A distribution-free description of fragmentation by blasting based on dimensional analysis

A model for fragmentation in bench blasting is developed from dimensional analysis adapted from asteroid collision theory, to which two factors have been added, one describing the discontinuities spacing and orientation and another the delay between successive contiguous shots. The formulae are calibrated by non-linear fits to 169 bench blasts in different sites and rock types, bench geometries and delay times, for which the blast design data and the size distributions of the muckpile obtained by sieving were available. Percentile sizes of the fragments distribution are obtained as the product of a rock mass structural factor, a rock strength-to-explosive energy ratio, a bench shape factor, a scale factor or characteristic size, and a function of the in-row delay. The rock structure is described by means of the joints? mean spacing and orientation with respect to the free face. The strength property chosen is the strain energy at rupture that, together with the explosive energy density forms a combined rock strength/explosive energy factor. The model is applicable from 5 to 100 percentile sizes, with all parameters determined from the fits significant to a 0.05 level. The expected error of the prediction is below 25 % at any percentile. These errors are half to one third of the errors expected with the best prediction models available to date

Differential conductance of a saddle-point constriction with a time-modulated gate-voltage

The effect of a time-modulated gate-voltage on the differential conductance $G$ of a saddle-point constriction is studied. The constriction is modeled by a symmetric saddle-point potential and the time-modulated gate-voltage is represented by a potential of the form $V_{0} \theta(a/2-|x-x_{c}|) \cos (\omega t)$. For $\hbar\omega$ less than half of the transverse subband energy level spacing, gate-voltage-assisted (suppressed) feature occurs when the chemical potential $\mu$ is less (greater) than but close to the threshold energy of a subband. As $\mu$ increases, $G$ is found to exhibit, alternatively, the assisted and the suppressed feature. For larger $\hbar\omega$, these two features may overlap with one another. Dip structures are found in the suppressed regime. Mini-steps are found in the assisted regime only when the gate-voltage covers region far enough away from the center of the constriction.Comment: 8 pages, 6 figure

The Drinfel'd twisted XYZ model

We construct a factorizing Drinfel'd twist for a face type model equivalent to the XYZ model. Completely symmetric expressions for the operators of the monodromy matrix are obtained.Comment: 15 pages, 4 figures, second preprint no. added, reference [14] added, typos correcte

Numerical Simulation of Rock Toughness Testing

The testing method of rock toughness is proposed by the international society of rock mechanics (ISRM), but the results may be influenced by the test pieces, and the details of the crack propagation and the stress intensity factors are not clarified through the testing. Also the experimental test requires tedious works for the preparation of test specimen and economical responsibility. The present study aims to simulate numerically the rock toughness testing which is proposed by ISRM. For this purpose, the authors propose a numerical method which can simulate the experimental testing, and they show the propriety of the proposed method by comparing the results with the experimental and other numerical methods. At the same time, they clarify the details of crack propagation behaviors in rocks, and show the change of the stress intensity factors. The proposed method is based on the displacement-type finite element method, and several techniques are introduced to obtain accurate solution of the mechanical behavior near the crack-tip area

ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semicircular bend specimen is herein presented. The specimen is semicircular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied