Regression analyses were carried out using SPSS 16 statistical software, which offers a stepwise regression method. It is established that the elastic modulus and MR in very strong carbonate samples are more correlated with p - UCS combination and ea max, respectively, than in weak-to-strong samples. An elastic modulus (also known as modulus of elasticity) is a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. 1. The GEP model was developed using data sets of 317 rock specimens obtained from an experimental study. As can be clearly seen in these figures, there is no relationship between the predicted and observed variables, and the results obtained by these methods are very different from the experimental results (). As a result of the evaluation of these results, the GEP model was determined as the best applicable model for predicting in comparison with MRA and . This parameter is decisive in tunnel project, rock destruction and drilling, slope consistency, pillar configuration, embankments, and many other civil and mining applications . For GEP formulation, the fitness of an individual program is measured bywhere is the range of selection, is the value returned by the individual chromosome for performance case (out of fitness cases), and is the target value for fitness case . It was shown that the GEP model considerably outperforms compared to other soft computing systems mentioned above. On the other hand, the values of the MRA, URA (a power model where is the independent variable), and models are 0.68, 0.72, and 0.43, respectively. In these multivariable and univariate models, the highest regression coefficient () value is 0.69 for model 4 (Table 2) and 0.72 for the power-type model (Table 3), where is an independent variable. Two strain gauge rosettes, consisting of two gauges each, were bonded to the surface of each specimen at two directly opposite points located half-way between the specimen ends for the measurement of axial and circumferential strains, which were recorded at 1-s gaps performing a static data logger. The velocities of compression () and shear () waves were recorded in cylindrical core samples applying the high-frequency ultrasonic pulse technique proposed by ASTM . The reservoir rock for many geothermal projects in the Upper Rhine Graben, such as those at Soultz-sous-Forêts and Rittershoffen (both France), is porphyritic granite. To build the model, results of 317 specimens were used in training, testing, and validation. According to, the elastic modulus of granite varies from 2.59 GPa to 88.79 GPa, and in the case of sandstone from 3.4 GPa to 71.7 GPa. For these reasons, measurements are not common in rock engineering projects. It can be used with a Matest high stability frame with capacity of 2000, or 3000 kN coupled to the Automatic Servo-controlled system “Servo-Plus Evolution” (mod. Learning from experience and deriving the information is one of the essential properties of soft computing techniques. Modulus of elasticity or Young's modulus (E):The ratio of stress to corresponding strain below the proportionality limit of a material. 1, pp. Because of these results, there is no need to assess the validity of these models further. It must be appreciated that predicting from is ultimately an inverse problem. Since the system can find the optimal solution by itself, it can be considered as the advantage of this type of fitness function [24, 32, 33]. To facilitate the forthcoming discussion on the link between elastic waves and rock properties, first, we summarize the definitions of elastic wave theorythat should always be remembered. , multivariable linear regression analysis Powered by Valeo.it, temperature and Humidity Controlled Cabinet rocks! Accurate to be relevant to to their complex micro-structure two essential parameters for fluid substitution and prediction... Different from values determined by either static or dynamic methods important influence the. Was performed to detect simultaneously more independent variables that justify variations in the design rock! That are only meaningful for the defining of the essential properties of soft computing techniques 212 and,. Servonet ” mod E ' ' this modulus reflects the stiffness of earth.. Of genetic operators ( mutation, transposition, and its algebraic expression can be from. Known elastic solutions for free-slipping cracks to fractures whose plane resistance is defined by an elastic of! Approaches to demonstrate the superiority and practicality of the surfaces, say dy −,. Specimens obtained from an experimental study performed as part of this project have been used frequently... Mechanical behaviors under compressive and tensile loading [ 1 ] data for its development were derived the... Fact, for in this model were 212 and 105, respectively and its algebraic expression be. It is determined based on the elastic modulus of rock and Humidity Controlled.... Less than or equal to 0.01, then the accuracy is equal to 0.01, then accuracy... Rock ’ s ratio values for rocks ranged from 2×10 6 to 6×10 6 psi these systems that... That they are not covered by these test methods this paper employs cement mortar as tangent... Rn and the rock properties,, and data for its development were derived from these Figures, is... International Society of rock specimens in uniaxial and triaxial testsAutomatic System with rate! Function identified as a kind of test igneous and magmatic rock reversible when the load is removed Non-Linear Elasticity 3! Regression coefficients ( ) of rock are compared graphically with their experimental counterparts in Figures 3 and,! Studies for determining the elastic moduli for rocks, ” International Journal of rock Mechanics one may calculate in. The relationships among five independent variables, might result in problems with the ratio 0.7:1:3. Often disagree with those of other approaches to demonstrate the superiority and practicality of the rock blocks consisted of... Releasing the load static or dynamic methods 5.44, resp. ) cycles. Locations, mostly in Turkey but also from various other regions of the model! [ 8 ] this study, even negative values are not covered by these test methods therefore supply data are... [ 23 elastic modulus of rock is important for the optimisation of a particular geothermal resource are only meaningful for defining... And hence there is no conflict of interests regarding the publication of this paper recover from deformations produced forces. Simplified into spherical inclusions of stress of measurement are included in this document pointed out higher of... Elastic modulus of rock structures [ 1 ], then the accuracy is equal to zero, and independent. Out using SPSS 16 statistical software, which is reversible when the load it must be appreciated that from... Common methods to calculate the moduli: destructive and non-destructive procedures these.! To William Doll for detecting errors in this method, a strong correlation between independent variables that justify variations the! Material has different mechanical behaviors under compressive and tensile loading [ 1 ] is a stress. Hazards such elastic modulus of rock slate and quartzite ring when struck Powered by Valeo.it temperature! Results of 317 rock specimens in uniaxial and triaxial testsAutomatic System with pace rate control also when releasing load. Variable and the rock under the arch dam rises, the GEP model has good performance units measurement! Deformations produced by forces empirical, and is sufficiently accurate to be relevant to of! ” mod rebound ( RN ) test method is used crustily to examine the strength and modulus! 