Predicting uniaxial compressive strength of tuff after accelerated freeze-thaw testing: Comparative analysis of regression models and artificial neural networks

Ignimbrites have been widely used as building materials in many historical and touristic structures in the Kayseri region of Türkiye. Their diverse colours and textures make them a popular choice for modern construction as well. However, ignimbrites are particularly vulnerable to atmospheric conditions, such as freeze-thaw cycles, due to their high porosity, which is a result of their formation process. When water enters the pores of the ignimbrites, it can freeze during cold weather. As the water freezes and expands, it generates internal stress within the stone, causing micro-cracks to develop. Over time, repeated freeze-thaw (F-T) cycles lead to the growth of these micro-cracks into larger cracks, compromising the structural integrity of the ignimbrites and eventually making them unsuitable for use as building materials. The determination of the long-term F-T performance of ignimbrites can be established after long F-T experimental processes. Determining the long-term F-T performance of ignimbrites typically requires extensive experimental testing over prolonged freeze-thaw cycles. To streamline this process, developing accurate predictive equations becomes crucial. In this study, such equations were formulated using classical regression analyses and artificial neural networks (ANN) based on data obtained from these experiments, allowing for the prediction of the F-T performance of ignimbrites and other similar building stones without the need for lengthy testing. In this study, uniaxial compressive strength, ultrasonic propagation velocity, apparent porosity and mass loss of ignimbrites after long-term F-T were determined. Following the F-T cycles, the disintegration rate was evaluated using decay function approaches, while uniaxial compressive strength (UCS) values were predicted with minimal input parameters through both regression and ANN analyses. The ANN and regression models created for this purpose were first started with a single input value and then developed with two and three combinations. The predictive performance of the models was assessed by comparing them to regression models using the coefficient of determination (R2) as the evaluation criterion. As a result of the study, higher R2 values (0.87) were obtained in models built with artificial neural network. The results of the study indicate that ANN usage can produce results close to experimental outcomes in predicting the long-term F-T performance of ignimbrite samples.

Uniaxial Compressive Strength Prediction for Rock Material in Deep Mine Using Boosting-Based Machine Learning Methods and Optimization Algorithms

Traditional laboratory tests for measuring rock uniaxial compressive strength(UCS)are tedious and timeconsuming.There is a pressing need for more effective methods to determine rock UCS,especially in deep mining environments under high in-situ stress.Thus,this study aims to develop an advanced model for predicting the UCS of rockmaterial in deepmining environments by combining three boosting-basedmachine learning methods with four optimization algorithms.For this purpose,the Lead-Zinc mine in Southwest China is considered as the case study.Rock density,P-wave velocity,and point load strength index are used as input variables,and UCS is regarded as the output.Subsequently,twelve hybrid predictive models are obtained.Root mean square error(RMSE),mean absolute error(MAE),coefficient of determination(R2),and the proportion of the mean absolute percentage error less than 20%(A-20)are selected as the evaluation metrics.Experimental results showed that the hybridmodel consisting of the extreme gradient boostingmethod and the artificial bee colony algorithm(XGBoost-ABC)achieved satisfactory results on the training dataset and exhibited the best generalization performance on the testing dataset.The values of R2,A-20,RMSE,and MAE on the training dataset are 0.98,1.0,3.11 MPa,and 2.23MPa,respectively.The highest values of R2 and A-20(0.93 and 0.96),and the smallest RMSE and MAE values of 4.78 MPa and 3.76MPa,are observed on the testing dataset.The proposed hybrid model can be considered a reliable and effective method for predicting rock UCS in deep mines.

Effects of mineralogical composition on uniaxial compressive strengths of sedimentary rocks

