A review of the tensile strength of rock was conducted to determine the relationship between direct tensile strength (DTS) and Brazilian tensile strength (BTS) and to examine the validity of estimating tensile strength from other measured properties, such as the crack initiation (CI) threshold. A data set was gathered from the existing literature where tensile values could be reliably correlated with unconfined compressive strength or CI values. It was determined that the BTS obtained in standard testing is generally greater than the equivalent DTS and that this relationship is rock type dependent. CI yields a reasonable estimate of tensile strength and this correlation is improved when the BTS values are reduced to DTS values by rock type specific correlations. The factor f, in DTS = f BTS, can be considered to be approximately 0.9 for metamorphic, 0.8 for igneous and 0.7 for sedimentary rocks. The relationships presented demonstrate that there is wide scatter in the available data for estimating tensile strength likely due to both specimen variability and testing configuration, including platen geometry and relative stiffness. Estimates of tensile strength should only be used for preliminary design purposes and measurements should be made to confirm preliminary assumptions for each design.

A Review of the Tensile Strength of Rock: Concepts and Testing

Time-series forecasting is an important research and application area. Much effort has been devoted over the past several decades to develop and improve the time-series forecasting models. This paper introduces a new time-series forecasting model based on the flexible neural tree (FNT). The FNT model is generated initially as a flexible multi-layer feed-forward neural network and evolved using an evolutionary procedure. Very often it is a difficult task to select the proper input variables or time-lags for constructing a time-series model. Our research demonstrates that the FNT model is capable of handing the task automatically. The performance and effectiveness of the proposed method are evaluated using time series prediction problems and compared with those of related methods.

Time-series forecasting using flexible neural tree model

Prediction of uniaxial compressive strength of rock samples using hybrid particle swarm optimization-based artificial neural networks

Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system

Many studies have shown that artificial neural networks (ANNs) are useful for predicting the unconfined compressive strength (UCS) of rocks. However, ANNs do have some deficiencies: they can get trapped in local minima and they have a slow learning rate. It is widely accepted that optimization algorithms such as particle swarm optimization (PSO) can improve ANN performance. This study investigated the application of a hybrid PSO-based ANN model to the prediction of rock UCS. To prepare a dataset for the predictive model, extensive laboratory tests (i.e., 160 tests in total) were conducted on 40 soft rock sample sets (mostly shale) presenting various weathering grades that were obtained from different excavation sites in Johor, Malaysia. The laboratory tests included the UCS test and other basic rock index tests (the Brazilian tensile strength test, point load index test, and ultrasonic test). When developing the predictive model of UCS, the results of the basic rock tests as well as the bulk densities of the samples were used as input parameters, while the UCS was set as the output of the predictive model. The value account for (VAF), root mean squared error (RMSE), and adjusted R
 2 (coefficient of determination) were utilized to check the performances of the predictive models. The high performance indices of the proposed model highlight the superiority of the PSO-based ANN model for UCS prediction.

Prediction of the unconfined compressive strength of soft rocks: a PSO-based ANN approach

Use of the block punch test to predict the compressive and tensile strengths of rocks

Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests

Crack-initiation stress of a rock under compression is the stress level that marks the initiation of the rock microfracturing process or in other words, the onset of new damage to the rock. This paper proposed a simple methodology with justifications to explore the feasibility of using total and effective porosities as estimators of crack-initiation stress of brittle crystalline rock materials under uniaxial compression. The validity/applicability of the proposed method was examined by an experimental study of granitic materials from Malanjkhand, Madhya Pradesh. It was found that effective porosity depicts better correlation with crack-initiation stress than with uniaxial compressive strength of the granitic materials. On the other hand, total porosity does not show any perceptible correlation with uniaxial compressive strength and crack-initiation stress. Plausible reasons for the nature of the obtained results were also explained in view of rock failure process under compression. It is concluded that following the proposed method, effective porosity can be used as a physical index to obtain a quick estimate of crack-initiation stress of the investigated rocks empirically.

Deepak Amban Mishra

Papers

Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system

Use of the block punch test to predict the compressive and tensile strengths of rocks

Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests

A Method for Estimating Crack-initiation Stress of Rock Materials by Porosity

Laboratory Triaxial Testing – from Historical Outlooks to Technical Aspects