The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

The effect of scale on the shear behaviour of joints is studied by performing direct shear tests on different sized replicas cast from various natural joint surfaces. The result show significant scale effects on both the shear strength and deformation characteristics. Scale effects are more pronounced in the case of rough, undulating joint types, whereas they are virtually absent for planar joints. The key factor is the involvement of different asperity sizes in controlling the peak behaviour of different lengths of joints. It is shown that as a results both the joint roughness coefficient (JRC) and the joint compression strength (JCS) reduce with increasing scale. The behaviour of multiple jointed masses with different joint spacing is also considered. It is found that despite unchanged roughness, jointed masses consisting of many small blocks have higher peak shear strength than jointed masses with larger joint spacing. These scale effects are related to the changing stiffness of a rock mass as the block size or joint spacing increases or decreases. Economic methods for obtaining scale-free estimates of shear strength are described.

Experimental studies of scale effects on the shear behaviour of rock joints

Boundary element methods in solid mechanics

A bibliometric based survey on AHP and TOPSIS methods has been conducted.Scopus database was employed to retrieve the required data for this analysis.Assessment of quantitative and qualitative bibliometric indicators was obtainable.Efficacy of these methods promotes the development of related research.More scientific research interests will be devoted to these methods in the future. In recent years, the employment of multiple criteria decision analysis (MCDA) techniques in solving complex real-world problems has increased exponentially. The willingness to build advanced decision models, with higher capabilities to support decision making in a wide range of applications, promotes the integration of MCDA techniques with efficient systems such as intelligence and expert systems, geographic information systems, etc. Amongst the most applied MCDA techniques are Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The development of a comprehensive perspective on research activities associated with the applications of these methods provides insights into the contributions of countries, institutes, authors and journals towards the advancements of these methods. Furthermore, it helps in identifying the status and trends of research. This in turn will help researchers in shaping up and improving future research activities and investments. To meet these aims, a bibliometric analysis based on data harvested from Scopus database was carried out to identify a set of bibliometric performance indicators (i.e. quantitative indicators such as productivity, and qualitative indicators such as citations and Hirsch index (h-index)). Additionally, bibliometric visualization maps were employed to identify the hot spots of research. The total research output was 10,188 documents for AHP and 2412 documents for TOPSIS. China took a leading position in AHP research (3513 documents; 34.5%). It was also the leading country in TOPSIS research (846 documents; 35.1%). The most collaborated country in AHP research was the United States, while in case of TOPSIS it was China. The United States had gained the highest h-index (78) in AHP research, while in TOPSIS it was Taiwan with h-index of 46. Expert Systems with Applications journal was the most productive journal in AHP (204; 2.0%) and TOPSIS research (125; 5.2%), simultaneously. University of Tehran, Iran and Islamic Azad University, Iran were the most productive institutions in AHP (173; 1.7%) and TOPSIS (115; 4.8%) research, simultaneously. The major hot topics that utilized AHP and will continue to be active include different applications of geographic information systems, risk modeling and supply chain management. While for TOPSIS, they are supply chain management and sustainability research. Overall, this analysis has shown increasing recognition of powerful of MCDA techniques to support strategic decisions. The efficacy of these methods in the previous context promotes their progress and advancements.

https://scholar.ptuk.edu.ps/bitstream/123456789/349/1/TOPSIS.pdf

A bibliometric-based survey on AHP and TOPSIS techniques

Soft computing techniques are becoming even more popular and particularly amenable to model the complex behaviors of most geotechnical engineering systems since they have demonstrated superior predictive capacity, compared to the traditional methods. This paper presents an overview of some soft computing techniques as well as their applications in underground excavations. A case study is adopted to compare the predictive performances of soft computing techniques including eXtreme Gradient Boosting (XGBoost), Multivariate Adaptive Regression Splines (MARS), Artificial Neural Networks (ANN), and Support Vector Machine (SVM) in estimating the maximum lateral wall deflection induced by braced excavation. This study also discusses the merits and the limitations of some soft computing techniques, compared with the conventional approaches available.

https://dr.ntu.edu.sg/bitstream/10356/146887/2/1-s2.0-S1674987119302361-main.pdf

State-of-the-art review of soft computing applications in underground excavations

Response by the authors to S. Yagiz discussion to the paper: J. Khademi Hamidi et al., Performance prediction of hard rock TBM using Rock Mass Rating (RMR) system [Tunnell. Undergr. Space Technol. 25 (2010) 333–345]

