. In, present study, neuro fuzzy system is applied to predict the rock Young's modulus to overcome the limitation of ANN and fuzzy logic. Total 85 dataset were used for training the network and 10 dataset for testing and validation of network rules. The network performance indices correlation coefficient, mean absolute percentage error (MAPE), root mean square error (RMSE), and variance account for (VAF) are found to be 0.6643, 7.583, 6.799, and 91.95 respectively, which endow with high performance of predictive neuro-fuzzy system to make use for prediction of complex rock parameter.     

A comparative study of generalized regression neural network approach and adaptive neuro-fuzzy inference systems for prediction of unconfined compressive strength of rocks

The engineering properties of rocks play a significant role in planning and designing of mining and civil engineering projects. A laboratory database of mechanical and engineering properties of rocks is always required for site characterization and mineral exploitation. Due to discontinuous and variable nature of rock masses, it is difficult to obtain all physicomechanical properties of rocks precisely. Prediction of unconfined compressive strength from seismic wave velocities (Compressional wave, Shear wave) and density of rock using generalized regression neural network (GRNN) and adaptive neuro-fuzzy inference systems (ANFIS) can be appropriate and alternate methods to minimize the time and cost of tests. GRNN and ANFIS models were trained with 41 data sets using conjugate gradient descent algorithms and hybrid learning algorithm, respectively. Performance of both the models was examined with 15 testing data sets. In the present study, obtained network performance indices such as correlation coefficient, mean absolute percentage error, root mean square error and variance account for indicate high performance of predictive capability of GRNN system and closer to actual data over the ANFIS.     

An assessment of total RMR classification system using unified simulation model based on artificial neural networks

Engineering design has great importance in the cost and safety of engineering structures. Rock mass rating (RMR) system has become a reliable and widespread pre-design system for its ease of use and variety in engineering applications such as tunnels, foundations, and slopes. In RMR system, six parameters are employed in classifying a rock mass: uniaxial compressive strength of intact rock material (UCS), rock quality designation (RQD), spacing of discontinuities (SD), condition of discontinuities (CD), condition of groundwater (CG), and orientation of discontinuities (OD). The ratings of the first three parameters UCS, RQD, and SD are determined via graphic readings where the last three parameters CD, CG, and OD are estimated by the tables that are composed of interval valued linguistic expressions. Because of these linguistic expresions, the estimated rating values of the last three become fuzzy especially when the related conditions are close to border of any two classes. In such cases, these fuzzy situations could lead up incorrect rock class estimations. In this study, an empirical database based on the linguistic expressions for CD, CG, and OD is developed for training Artificial Neural Network (ANN) classifiers. The results obtained from graphical readings and ANN classifiers are unified in a simulation model (USM). The data obtained from five different tunnels, which were excavated for derivation purpose, are used to evaluate classification results of conventional method and proposed model. Finally, it is noted that more accurate and realistic ratings are reached by means of proposed model.     

Assessment of plastic zones surrounding the power station cavern using numerical,fuzzy and statistical models

Plastic zones evaluation around the powerhouse caverns is a very crucial issue in designing and constructing these structures and accurate determination of their related optimum support systems. Due to inherent difficulties during the field measurement of plastic zones around the powerhouse caverns and shortcomings of the available methods in this field, applying new predictive models is an attractive and helpful topic. Accordingly, plastic zones around the powerhouse caverns have been investigated in this research using numerical analysis (NA), fuzzy inference system (FIS) and multivariate regression (MVR) model. Based on the numerical simulations, a new predictive equation has been developed to determine the plastic zone at middle point of sidewall and induced key point around a cavern. The basic parameters including rock geomechanical properties and geometrical characteristics of cavern structures have been considered as input variables in plastic zones modeling at middle points of roof, floor, left sidewall and right sidewall as well as at key point. For FIS and MVR models construction, sufficient datasets were introduced based on the numerical simulations. Performance of established models has been assessed applying testing dataset and utilizing powerful statistical indices. Accordingly, it is proved that the derived results from FIS and NA models are more precise than MVR model and they are more satisfactory in plastic zone estimation. Finally, parametric study results revealed that lateral stress coefficient, depth of overburden and rock mass rating are the most effectual parameters and tensile strength is the least influencing parameter on the plastic zone around a cavern.