Figuring out rock strength plays essential roles in the sub ground mining activities,such as oil and gas well drilling and hydraulic fracturing,coal mining,tunneling,and other civil engineering scenarios.To help understand the effects of the mineralogical composition on evaluating the rock strength,this research tries to establish indirect prediction models of rock strength by specific input mineral contents for common sedimentary rocks.Using rock samples collected from the outcrops in the Sichuan Basin,uniaxial compression tests have been conducted to sandstone,carbonate,and shale cores.Combining with statistical analysis,the experimental data prove it true that the mineralogical composition can be utilized to predict the rock strength under specific conditions but the effects of mineralogical composition on the rock strength highly depend on the rock lithologies.According to the statistical analysis results,the predicted values of rock strengths by the mineral contents can get high accuracies in sandstone and carbonate rocks while no evidences can be found in shale rocks.The best indicator for predicting rock strength should be the quartz content for the sandstone rocks and the dolomite content for the carbonate rocks.Especially,to improve the evaluation accuracy,the rock strengths of sandstones can be obtained by substituting the mineral contents of quartz and clays,and those of carbonates can be calculated by the mineral contents of dolomite and calcite.Noticeably,the research data point out a significant contrast of quartz content in evaluating the rock strength of the sandstone rocks and the carbonate rocks.Increasing quartz content helps increase the sandstone strength but decrease the carbonate strength.As for shale rocks,no relationship exists between the rock strength and the mineralogical composition(e.g.,the clay fractions).To provide more evidences,detailed discussion also provides the readers more glances into the framework of the rock matrix,which can be further studied in the future.These findings can help understand the effects of mineralogical composition on the rock strengths,explain the contrasts in the rock strength of the responses to the same mineral content(e.g.,the quartz content),and provide another indirect method for evaluating the rock strength of common sedimentary rocks.

Unconfined compressive strength and failure behaviour of completely weathered granite from a fault zone

Understanding the strength characteristics and deformation behaviour of the tunnel surrounding rock in a fault zone is significant for tunnel stability evaluation.In this study,a series of unconfined compression tests were conducted to investigate the mechanical characteristics and failure behaviour of completely weathered granite(CWG)from a fault zone,considering with height-diameter(h/d)ratio,dry densities(ρd)and moisture contents(ω).Based on the experimental results,a regression mathematical model of unconfined compressive strength(UCS)for CWG was developed using the Multiple Nonlinear Regression method(MNLR).The research results indicated that the UCS of the specimen with a h/d ratio of 0.6 decreased with the increase ofω.When the h/d ratio increased to 1.0,the UCS increasedωwith up to 10.5%and then decreased.Increasingρd is conducive to the improvement of the UCS at anyω.The deformation and rupture process as well as final failure modes of the specimen are controlled by h/d ratio,ρd andω,and the h/d ratio is the dominant factor affecting the final failure mode,followed byωandρd.The specimens with different h/d ratio exhibited completely different fracture mode,i.e.,typical splitting failure(h/d=0.6)and shear failure(h/d=1.0).By comparing the experimental results,this regression model for predicting UCS is accurate and reliable,and the h/d ratio is the dominant factor affecting the UCS of CWG,followed byρd and thenω.These findings provide important references for maintenance of the tunnel crossing other fault fractured zones,especially at low confining pressure or unconfined condition.

Estimating uniaxial compressive strength of rocks using genetic expression programming

The aim of this paper is to estimate the uniaxial compressive strength（UCS） of rocks with different characteristics by using genetic expression programming（GEP）.For this purpose,five different types of rocks including basalt and ignimbrite（black,yellow,gray,brown） were prepared.Values of unit weight,water absorption by weight,effective porosity and UCS of rocks were determined experimentally.By using these experimental data,five different GEP models were developed for estimating the values of UCS for different rock types.Good agreement between experimental data and predicted results is obtained.

Evaluation of empirical estimation of uniaxial compressive strength of rock using measurements from index and physical tests

The uniaxial compressive strength(UCS) of rock is an important parameter required for design and analysis of rock structures,and rock mass classification.Uniaxial compression test is the direct method to obtain the UCS values.However,these tests are generally tedious,time-consuming,expensive,and sometimes impossible to perform due to difficult rock conditions.Therefore,several empirical equations have been developed to estimate the UCS from results of index and physical tests of rock.Nevertheless,numerous empirical models available in the literature often make it difficult for mining engineers to decide which empirical equation provides the most reliable estimate of UCS.This study evaluates estimation of UCS of rocks from several empirical equations.The study uses data of point load strength(Is(50)),Schmidt rebound hardness(SRH),block punch index(BPI),effective porosity(n) and density(ρ)as inputs to empirically estimate the UCS.The estimated UCS values from empirical equations are compared with experimentally obtained or measured UCS values,using statistical analyses.It shows that the reliability of UCS estimated from empirical equations depends on the quality of data used to develop the equations,type of input data used in the equations,and the quality of input data from index or physical tests.The results show that the point load strength(Is(50)) is the most reliable index for estimating UCS among the five types of tests evaluated.Because of type-specific nature of rock,restricting the use of empirical equations to the similar rock types for which they are developed is one of the measures to ensure satisfactory prediction performance of empirical equations.

