The Consolidated Mathews Stability Graph for Open Stope Design

The stability graph method of stope design is one of the most widely used methods of stability assessments of stopes in underground polymetallic mines. The primary objective of this work is to introduce a new stability chart, which includes all relevant case histories, and to exclude parameters with uncertainties in the determination of stability number. The modified stability number was used to achieve this goal, and the Extended Mathews database was recalculated and compared with the new stability graph. In this study, a new refined Consolidated stability graph was developed by excluding the entry mining methods data from the Extended graph data, and only the non-entry methods data was used. The applicability of the proposed Consolidated stability chart was demonstrated by an open stope example. The stability for each stope surface was evaluated by a probabilistic approach employing a logistic regression model and the developed Consolidated stability chart. Comparing the stability analysis results with that of other published works of the same example shows that the determined Consolidated chart, in which the entry-method data is excluded, produces a more conservative and safer design. In conclusion, the size and quality of the dataset dictate the reliability of this approach.

Rocking Blocks Stability under Critical Pulses from Near-Fault Earthquakes Using a Novel Energy Based Approach

Following the seminal work of Housner, a novel energy based critical pulse theoretical model is derived to assess the seismic stability of rocking rigid blocks under single pulses from near-fault earthquakes. It is shown that overturning is conditional on the availability of sufficient kinetic energy in the exciting pulse and on the inception of rocking. The theoretical model is shown to be in good agreement with discrete element method numerical simulations for similar blocks of sizes 0.5, 1, and 20 m. Similitude rules are established to scale between block sizes and pulse types and tested successfully. The results agree with available experimental data. The proposed stability chart approach provides a practical and simple alternative to the presentation and study of the stability and overturning of blocks published by others in the frequency spectrum domain. For any given rigid block or inverted pendulum structure the model or normalized stability charts provide a method to determine the characteristic period and peak acceleration required for overturning and by extension to identify the critical content of the dominant pulse of a given earthquake signal. Alternatively, the approach could be used in archaeoseismology to identify the characteristics of the dominant pulse content of past earthquakes based on their impacts on various historical and heritage structures.

Faraday waves on a cylindrical fluid filament – generalised equation and simulations

We perform linear stability analysis of an interface separating two immiscible, inviscid, quiescent fluids subject to a time-periodic body force. In a generalised, orthogonal coordinate system, the time-dependent amplitude of interfacial perturbations, in the form of standing waves, is shown to be governed by a generalised Mathieu equation. For zero forcing, the Mathieu equation reduces to a (generalised) simple harmonic oscillator equation. The generalised Mathieu equation is shown to govern Faraday waves on four time-periodic base states. We use this equation to demonstrate that Faraday waves and instabilities can arise on an axially unbounded, cylindrical capillary fluid filament subject to radial, time-periodic body force. The stability chart for solutions to the Mathieu equation is obtained through numerical Floquet analysis. For small values of perturbation and forcing amplitude, results obtained from direct numerical simulations (DNS) of the incompressible Euler equation (with surface tension) show very good agreement with theoretical predictions. Linear theory predicts that unstable Rayleigh–Plateau modes can be stabilised through forcing. This prediction is borne out by DNS results at early times. Nonlinearity produces higher wavenumbers, some of which can be linearly unstable due to forcing and thus eventually destabilise the filament. We study axisymmetric as well as three-dimensional perturbations through DNS. For large forcing amplitude, localised sheet-like structures emanate from the filament, suffering subsequent fragmentation and breakup. Systematic parametric studies are conducted in a non-dimensional space of five parameters and comparison with linear theory is provided in each case. Our generalised analysis provides a framework for understanding free and (parametrically) forced capillary oscillations on quiescent base states of varying geometrical configurations.

A Case Study Based Slope Stability Analysis at Chittagong City, Bangladesh

Heavy rainfall occurs almost every year in Bangladesh and induces landslides in the hilly regions of this country. Among them the Chittagong City has the worst scenario―as there lives a dense population, extending from the plain lands to the hilly area. So, for risk mitigation and management in this landslide prone city, slope safety margin should be determined. From this context, this article presents factor of safety (FS) values in terms of landslide hazard at Chittagong city, based on geotechnical parameters and slope geometry. Thus a preliminary idea on the allowable stress for slope design could be made from this study. In total, 16 hazard sites of the 2007 and 2008, rainfall induced, landslides were examined as a case study along with subsequent collection of in situ soil samples of the failed slopes for geotechnical laboratory analysis. For FS calculation, the limit equilibrium method for infinite slopes was deployed along with the Cousins’ stability chart. FS values from 0.94 to 1.57 were found at the hazard sites. The results imply that FS value more than 1.57 should be used for slope safety margin. Moreover, from a probabilistic approach, the authors recommend FS > 1.80 as optimum value for the region. Furthermore, a relationship between slope height to slope length ratio, or slope angle and FS was established for this region for a quick calibration of FS value by simple on-field measurement of slope parameters. It is expected that this scenario based finding would contribute in mitigation of landslide hazard risk at the study area. Additionally, site specific FS values were presented in a map by color indexing. This research could ascertain the location wise slope strength requirement and be considered as a guideline for future calculation for slope safety design against rainfall triggered landslides in this city.