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.

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.

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.

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.

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.

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.

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.

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.

Failure behavior and strength model of blocky rock mass with and without rockbolts

To better understand the failure behaviours and strength of bolt-reinforced blocky rocks,large scale extensive laboratory experiments are carried out on blocky rock-like specimens with and without rockbolt reinforcement.The results show that both shear failure and tensile failure along joint surfaces are observed but the shear failure is a main controlling factor for the peak strength of the rock mass with and without rockbolts.The rockbolts are necked and shear deformation simultaneously happens in bolt reinforced rock specimens.As the joint dip angle increases,the joint shear failure becomes more dominant.The number of rockbolts has a significant impact on the peak strain and uniaxial compressive strength(UCS),but little influence on the deformation modulus of the rock mass.Using the Winkler beam model to represent the rockbolt behaviours,an analytical model for the prediction of the strength of boltreinforced blocky rocks is proposed.Good agreement between the UCS values predicted by proposed model and obtained from experiments suggest an encouraging performance of the proposed model.In addition,the performance of the proposed model is further assessed using published results in the literature,indicating the proposed model can be used effectively in the prediction of UCS of bolt-reinforced blocky rocks.

Strength regularity and failure criterion of plain HSHPC under biaxial compression after exposure to high temperatures

Biaxial compression tests are performed on 100 mm × 100 mm × 100 mm cubic specimens of plain high-strength highperformance concrete （HSHPC） at seven kinds of stress ratios, σ2：σ3 =0 ： - 1, -0.20 ： - 1, -0.30 ： - 1, -0.40 ： - 1, -0.50 ： -1, -0. 75 ： - 1, and - 1.00 ： - 1 after exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600 ℃, using a large static-dynamic true triaxial machine. Frictionreducing pads are three layers of plastic membranes with glycerine in-between for the compressive loading plane. Failure modes of the specimens are described. The two principally static compressive strengths are measured. The influences of the temperatures and stress ratios on the biaxial strengths of HSHPC after exposure to high temperatures are also analyzed. The experimental results show that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease completely with the increase in temperature; the ratios of the biaxial to its uniaxial compressive strengths depend on the stress ratios and brittleness-stiffness of HSHPC after exposure to different high temperatures. The formula of the Kupfer-Gerstle failure criterion modified with the temperature and stress ratio parameters for plain HSHPC is proposed.

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.

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.

Selection of regression models for predicting strength and deformability properties of rocks using GA

Recently,many regression models have been presented for prediction of mechanical parameters of rocks regarding to rock index properties.Although statistical analysis is a common method for developing regression models,but still selection of suitable transformation of the independent variables in a regression model is diffcult.In this paper,a genetic algorithm(GA)has been employed as a heuristic search method for selection of best transformation of the independent variables(some index properties of rocks)in regression models for prediction of uniaxial compressive strength(UCS)and modulus of elasticity(E).Firstly,multiple linear regression(MLR)analysis was performed on a data set to establish predictive models.Then,two GA models were developed in which root mean squared error(RMSE)was defned as ftness function.Results have shown that GA models are more precise than MLR models and are able to explain the relation between the intrinsic strength/elasticity properties and index properties of rocks by simple formulation and accepted accuracy.

Rock strength interval analysis using theory of testing blind data and interval estimation

The concepts of rock strength intervals are presented in this work, furthermore, central values of intervals and their corresponding credibility are provided using two-case study based on blind data theory and fuzzy interval estimation. 60 granite specimens are first tested, the compressive strength interval and tensile strength interval are [ 103.68, 219.6 l ] and [7.53, 11,86] MPa, while the tested mean values of compressive strength and tensile strength are 152.86 and 10.14 MPa, the credibilities are less than 58.4% and around 70.4%, respectively, the credibility of shear strength is between 40% and 60%. Then 70 other rock specimens are designed and tested, the similar conclusions can be reached. The results show that the conventional definite values are the particular values within the intervals, and the credibility of them often fails to reach the high-precision engineering requirement. The results demonstrate the feasibility and application potential of this proposed algorithm for the engineering practice. The references for engineering value selection of rock strength under different credibility or according to frequency distribution of central values are provided to increase the reliability and precision of calculation.