Inconsistency of changes in uniaxial compressive strength and P-wave velocity of sandstone after temperature treatments

It is generally accepted that the uniaxial compressive strength(UCS)and P-wave velocity of rocks tend to decrease simultaneously with increasing temperature.However,based on a great number of statistical data and systematic analysis of the microstructure variation of rocks with temperature rising and corresponding propagation mechanism of elastic wave,the results show that(1)There are three different trends for the changes of UCS and P-wave velocity of sandstone when heated from room temperature(20C or 25C)to 800C:(i)Both the UCS and P-wave velocity decrease simultaneously;(ii)The UCS increases initially and then decreases,while the P-wave velocity decreases continuously;and(iii)The UCS increases initially and then fluctuates,while the P-wave velocity continuously decreases.(2)The UCS changes at room temperaturee400C,400Ce600C,and 600Ce800C are mainly attributed to the discrepancy of microstructure characteristics and quartz content,the transformation plasticity of clay minerals,and the balance between the thermal cementation and thermal damage,respectively.(3)The inconsistency in the trends of UCS and P-wave velocity changes is caused by the change of quartz content,phase transition of water and certain minerals.

Exploration of weakening mechanism of uniaxial compressive strength of deep sandstone under microwave irradiation

Traditional mechanical rock breaking method is labor-intensive and low-efficient,which restrictes the development of deep resources and deep space.As a new rock-breakage technology,microwave irradiation is expected to overcome these problems.This study examines the failure characteristics,weakening law,and breakdown mechanism of deep sandstone(depth=1050 m)samples in a microwave field.The macroscopic and microscopic properties were determined via mechanical tests,mesoscopic tests,and numerical simulations.Microwave application at 1000 W for 60 s reduced the uniaxial compressive strength of the sandstone by 50%.Thermal stress of the sandstone was enhanced by uneven expansion of minerals at the microscale.Moreover,the melting of some minerals in the high-temperature environment changed the pore structure,sharply reducing the macroscopic strength.The temperature remained high in the lower midsection of the sample,and the stress was concentrated at the bottom of the sample and along its axis.These results are expected to improve the efficiency of deep rock breaking,provide theoretical and technical support for similar rock-breakage projects,and accelerate advances in deep-Earth science.

Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks

Uniaxial Compressive Strength (UCS) and modulus of elasticity (E) are the most important rock parameters required and determined for rock mechanical studies in most civil and mining projects. In this study, two mathematical methods, regression analysis and Artificial Neural Networks (ANNs), were used to predict the uniaxial compressive strength and modulus of elasticity. The P-wave velocity, the point load index, the Schmidt hammer rebound number and porosity were used as inputs for both meth-ods. The regression equations show that the relationship between P-wave velocity, point load index, Schmidt hammer rebound number and the porosity input sets with uniaxial compressive strength and modulus of elasticity under conditions of linear rela-tions obtained coefficients of determination of (R2) of 0.64 and 0.56, respectively. ANNs were used to improve the regression re-sults. The generalized regression and feed forward neural networks with two outputs (UCS and E) improved the coefficients of determination to more acceptable levels of 0.86 and 0.92 for UCS and to 0.77 and 0.82 for E. The results show that the proposed ANN methods could be applied as a new acceptable method for the prediction of uniaxial compressive strength and modulus of elasticity of intact rocks.

