Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.

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.

Experiment and simulation of creep performance of basalt fibre asphalt mortar under uniaxial compressive loadings

The creep performance of basalt fibre（BF）reinforced in asphalt mortar under uniaxial compressive loadings is investigated. The samples of basalt fibre asphalt mortar（BFAM） with different BF mass fractions（0. 1%,0. 2%, and 0. 5%） and without BF in asphalt mixture are prepared, and then submitted for the compressive strength test and corresponding creep test at a high in-service temperature.Besides, numerical simulations in finite element ABAQUS software were conducted to model the compressive creep test of mortar materials, where the internal structure of the fibre mortar was assumed to be a two-component composite material model such as fibre and mortar matrix. Finally, the influence factors of rheological behaviors of BFAM are further analyzed. Results indicate that compared to the control sample, the compressive strength of BFAM samples has a significant increase, and the creep and residual deformation are decreased. However, it also shows that the excessive fibre, i.e. with the BF content of 0. 5%, is unfavorable to the high-temperature stability of the mortar. Based on the analysis results, the prediction equations of parameters of the Burgers constitutive model for BFAM are proposed by considering the fibre factors.

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.

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.

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.

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.

Experimental research on creep behaviors of sandstone under uniaxial compressive and tensile stresses

The consideration of time dependence is essential for the study of deformation and fracturing processes of rock materials, especially for those subjected to strong compressive and tensile stresses. In this paper, the self-developed direct tension device and creep testing machine RLW-2000M are used to conduct the creep tests on red sandstone under uniaxial compressive and tensile stresses. The short-term and long-term creep behaviors of rocks under compressive and tensile stresses are investigated, as well as the long-term strength of rocks. It is shown that, under low-stress levels, the creep curve of sandstone consists of decay and steady creep stages; while under high-stress levels, it presents the accelerated creep stage and creep fracture presents characteristics of brittle materials. The relationship between tensile stress and time under uniaxial tension is also put forward. Finally, a nonlinear viscoelastoplastic creep model is used to describe the creep behaviors of rocks under uniaxial compressive and tensile stresses.

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.

Damage and failure rule of rock undergoing uniaxial compressive load and dynamic load

For understanding the damage and failure rule of rock under different uniaxial compressive loads and dynamic loads, tests on red sandstone were carried out on Instron 1342 electro-servo controlled testing system with different uniaxial compressive loads of 0, 2, 4 and 6 MPa. It is found that peak stress, peak strain, elastic modulus and total strain energy decrease with the increase of static compressive stress. Based on the test results, the mechanism on damage and failure of rock was analyzed, and according to the equivalent strain hypothesis, a new constitutive model of elastic-plastic damage was established, and then the calculated results with the established model were compared with test results to show a good agreement. Furthermore the rule of releasing ratio of damage strain energy was discussed.

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.

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.

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.

Prediction of uniaxial compressive strength of rock based on lithology using stacking models

Uniaxial compressive strength(UCS)of rock is an essential parameter in geotechnical engineering.Point load strength(PLS),P-wave velocity,and Schmidt hammer rebound number(SH)are more easily obtained than UCS and are extensively applied for the indirect estimation of UCS.This study collected 1080 datasets consisting of SH,P-wave velocity,PLS,and UCS.All datasets were integrated into three categories(sedimentary,igneous,and metamorphic rocks)according to lithology.Stacking models combined with tree-based models and linear regression were developed based on the datasets of three rock types.Model evaluation showed that the stacking model combined with random forest and linear regression was the optimal model for three rock types.UCS of metamorphic rocks was less predictable than that of sedimentary and igneous rocks.Nonetheless,the proposed stacking models can improve the predictive performance for UCS of metamorphic rocks.The developed predictive models can be applied to quickly predict UCS at engineering sites,which benefits the rapid and intelligent classification of rock masses.Moreover,the importance of SH,P-wave velocity,and PLS were analyzed for the estimation of UCS.SH was a reliable indicator for UCS evaluation across various rock types.P-wave velocity was a valid parameter for evaluating the UCS of igneous rocks,but it was not reliable for assessing the UCS of metamorphic rocks.

A whole process damage constitutive model for layered sandstone under uniaxial compression based on Logistic function

Bedding structural planes significantly influence the mechanical properties and stability of engineering rock masses.This study conducts uniaxial compression tests on layered sandstone with various bedding angles(0°,15°,30°,45°,60°,75°and 90°)to explore the impact of bedding angle on the deformational mechanical response,failure mode,and damage evolution processes of rocks.It develops a damage model based on the Logistic equation derived from the modulus’s degradation considering the combined effect of the sandstone bedding dip angle and load.This model is employed to study the damage accumulation state and its evolution within the layered rock mass.This research also introduces a piecewise constitutive model that considers the initial compaction characteristics to simulate the whole deformation process of layered sandstone under uniaxial compression.The results revealed that as the bedding angle increases from 0°to 90°,the uniaxial compressive strength and elastic modulus of layered sandstone significantly decrease,slightly increase,and then decline again.The corresponding failure modes transition from splitting tensile failure to slipping shear failure and back to splitting tensile failure.As indicated by the modulus’s degradation,the damage characteristics can be categorized into four stages:initial no damage,damage initiation,damage acceleration,and damage deceleration termination.The theoretical damage model based on the Logistic equation effectively simulates and predicts the entire damage evolution process.Moreover,the theoretical constitutive model curves closely align with the actual stress−strain curves of layered sandstone under uniaxial compression.The introduced constitutive model is concise,with fewer parameters,a straightforward parameter determination process,and a clear physical interpretation.This study offers valuable insights into the theory of layered rock mechanics and holds implications for ensuring the safety of rock engineering.

Estimation of rock uniaxial compressive strength for an Iranian carbonate oil reservoir: Modeling vs. artificial neural network application

Estimation of rock mechanic parameters is an important issue in reservoir management.Uniaxial compressive strength(UCS)and elastic modulus are the most important factors in determining the rock mechanic parameters in petroleum engineering studies.Accessibility to the parameters in fields such as designing fracture,analyzing of wellbore stability and drilling programming are very useful.The most accurate method to assign the aforementioned parameters is measuring these parameters in a laboratory.Laboratory determination of these parameters is problematic work due to technology issues,lack of laboratory equipment and coring problems in oil and gas wells,so indirect estimation of these parameters is required.Using well log data is the cheapest and most available approach in order to indirectly estimate these parameters.In this investigation,different models including multiple linear regression(MLR)and artificial neural network(ANN)(i.e.,multi linear perceptron(MLP)and radial basis function(RBF))were utilized for prediction of UCS via the three parameters of porosity,density and water saturation.These data were obtained from analysis of sonic,neutron,gamma ray and electric logs.The best results were obtained from a 3-15-1 MLP network which included one hidden layer and 15 neurons from the hidden layer using the trial and error method,and a 3-17-1 RBF which included 17 hidden neurons and a spread ò of 1.6.The core data from one of the carbonate Iranian oil fields(Asmari reservoir)were utilized for training,validation and testing of the networks,and correlation coefficients of 0.68,0.90 and 0.83 were obtained for MLR,MLP and RBF,respectively.

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.