Modified RMR to determine rock mass quality, study case of diversion tunnel in Meninting Dam, West Nusa Tenggara, Indonesia

The Meninting Dam under construction on Lombok Island, West Nusa Tenggara, Indonesia, requires a good planning to build a diversion tunnel to support its development and mobilization. The diversion tunnel is planned to be built through rocks with medium to poor rock mass quality. The planning stage involves various parameters, i.e., the rock mass classification, using either the RMR or GSI method. Converting values from one method to another makes planning work easier. However, the constraints found were the limitations of the observational data, such as discontinuity conditions. The objective of this article is to discuss the alternative depiction of discontinuity conditions in rock mass using RMR method. An alternative equation was developed to obtain a prediction model for determining the RMR value, based on GSI data. The evaluation showed that the mathematical models developed in this research had a small gap of error compared to other values. The models then can be used to predict RMR value based on GSI data and vice versa, with a higher degree of accuracy and precision according to the actual rock surface conditions, especially in the construction site of diversion tunnel at Meninting Dam.

On the Hochstadt–Lieberman problem for the Dirac operator with discontinuity

Using the input data – the spectrum of the Dirac operator with discontinuity, the potential on the half-interval and one boundary condition as well as discontinuity conditions – this paper presents a uniqueness theorem and the solvability conditions of the potential on the whole interval, and provides a reconstruction algorithm of the solution to this kind of inverse problems.

Inverse problem for Sturm-Liouville operators on a curve

he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.

Rock mass strength as link between geology and topography in the Can-abag mountain range, Southern Leyte, Philippines

Rock mass strength is used to characterize the influence of geology on the topography of the Can-abag mountain range in Southern Leyte, Philippines. A geologic model comprised of Jurassic to Cretaceous ultramafic rocks (UM), pre-Miocene fine clastic rocks (FC1), Middle Miocene limestones (LS1), Late Miocene to Late Pliocene coarse clastic rocks (CC), Late Miocene to Early Pliocene fine clastic rocks (FC2), and Late Pliocene limestones (LS2) is proposed for the study area. Five litho-structural units are derived from this model for use in the succeeding discussion: coarse clastic rocks west and east of the Can-abag ridge (CCw, CCe), fine clastic rocks (FC), limestones (LS) and ultramafic rocks (UM). FC and UM, both having weak rock mass strengths, are prone to isotropic slope failures, and are characterized by low-gradient, low curvature terrain. LS has high rock mass strengths, but because of limited topographic relief development, exhibits low-gradient, low curvature terrain similar to the weak rock masses. CCw and CCe both have high rock mass strengths and are characterized by high gradient, high curvature terrain. The former has slightly lower gradient and higher curvature than the latter due to the dominance of channelized transport processes. The latter, on the other hand, is influenced by steeply-dipping planar discontinuities which facilitate episodic massive landslides, which in turn reduce the curvature of the underlying unit. The weak rock mass strength of FC is mainly due to the inherent weakness of the fine-grained intact rock. In contrast, UM, which has high intact rock strengths due to the crystalline texture, is reduced to a weak rock mass by numerous discontinuities attributed to the long history of tectonic deformation. CCw and CCe, while having low intact rock strengths just above that of FC, have higher rock mass strengths because of good discontinuity conditions. LS has high rock mass strengths because of high intact rock strengths and good discontinuity conditions. Regional geologic structures such as bedding and fault planes provide potential conditions for planar slope failures within the rock masses. However, failures are spatially limited by the geometric relationships between the geologic structures and the existing topography. Steeply-dipping structures have direct significant contributions to massive landslides in terrains underlain by materials with strong isotropic rock mass strengths, such as in CCe. The geologic environment – lithology, structures, stratigraphy, tectonic history – provides the material base on which surface processes act on to create the present landform. Rock mass strength, as a geomechanical manifestation of the geologic environment and as a physically-based and quantifiable concept, provided a good framework for understanding and explaining the spatial variability of topographic characteristics in relation to the geologic materials of the Can-abag mountain range in Southern Leyte, Philippines. Some remarks regarding the use of gradient distributions in rock mass strength characterization, the use of slope gradient in landslide susceptibility analysis, and frequency-magnitude of landslides are put forward.