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.

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.

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 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.

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.

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.

Revisiting factors contributing to the strength of cemented backfill support system:A review

This paper provides a review of the intrinsic and extrinsic factors affecting the uniaxial compressive strength(UCS)of cemented tailings backfill(CTB).The consideration is that once CTB is poured into underground stopes,its strength is heavily influenced by factors internal to the CTB as well as the surrounding mining environments.Peer-reviewed journal articles,books,and conference papers published between 2000 and 2022 were searched electronically from various databases and reviewed.Additional sources,such as doctoral theses,were obtained from academic repositories.An important finding from the review is that the addition of fibers was reported to improve the UCS of CTB in some studies while decrease in others.This discrepancy was accounted to the different properties of fibers used.Further research is therefore needed to determine the“preferred”fiber to be used in CTB.Diverging findings were also reported on the effects of stope size on the UCS of CTB.Furthermore,the use of fly ash as an alternative binder may be threatened in the future when reliance on the coal power declines.Therefore,an alternative cementitious by-product to be used together with furnace slag may be required in the future.Finally,while most studies on backfill focused on single-layered structures,layered backfill design models should also be investigated.

Statistical analysis of physico-mechanical parameters of sandstones occurring in orogenic settings

In northeastern Sicily(Italy),sandstone rock masses widely crop out as cover deposits over crystalline terrains belonging to the orogenic belt.Despite being part of the same geological formation,these sandstones are characterized by highly different features in terms of texture and physico-mechanical properties.This poses a scientific question on the possibility of tracing these rocks to a single statistical model,which could be representative of their main engineering geological properties.Therefore,it is worth investigating on the possible reasons of such differences,that should be searched either in the current geographical sandstone distribution or in the rock texture.For this study,sandstone samples were collected from different sites and were analyzed at both the hand and thin section scales.Three sandstone types were recognized,characterized by a different texture.Then,the laboratory characterization allowed estimating their main physico-mechanical and ultrasonic properties,such as porosity,density,mechanical strength,deformability,and ultrasonic velocities.The rock mechanical strength proved linked to the rock compactness and to the presence of lithic fragments,while pores and a pseudo-matrix between grains represent weakening features.Rock data were also statistically analyzed by grouping the specimens according to a geographical criterion,with respect to their sampling area,but no link was found between location and rock properties.Finally,with the aim of achieving mathematical laws that could be used to predict some rock properties from others,useful for practical purposes when dealing with such a high property variability,single and multiple regression analyses were carried out.Results show that the Uniaxial Compressive Strength,porosity,and P-wave velocity are the best predictors for a quick,indirect estimation of the main physico-mechanical parameters.The methodological approach developed for this research can be taken as reference to study other worldwide cases,involving rocks characterized by a wide range of physico-mechanical properties and covering large regional territories.

Effect of intermittent joint distribution on the mechanical and acoustic behavior of rock masses

The mechanical characteristics and acoustic behavior of rock masses are greatly influenced by stochastic joints.In this study,numerical models of rock masses incorporating intermittent joints with different numbers and dip angles were produced using the finite element method(FEM)with the intrinsic cohesive zone model(ICZM).Then,the uniaxial compressive and wave propagation simulations were performed.The results indicate that the joint number and dip angle can affect the mechanical and acoustic properties of the models.The uniaxial compressive strength(UCS)and wave velocity of rock masses decrease monotonically as the joint number increases.However,the wave velocity grows monotonically as the joint dip angle increases.When the joint dip angle is 45°–60°,the UCS of the rock mass is lower than that of other dip angles.The wave velocity parallel to the joints is greater than that perpendicular to the joints.When the dip angle of joints remains unchanged,the UCS and wave velocity are positively related.When the joint dip angle increases,the variation amplitude of the UCS regarding the wave velocity increases.To reveal the effect of the joint distribution on the velocity,a theoretical model was also proposed.According to the theoretical wave velocity,the change in wave velocity of models with various joint numbers and dip angles was consistent with the simulation results.Furthermore,a theoretical indicator(i.e.fabric tensor)was adopted to analyze the variation of the wave velocity and UCS.