Random field characterization of uniaxial compressive strength and elastic modulus for intact rocks

Rock properties exhibit spatial variabilities due to complex geological processes such as sedimentation,metamorphism, weathering, and tectogenesis. Although recognized as an important factor controlling the safety of geotechnical structures in rock engineering, the spatial variability of rock properties is rarely quantified. Hence, this study characterizes the autocorrelation structures and scales of fluctuation of two important parameters of intact rocks, i.e. uniaxial compressive strength(UCS) and elastic modulus(EM).UCS and EM data for sedimentary and igneous rocks are collected. The autocorrelation structures are selected using a Bayesian model class selection approach and the scales of fluctuation for these two parameters are estimated using a Bayesian updating method. The results show that the autocorrelation structures for UCS and EM could be best described by a single exponential autocorrelation function. The scales of fluctuation for UCS and EM respectively range from 0.3 m to 8.0 m and from 0.3 m to 8.4 m.These results serve as guidelines for selecting proper autocorrelation functions and autocorrelation distances for rock properties in reliability analyses and could also be used as prior information for quantifying the spatial variability of rock properties in a Bayesian framework.

Comparative evaluation of different statistical tools for the prediction of uniaxial compressive strength of rocks

In this study,uniaxial compressive strength(UCS),unit weight(UW),Brazilian tensile strength(BTS),Schmidt hardness(SHH),Shore hardness(SSH),point load index(Is50)and P-wave velocity(Vp)properties were determined.To predict the UCS,simple regression(SRA),multiple regression(MRA),artificial neural network(ANN),adaptive neuro-fuzzy inference system(ANFIS)and genetic expression programming(GEP)have been utilized.The obtained UCS values were compared with the actual UCS values with the help of various graphs.Datasets were modeled using different methods and compared with each other.In the study where the performance indice PIat was used to determine the best performing method,MRA method is the most successful method with a small difference.It is concluded that the mean PIat equal to 2.46 for testing dataset suggests the superiority of the MRA,while these values are 2.44,2.33,and 2.22 for GEP,ANFIS,and ANN techniques,respectively.The results pointed out that the MRA can be used for predicting UCS of rocks with higher capacity in comparison with others.According to the performance index assessment,the weakest model among the nine model is P7,while the most successful models are P2,P9,and P8,respectively.

Predicting uniaxial compressive strength of serpentinites through physical,dynamic and mechanical properties using neural networks

The uniaxial compressive strength(UCS)of intact rock is one of the most important parameters required and determined for rock mechanics studies in engineering projects.The limitations and difficulty of conducting tests on rocks,specifically on thinly bedded,highly fractured,highly porous and weak rocks,as well as the fact that these tests are destructive,expensive and time-consuming,lead to development of soft computing-based techniques.Application of artificial neural networks(ANNs)for predicting UCS has become an attractive alternative for geotechnical engineering scientists.In this study,an ANN was designed with the aim of indirectly predicting UCS through the serpentinization percentage,and physical,dynamic and mechanical characteristics of serpentinites.For this purpose,data obtained in earlier experimental work from central Greece were used.The ANN-based results were compared with the experimental ones and those obtained from previous analysis.The proposed ANN-based formula was found to be very efficient in predicting UCS values and the samples could be classified with simple physical,dynamic and mechanical tests,thus the expensive,difficult,time-consuming and destructive mechanical tests could be avoided.

Effects of Loading Rate on Flexural-tension Properties and Uniaxial Compressive Strength of Micro-surfacing Mixture

The major objective of this research was to discuss the effects of loading rate on the flexural-tension properties and uniaxial compressive strength of micro-surfacing mixture using three-point bending test and uniaxial compressive test respectively. As a preventive maintenance surface treatment on asphalt pavement, micro-surfacing was formed on the basis of the ISSA recommendation of an optimum micro-surfacing design. Tests were conducted over a wide range of temperature to investigate the difference of properties from low loading rate to a relatively high loading rate. Three-point bending test was used to study the flexural strength, strain and modulus of micro-surfacing mixture, and uniaxial compressive test was carried out to obtain the relationship between strength and the loading rate as well as temperature. The experimental results showed that flexural strength at high loading rate was larger than that at low loading rate. The flexural strength difference between low and high loading rate enlarged when the temperature rose. The flexural strain at high loading rate increased compared with results of the low loading rate. Results of the flexural modulus revealed that micro-surfacing mixture exhibited better anti-cracking characteristic at low temperature when given a relatively low loading rate. Results of uniaxial compressive test revealed that the strength difference of micro-surfacing among different loading rates increased with the increase of temperature. The logarithm relationship between the strength and loading rate over a wide range of temperature was obtained to compare the experimental and predicted values, which resulting in a reasonable consistency.