The fractures geometrical characteristics can be calculated by various sampling methods in 1 dimension (1D) & 2 dimensions (2D). The Discrete Fracture Network (DFN) simulation results show some of the equations are suitable for calculation of mean trace length and the difference between actual value and their values is less than 15%. Apparent density is dependent on scale, but the Mauldon’s estimators are independent of scale despite the variation in fracture length. For all joint sets, the difference of apparent areal intensity by samplings windows and circular estimator is less than 5% proportionate to actual value. A reduction of Fisher constant doesn’t have much effect on mean trace length of the fractures with length less than 1.5 m, but it results in a 21% difference for fractures with length longer than 1.5 m. Variation of this parameter affects the density, too and the difference can be 5% to 10% depending on fracture length. But, variation in Fisher constant doesn’t have any effect on areal intensity for fractures with length less than 2 m.

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Effect of Shape and Size of Sampling Window on the Determination of Average Length, Intensity and Density of Trace Discontinuity

Analysis of Permeability Using BPF, ANFIS & SOM

Rock failure mechanism is one of the most important issues in rock mechanics engineering which plays a key role in the stability analysis of various structures. Therefore, different failure criteria have been proposed to understand the failure mechanism of rocks. One of the most commonly used rock failure criteria is the Hoek-Brown criterion, in which there is a parameter called mi, which is very important to the response provided by this criterion. Due to the importance of conducting extensive studies on this parameter, in this current research, by performing a series of experimental triaxial compressive strength test and numerical simulating in PFC-2D code, the effect of the Hoek-Brown constant mi on the failure mechanism and crack growth of different rocks has been studied. Based on the results of this study, it was found that the effect of parameter mi on the failure mechanism of different rocks varied according to the type of rocks, and the greatest effect of this parameter was on the peak strength of rocks. In addition, it was found that under higher lateral pressures, there are less destructive cracks in rocks, and as a result, they show more ductile behaviour.

/pdf/numerical-and-experimental-research-of-rock-failure-4b1qlbwk0i.pdf

Numerical and experimental research of rock failure mechanism and its dependence on mi Hoek-Brown failure criterion

A rock failure criterion is very important for prediction of the ultimate strength in rock mechanics and geotechnics; it is determined for rock mechanics studies in mining, civil, and oil wellborn drilling operations. Also shales are among the most difficult to treat formations. Therefore, in this research work, using the artificial neural network (ANN), a model was built to predict the ultimate strength of shale, and comparison was made with support vector machine (SVM), multiple linear regression models, and the widely used conventional polyaxial failure criteria in the stability analysis of rock structures, Drucker-Prager, and Mogi-Coulomb. For building the model, the corresponding results of triaxial and polyaxial tests have been performed on shales by various researchers. They were collected from reliable published articles. The results obtained showed that a feed forward back propagation multi-layer perceptron (MLP) was used and trained using the Levenberg–Marquardt algorithm, and the 2-4-1 architecture with root-mean-square-error (RMSE) of 24.41 exhibits a better performance in predicting the ultimate strength of shale in comparison with the investigated models. Also for further validation, triaxial tests were performed on the deep shale specimens. They were prepared from the Ramshire oilfield in SW Iran. The results obtained were compared with ANN, SVM, multiple linear regression models, and the conventional failure criterion prediction. They showed that the ANN model predicted ultimate strength with a minimum error and RMSE being equal to 43.81. Then the model was used for prediction of the threshold broken pressure shale layer in the Gachsaran oilfield in Iran. For this, a vertical and horizontal stress was calculated based on a depth of shale layer. The threshold broken pressure was calculated for the beginning and ending of a shale layer to be 154.21 and 167.98 Mpa, respectively.

http://jme.shahroodut.ac.ir/article_1012_dd05eada9dcd60e83ab50b7b9ff8bf0f.pdf

Kourosh Shahriar

Papers

Response by the authors to S. Yagiz discussion to the paper: J. Khademi Hamidi et al., Performance prediction of hard rock TBM using Rock Mass Rating (RMR) system [Tunnell. Undergr. Space Technol. 25 (2010) 333–345]

Effect of Shape and Size of Sampling Window on the Determination of Average Length, Intensity and Density of Trace Discontinuity

Analysis of Permeability Using BPF, ANFIS & SOM

Numerical and experimental research of rock failure mechanism and its dependence on mi Hoek-Brown failure criterion

Prediction of ultimate strength of shale using artificial neural network