FAILURE MODE AND CONSTITUTIVE MODEL OF PLAIN HIGH-STRENGTH HIGH-PERFORMANCE CONCRETE UNDER BIAXIAL COMPRESSION AFTER EXPOSURE TO HIGH TEMPERATURES

An orthotropic constitutive relationship with temperature parameters for plain highstrength high-performance concrete （HSHPC） under biaxial compression is developed. It is based on the experiments performed for characterizing the strength and deformation behavior at two strength levels of HSHPC at 7 different stress ratios including a=σs ： σ3=0.00：-1,-0.20：-1,-0.30 ： -1,-0.40：-1,-0.50：-1,-0.75：-1,-1.00：-1, after the exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600℃, and using a large static-dynamic true triaxial machine. The biaxial tests were performed on 100 mm×100 mm×100 mm cubic specimens, and friction-reducing pads were used consisting of three layers of plastic membrane with glycerine in-between for the compressive loading plane. Based on the experimental results, failure modes of HSHPC specimens were described. The principal static compressive strengths, strains at the peak stress and stress-strain curves were measured; and the influence of the temperature and stress ratios on them was also analyzed. The experimental results showed that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease dramatically with the increase of temperature. The ratio of the biaxial to its uniaxial compressive strength depends on the stress ratios and brittleness-stiffness of HSHPC after exposure to different temperature levels. Comparison of the stress-strain results obtained from the theoretical model and the experimental data indicates good agreement.

Strength prediction model for water-bearing sandstone based on nearinfrared spectroscopy

The strength of water-bearing rock cannot be obtained in real time and by nondestructive experiments,which is an issue at cultural relics protection sites such as grotto temples.To solve this problem,we conducted a near-infrared spectrum acquisition experiment in the field and laboratory uniaxial compression strength tests on sandstone that had different water saturation levels.The correlations between the peak height and peak area of the nearinfrared absorption bands of the water-bearing sandstone and uniaxial compressive strength were analyzed.On this basis,a strength prediction model for water-bearing sandstone was established using the long short-term memory full convolutional network(LSTM-FCN)method.Subsequently,a field engineering test was carried out.The results showed that:(1)The sandstone samples had four distinct characteristic absorption peaks at 1400,1900,2200,and 2325 nm.The peak height and peak area of the absorption bands near 1400 nm and 1900 nm had a negative correlation with uniaxial compressive strength.The peak height and peak area of the absorption bands near 2200 nm and 2325 nm had nonlinear positive correlations with uniaxial compressive strength.(2)The LSTM-FCN method was used to establish a strength prediction model for water-bearing sandstone based on near-infrared spectroscopy,and the model achieved an accuracy of up to 97.52%.(3)The prediction model was used to realize non-destructive,quantitative,and real-time determination of uniaxial compressive strength;this represents a new method for the non-destructive testing of grotto rock mass at sites of cultural relics protection.

Correlations between direct and indirect strength test methods

The difficulties associated with performing direct compression strength tests on rocks lead to the development of indirect test methods for the rock strength assessment. Indirect test methods are simple, more economical, less time-consuming, and easily adaptable to the field. The main aim of this study was to derive correlations between direct and indirect test methods for basalt and rhyolite rock types from Carlin trend deposits in Nevada. In the destructive methods, point load index, block punch index, and splitting tensile strength tests are performed. In the non-destructive methods, Schmidt hammer and ultrasonic pulse velocity tests are performed. Correlations between the direct and indirect compression strength tests are developed using linear and nonlinear regression analysis methods. The results show that the splitting tensile strength has the best correlation with the uniaxial compression strength.Furthermore, the Poisson's ratio has no correlation with any of the direct and indirect test results.

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.