     

Identification and sizing of the entirely visible rocks from a 3D surface data segmentation of laboratory rock piles

Once segmentation of 3D surface data of a rock pile has been performed, the next task is to determine the visibility of the surface rocks. A region boundary-following algorithm that accommodates irregularly spaced 3D coordinate data is presented for determining this visibility. We examine 3D surface segmentations of laboratory rock piles and determine which regions in the segmentation correspond to entirely visible rocks, and which correspond to overlapped or partially visible rocks. This is a significant distinction as it allows accurate size determination of entirely visible rocks, separate handling of partially visible rocks, and prevents erroneous bias resulting from mishandling partially visible rocks as smaller entirely visible rocks. Literature review indicates that other rock pile sizing techniques fail to make this distinction. The rock visibility results are quantified by comparison to manual surface classifications of the laboratory piles and the size results are quantified by comparison to the sieve size.     

An efficient time series forecasting model based on fuzzy time series

In this paper, we present a new model to handle four major issues of fuzzy time series forecasting, viz., determination of effective length of intervals, handling of fuzzy logical relationships (FLRs), determination of weight for each FLR, and defuzzification of fuzzified time series values. To resolve the problem associated with the determination of length of intervals, this study suggests a new time series data discretization technique. After generating the intervals, the historical time series data set is fuzzified based on fuzzy time series theory. Each fuzzified time series values are then used to create the FLRs. Most of the existing fuzzy time series models simply ignore the repeated FLRs without any proper justification. Since FLRs represent the patterns of historical events as well as reflect the possibility of appearances of these types of patterns in the future. If we simply discard the repeated FLRs, then there may be a chance of information lost. Therefore, in this model, it is recommended to consider the repeated FLRs during forecasting. It is also suggested to assign weights on the FLRs based on their severity rather than their patterns of occurrences. For this purpose, a new technique is incorporated in the model. This technique determines the weight for each FLR based on the index of the fuzzy set associated with the current state of the FLR. To handle these weighted FLRs and to obtain the forecasted results, this study proposes a new defuzzification technique. The proposed model is verified and validated with three different time series data sets. Empirical analyses signify that the proposed model have the robustness to handle one-factor time series data set very efficiently than the conventional fuzzy time series models. Experimental results show that the proposed model also outperforms over the conventional statistical models.     

Applying several machine learning approaches for prediction of unconfined compressive strength of stabilized pond ashes

This paper evaluates the potential of five modeling approaches, namely M5 model tree, random forest, artificial neural networks, support vector machines and Gaussian processes, for the prediction of unconfined compressive strength of stabilized pond ashes with lime and lime sludge. The study not only presents five models for the same set of data but also compares the overall performance of them. Dataset used consists of 255 samples acquired from laboratory experiments. Out of the total, 170 randomly chosen samples were used for training and remaining 85 were used for testing the models. Input dataset consists of eight parameters (uniformity coefficient, coefficient of curvature, maximum dry density, optimum moisture content, lime, lime sludge, curing period and 7-day soaked California bearing ratio), while the output is UCS value at 7, 28, 45, 90 and 180 days of curing. Comparisons of results propose that Gaussian processes modeling strategy works well and the overall performance was substantially nearer to the exact agreement line. As a result of GP model, higher value of CC = 0.997 and lower values of RMSE = 23.016 kPa and MAE = 16.455 were obtained for testing the dataset. Sensitivity analysis suggests that lime, lime sludge, curing period and California bearing ratio are the significant parameters for predicting the unconfined compressive strength of stabilized pond ashes. The results confirmed that GP models are in a position to predict the unconfined compressive strength of stabilized pond ashes with an excessive degree of accuracy; however, GP modeling approach proves that this approach is more economical and less difficult in comparison with tedious laboratory work.

     

Computer vision-based rock modelling

This paper deals with the application of computer vision to mining automation. In particular, it presents results from an on-going research project investigating the automation of the rock-breaking process, a process typical of underground hardrock mining. The objective of this research is to investigate the use of computer vision to identify and locate the oversized lumps remaining on a grizzly (metal sieve) after blasting, for the secondary rock-breaking operation. Range images of rocks are acquired in our laboratory using the NRCC/McGill laser rangefinder. Rock-pile images are segmented into parts (rocks) based on their surface characteristics. Finally, superquadric models are fit to the segmented range data to characterize the 3D shape of each rock.