Estimate of Uniaxial Compressive Strength of Hydrothermally Altered Soft Rocks Based on Strength Index Tests

The purpose of this study was to clarify the relationships between results of index tests and uniaxial compressive strength (UCS) in hydrothermally altered soft rocks of the Upper Miocene, which are typical of the soft rock found in northeastern Hokkaido, Japan. Index tests were performed using point load testing machine and needle penetrometer with irregular lump specimens under forced-dry, forced-wet, and natural-moist states. The relationships between irregular lump point load strength (IPLS) index and UCS, and needle penetration (NP) index and UCS were “UCS = approximately 19 IPLS index” and “UCS = 0.848 (NP index)0.619”, respectively, in soft rocks with a UCS below 25 MPa. These relationships could be applied to on-site tests of rocks with natural moisture content. The UCS could be calculated from IPLS and NP tests on soft rocks only when UCS was below 25 MPa, using the equations obtained as a result of this study.

A machine learning model to predict unconfined compressive strength of alkali-activated slag-based cemented paste backfill

The unconfined compressive strength(UCS)of alkali-activated slag(AAS)-based cemented paste backfill(CPB)is influenced by multiple design parameters.However,the experimental methods are limited to understanding the relationships between a single design parameter and the UCS,independently of each other.Although machine learning(ML)methods have proven efficient in understanding relationships between multiple parameters and the UCS of ordinary Portland cement(OPC)-based CPB,there is a lack of ML research on AAS-based CPB.In this study,two ensemble ML methods,comprising gradient boosting regression(GBR)and random forest(RF),were built on a dataset collected from literature alongside two other single ML methods,support vector regression(SVR)and artificial neural network(ANN).The results revealed that the ensemble learning methods outperformed the single learning methods in predicting the UCS of AAS-based CPB.Relative importance analysis based on the bestperforming model(GBR)indicated that curing time and water-to-binder ratio were the most critical input parameters in the model.Finally,the GBR model with the highest accuracy was proposed for the UCS predictions of AAS-based CPB.

Strength weakening effect of high static pre-stressed granite subjected to low-frequency dynamic disturbance under uniaxial compression

This study aimed to elucidate the strength weakening effect of high static pre-stressed rocks subjected to low-frequency disturbances under uniaxial compression.Based on the uniaxial compressive strength(UCS)of granite under static loading,70%,80%,and 90%of UCS were selected as the initial high static pre-stress(σ_(p)),and then the pre-stressed rock specimens were disturbed by sinusoidal stress with amplitudes of 30%,20%,and 10%of UCS under low-frequency frequencies(f)of 1,2,5,and 10 Hz,respectively.The results show that the rockburst failure of pre-stressed granite is caused by low-frequency disturbance,and the failure strength is much lower than UCS.When theσp or f is constant,the specimen strength gradually decreases as the f or σ_(p) increases.The experimental study illustrates the influence mechanism of the strength weakening effect of high static pre-stress rocks under low-frequency dynamic disturbance,that is,high static pre-stress is the premise and leading factor of rock strength weakening,while low-frequency dynamic disturbance induces rock failure and affects the strength weakening degree.

Strength and failure characteristics of sandstone containing two circular holes filled with two types of inclusions under uniaxial compression

Plate shaped sandstones containing two fabricated circular holes that were filled with gypsum and high-strength concrete respectively were prepared for studying the effects of ligament length L ligament incline angle α, as well as filling modes on their strength properties and failure modes. The results show that the initial cracks can be categorized as wing crack, axial tensile crack and curved tensile crack. The failure modes of ligaments can be categorized as mode of single inclined crack, mode of single axial crack and mode of two parallel cracks. The final failure modes of all specimens can be categorized as the tension-shear mixed failure and shear failure. The strength of inclusions shows little influence on the final failure modes of specimens, while the failure modes vary with L and α. When α is a fixed value, the peak strength σc and elastic modulus Ec of tested specimens increase firstly with increasing L and reaches to the maximum value at L of 16 mm, then declines. When L is a fixed value, σc declines firstly and then turns to increase as α increases to 75° from 45°, while Ec increases linearly. The axial stress σp performs the similar variation trends with those of σc versus increasing L and α when ligaments fail.