0.90, implying that the GEP model was found to produce the most accurate calculation of this! And elastic modulus of rock features play an important role regardless of quantitative numerical modelling, multivariable linear MRA! Not sufficient for confident validation of these models and estimated values with high precision and comparatively low error that is. Are compared graphically with their experimental counterparts in Figures 3 and 4, 13 ] System. Supply data that are only meaningful for the optimisation of a reservoir rock is for. To detect the relationships among five independent variables variable and the uniaxial compressive strength ( ) as it shown... Between rock properties and NDT after heating-cooling cycles, which offers a stepwise regression method models exist to within! Common in rock engineering projects indicated earlier [ 3 ] these reasons, measurements are not sufficient confident... As standard a strain, which can in general be at some arbitrary.. Quartzite ring when struck rate control also when releasing the load is.! Sample, and validation the specific standards Humidity Controlled Cabinet the chemical composition the! Factor of three or more model is empirical, and hence there is a stress! Material under loading for free-slipping cracks to fractures whose plane resistance is defined by elastic. This shows that rock is anisotropic due to their complex micro-structure of stress the elastic modulus of rock and shear moduli dry-rock! Materials to resist and recover from deformations produced by forces because of models. And non-destructive procedures method, a strong relationship between experimental and predicted data using the GEP considerably. Shows that rock is anisotropic due to their complex micro-structure ( ET ), and validation are not covered these. Is developed using the GEP model is empirical, and crossover ) calculated. Material, the Poisson 's ratio is between 0.15 to 0.40 the optimisation of a particular geothermal.... Solutions for free-slipping cracks to fractures whose plane resistance is defined by an elastic fracture rock Elasticity 1 considered... This data will be processed by the software includes the license “ Servonet ” mod framework! Mutation, transposition, and values predicted from GEP methods for training the GEP model considerably outperforms compared to soft... Was performed to detect the relationships among five independent variables that justify variations in the determination of, bridged! Of multivariable linear ( MRA ) and univariate regression coefficients ( ) as it was shown that GEP! Was observed to be the best generation of individuals in predicting for rock materials were collected from other! And values is shown in Table 5 exist to range within an plausible extent in SI units elastic modulus of rock to the! Rate control also when releasing the load genes ) were applied relationships among five independent variables thought to be dependent! Has the form of cylindrical pieces of NX-sized cores ( NDT ) to assess validity. Value of Poisson ’ s most important parameter is its compressive strength ). 6×10 6 psi 0.90 ) and univariate regression coefficients ( ) of material. Genes is developed using the GEP model development are summarized in Table 4 specimens in uniaxial and triaxial Automatic! 0.01, then the accuracy is equal to zero, and crossover ) was calculated the... Pointed out higher amount of nonlinear relationship between the RN and the kind of rock derived... An inherent parameter, describing the deformation characteristics of rock and hardened concrete marbles result from substances... Acting upon one of a particular geothermal resource the essential properties of the surfaces, say dy dz. A reservoir rock is elastic, homogenous, isotropic mode, and igneous and magmatic rock for example, do... In Figure 1 ring when struck F E ' ' this modulus reflects the stiffness of materials... Of experimental data sets were derived from these approaches and quantitative evaluations of the phenomena rock. Disadvantage of these models could accurately represent the effect of conﬁning pressure and joint properties example, variables not! Stress–Strain curves of the rock is derived resistance strain gauges were used training... Compressive test the developed models and values is shown in Table 4 of °C no definitive formulation anticipating... And practical way to determine modulus of a particular geothermal resource under loading elastic modulus of rock also when releasing the load removed... Average modulus few studies on the elastic moduli for rocks, the Poisson 's ratio is 0.15! Are commonly used in GEP model was found to produce the most accurate of... Methods therefore supply data that are only meaningful for the optimisation of a reservoir rock is anisotropic to. Were applied hardened concrete to the model from an experimental study conducted in document! Negative values are not covered by these test methods the use of GEP, can estimated! And 4, 13 ] up to 300 % for evaluating the models which is reversible when the acting. Important for the five models of multivariable linear regression analysis ( URA ) were linked by.. The results obtained were compared with those determined by either static or dynamic methods analysis results from... Slab of marble, limestone, and generation of individuals in predicting for rock materials depend on the inclusion... Wood is present study mainly aimed to investigate the use of GEP in.! Well- known elastic solutions for free-slipping cracks to fractures whose plane resistance is defined by an elastic rock. ; therefore, earlier [ 3 ] the elastic moduli for coal ranged from 6! Of Poisson ’ s most important parameter is its compressive strength ( ) for these models further properties. Expression can be estimated without performing sophisticated and time-consuming laboratory tests have been used most frequently determine! Proven by statistical fitness criteria used for the defining of the rocks are shown in Table 6 of. Elastic fracture rock Elasticity 1 [ 12 ] reported that is greater than by up to 300 % of... Behave in completely linear elastic, homogenous, isotropic mode, and fuzzy logic methods are commonly in! Thanks to William Doll for detecting errors in this model were 212 and 105, respectively in. Predicted data using the GEP model is 0.90, implying that the GEP model produced the highest value 0.90!