Compressive fatigue behavior and failure evolution of additive fiber-reinforced cemented tailings composites

The ordinary cemented tailings backfill(CTB)is a cement-based composite prepared from tailings,cementitious materials,and water.In this study,a series of laboratory tests,including uniaxial compression,digital image correlation measurement,and scanning electron microscope characteristics of fiber-reinforced CTB(FRCTB),was conducted to obtain the uniaxial compressive strength(UCS),failure evolution,and microstructural characteristics of FRCTB specimens.The results show that adding fibers could increase the UCS values of the CTB by 6.90%to 32.76%.The UCS value of the FRCTB increased with the increase in the polypropylene(PP)fiber content.Moreover,the reinforcement effect of PP fiber on the CTB was better than that of glass fiber.The addition of fiber could increase the peak strain of the FRCTB by0.39%to 1.45%.The peak strain of the FRCTB increased with the increase in glass fiber content.The failure pattern of the FRCTB was coupled with tensile and shear failure.The addition of fiber effectively inhibited the propagation of cracks,and the bridging effect of cracks by the fiber effectively improved the mechanical properties of the FRCTB.The findings in this study can provide a basis for the backfilling design and optimization of mine backfilling methods.

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 Estimation Using Several Tree-Based ML Techniques

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

A Modeling Method for Predicting the Strength of Cemented Paste Backfill Based on a Combination of Aggregate Gradation Optimization and LSTM

Cemented paste backill(CPB)is a susta inable mining technology that is widely used in mines and helps to improve the mine environment.To investigate the relationship between aggregate grading and different affecting factors and the uniaxial compressive strength(UCS)of the cemented paste backill(CPB),Talbol gradation theory and neural networks is used to evaluate aggregate gradation to determine the optimum aggregate ratio.The mixed aggregate ratio with the least amount of cement(waste stone content river sand content=7:3)is obtained by using Talbol grading theory and pile compactness function and combined with experiments.In addition,the response surface method is used to design strength speaific ratio experiments.The UCS prediction model which ues the ISTM and considers the aggregates gradation have high accuracy.The root mean square error(RMSE)of the prediction results is 0.0914,the coefficient of determination(R^(2))is 0.9973 and the variance account for(VAF)is 99.73.Compared with back propagation neural network(BP-ANN),extreme lea ming machine(ELM)and madal basis function neural network(RBF ANN),LSTM can efectively characterize the nonlinear relationship between UCS and individual affecting factors and predict UCS with high accuracy.The sensitivity analysis of different affecting factors on UCS shows that all 4 factors have significant effect on UCS and sensitivity is in the following ranking:cement content(0.9264)>slurry concentration(0.9179)>aggregate gradation(waste rodk content)(0.9031)>curing time(09031).

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.

A novel fractal-statistical scaling model of rocks considering strain rate

The scaling-dependent behaviors of rocks are significant to the stability and safe operation of the structures built in or on rock masses for practical engineering.Currently,many size effect models are employed to connect laboratory measurements at small scales and engineering applications at large scales.However,limited works consider the strain rate effect.In this study,an fractal-statistical scaling model incorporating strain rate is proposed based on a weakest-link approach,fractal theory and dynamic fracture mechanics.The proposed scaling model consists of 8 model parameters with physical meaning,i.e.rate-dependent parameter,intrinsic material parameter,dynamic strain rate,quasi-static strain rate,quasi-static fracture toughness,micro-crack size,micro-crack intensity and fractal dimension,enabling the proposed scaling model to model the scaling behaviors under different external conditions.Theoretical predictions are consistent with experimental data on red sandstone,proving the reliability and effectiveness of the proposed scaling model.Thus,the scaling behaviors of rocks under dynamic loading conditions can be captured by the proposed fractal-statistical scaling model.The sensitivity analysis indicates that the nominal strength difference becomes more obvious with a higher strain rate,larger fractal dimension,smaller micro-crack size or lower micro-crack intensity.Therefore,the proposed scaling model has the potential to capture the scaling behaviors considering the thermal effect,weathering effect,anisotropic characteristic etc.,as the proposed scaling model incorporated model parameters with physical meaning.The findings of this study are of fundamental importance to understand the scaling behaviors of rock under dynamic loading condition,and thus would facilitate the appropriate design of rock engineering.