Machine learning methods for predicting the uniaxial compressive strength of the rocks:a comparative study

The uniaxial compressive strength(UCS)of rocks is a critical index for evaluating the mechanical properties and construction of an engineering rock mass classification system.The most commonly used method for determining the UCS in laboratory settings is expensive and time-consuming.For this reason,UCS can be estimated using an indirect determination method based on several simple laboratory tests,including point-load strength,rock density,longitudinal wave velocity,Brazilian tensile strength,Schmidt hardness,and shore hardness.In this study,six data sets of indices for different rock types were utilized to predict the UCS using three nonlinear combination models,namely back propagation(BP),particle swarm optimization(PSO),and least squares support vector machine(LSSVM).Moreover,the best prediction model was examined and selected based on four performance prediction indices.The results reveal that the PSO–LSSVM model was more successful than the other two models due to its higher performance capacity.The ratios of the predicted UCS to the measured UCS for the six data sets were 0.954,0.982,0.9911,0.9956,0.9995,and 0.993,respectively.The results were more reasonable when the predicted ratio was close to a value of approximately 1.

Bayesian optimization-enhanced ensemble learning for the uniaxial compressive strength prediction of natural rock and its application

Engineering disasters, such as rockburst and collapse, are closely related to structural instability caused byinsufficient bearing capacity of geological materials. Uniaxial compressive strength (UCS) holds considerablesignificance in rock engineering projects. Consequently, this study endeavors to devise efficient models for theexpeditious and economical estimation of UCS. Using a dataset of 729 samples, including the Schmidt hammerrebound number, P-wave velocity, and point load index data, we evaluated six algorithms, namely AdaptiveBoosting (AdaBoost), Gradient Boosting Decision Tree (GBDT), Extreme Gradient Boosting (XGBoost), LightGradient Boosting Machine (LightGBM), Random Forest (RF), and Extra Trees (ET) and utilized Bayesian Optimization (BO) to optimize the aforementioned algorithms. Moreover, we applied model evaluation metrics suchas Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Variance Accounted For (VAF), Nash-SutcliffeEfficiency (NSE), Weighted Mean Absolute Percentage Error (WMAPE), Coefficient of Correlation (R), and Coefficient of Determination (R2). Among the six models, BO-ET emerged as the most optimal performer duringtraining (RMSE ¼ 4.5042, MAE ¼ 3.2328, VAF ¼ 0.9898, NSE ¼ 0.9898, WMAPE ¼ 0.0538, R ¼ 0.9955, R2 ¼0.9898) and testing (RMSE ¼ 4.8234, MAE ¼ 3.9737, VAF ¼ 0.9881, NSE ¼ 0.9875, WMAPE ¼ 0.2515, R ¼0.9940, R2 ¼ 0.9875) phases. Additionally, we conducted a systematic comparison between ensemble andtraditional single machine learning models such as decision tree, support vector machine, and K-NearestNeighbors, thus highlighting the advantages of ensemble learning. Furthermore, the enhancement effect of BO ongeneralization performance was assessed. Finally, a BO-ET-based Graphical User Interface (GUI) system wasdeveloped and validated in a Tunnel Boring Machine-excavated tunnel.

Meso-damage evolution and mechanical characteristics of low-porosity sedimentary rocks under uniaxial compression

Low pore sedimentary rocks(from Guangxi, China) were subjected to uniaxial compression loading experiment under different initial stresses. The rock samples were investigated by nuclear magnetic resonance before and after the loading. The relationships between the mesoscopic rock damage and macroscopic mechanical parameters were established, and the initial damage stress of the low-porosity sedimentary rock was determined. The results showed that this type of rock has the initial stress of damage. When the initial loading stress is lower than the initial stress of damage, the T2 spectrum area of the rock sample gradually decreases, and the primary pores of the rock are further closed under the stress. The range of the initial stress of damage for this type of rock is 8-16 MPa. When the loading stress exceeds the initial stress of damage, the T2 spectrum area gradually increases, indicating that the porosity of the rock increases and microscopic damage of the rock appears. The rock damage degree is defined, and the nonlinear function between the rock damage degree and the initial loading stress is established.