Mathematical Problems in Rock Mechanics and Rock Engineering

With increasing requirements for energy, resources and space, rock engineering projects are being constructed more often and are operated in large-scale environments with complex geology. Meanwhile, rock failures and rock instabilities occur more frequently, and severely threaten the safety and stability of rock engineering projects. It is well-recognized that rock has multi-scale structures and involves multi-scale fracture processes. Meanwhile, rocks are commonly subjected simultaneously to complex static stress and strong dynamic disturbance, providing a hotbed for the occurrence of rock failures. In addition, there are many multi-physics coupling processes in a rock mass. It is still difficult to understand these rock mechanics and characterize rock behavior during complex stress conditions, multi-physics processes, and multi-scale changes. Therefore, our understanding of rock mechanics and the prevention and control of failure and instability in rock engineering needs to be furthered. The primary aim of this Special Issue “Mathematical Problems in Rock Mechanics and Rock Engineering” is to bring together original research discussing innovative efforts regarding in situ observations, laboratory experiments and theoretical, numerical, and big-data-based methods to overcome the mathematical problems related to rock mechanics and rock engineering. It includes 12 manuscripts that illustrate the valuable efforts for addressing mathematical problems in rock mechanics and rock engineering

A proposed framework for characterising uncertainty and variability in rock mechanics and rock engineering

This thesis develops a novel understanding of the fundamental issues in characterising and propagating unpredictability in rock engineering design. This unpredictability stems from the inherent complexity and heterogeneity of fractured rock masses as engineering media. It establishes the importance of: a) recognising that unpredictability results from epistemic uncertainty (i.e. resulting from a lack of knowledge) and aleatory variability (i.e. due to inherent randomness), and; b) the means by which uncertainty and variability associated with the parameters that characterise fractured rock masses are propagated through the modelling and design process. Through a critical review of the literature, this thesis shows that in geotechnical engineering – rock mechanics and rock engineering in particular – there is a lack of recognition in the existence of epistemic uncertainty and aleatory variability, and hence inappropriate design methods are often used. To overcome this, a novel taxonomy is developed and presented that facilitates characterisation of epistemic uncertainty and aleatory variability in the context of rock mechanics and rock engineering. Using this taxonomy, a new framework is developed that gives a protocol for correctly propagating uncertainty and variability through engineering calculations. The effectiveness of the taxonomy and the framework are demonstrated through their application to simple challenge problems commonly found in rock engineering. This new taxonomy and framework will provide engineers engaged in preparing rock engineering designs an objective means of characterising unpredictability in parameters commonly used to define properties of fractured rock masses. These new tools will also provide engineers with a means of clearly understanding the true nature of unpredictability inherent in rock mechanics and rock engineering, and thus direct selection of an appropriate unpredictability model to propagate unpredictability faithfully through engineering calculations. Thus, the taxonomy and framework developed in this thesis provide practical tools to improve the safety of rock engineering designs through an improved understanding of the unpredictability concepts.Open Acces

Using engineering geosciences mapping and GIS-based tools for georesources management: lessons learned from rock quarrying

The heterogeneity of the geological properties of rock masses is very important in engineering geosciences and rock engineering issues. The study of discontinuous rock masses has developed enormously. In particular, the assessment of in situ block size plays a key role in rock engineering design projects such as mining, quarrying and highway cutting operations. The application of Geographic Information Systems to engineering geosciences has become more common. In this article, the importance of an integrative comprehensive approach to rock engineering is discussed in the context of quarrying operations, i.e., from field mapping surveys to geomechanical assessment. This approach led us to a better understanding of the appropriateness of exploitation of raw material aggregates and to reduced uncertainty about sustainability of georesources in relation to their management and the environment.info:eu-repo/semantics/publishedVersio

Elastic wave measurement in rock engineering

Imperial Users onl

Eurocode 7 and rock engineering design: The case of rockfall protection barriers

The Eurocode 7 or EC7 is the Reference Design Code (RDC) for geotechnical design including rock engineering design within the European Union (EU). Moreover, its principles have also been adopted by several other countries, becoming a key design standard for geotechnical engineering worldwide. It is founded on limit state design (LSD) concepts, and the reliability of design is provided mainly by a semi-probabilistic method based on partial factors. The use of partial factors is currently an advantage, mainly for the simplicity in its applicability, and a limitation, especially concerning geotechnical designs. In fact, the application of partial factors to geotechnical design has proven to be difficult. In this paper, the authors focus on the way to apply EC7 principles to rock engineering design by analyzing the design of rockfall protection structures as an example. A real case of slope subjected to rockfall is reported to outline the peculiarity connected to rock engineering. The main findings are related to the complementarity of the reliability-based design (RBD) approach within EC7 principles and the possibility of overcoming the limitations of a partial factor approach to this type of engineering problem

Eurocode 7 and rock engineering design: The case of rockfall protection barriers

The Eurocode 7 or EC7 is the Reference Design Code (RDC) for geotechnical design including rock engineering design within the European Union (EU). Moreover, its principles have also been adopted by several other countries, becoming a key design standard for geotechnical engineering worldwide. It is founded on limit state design (LSD) concepts, and the reliability of design is provided mainly by a semi-probabilistic method based on partial factors. The use of partial factors is currently an advantage, mainly for the simplicity in its applicability, and a limitation, especially concerning geotechnical designs. In fact, the application of partial factors to geotechnical design has proven to be difficult. In this paper, the authors focus on the way to apply EC7 principles to rock engineering design by analyzing the design of rockfall protection structures as an example. A real case of slope subjected to rockfall is reported to outline the peculiarity connected to rock engineering. The main findings are related to the complementarity of the reliability-based design (RBD) approach within EC7 principles and the possibility of overcoming the limitations of a partial factor approach to this type of engineering problem

Numerical modeling for the evaluation of grout penetration in fractured rock masses

Grouting aims to reduce the permeability of rock mass below the required value and has been widely used in rock engineering field for a long time

Selected Papers from the 11th Asian Rock Mechanics Symposium (ARMS 11)

The problem of rock mechanics and engineering is an old and new subject encountered by human beings in their struggle with nature for survival and development. To call it ancient means that it has a long history; however, speaking of it as brand-new refers to the continuous emergence of new problems and new situations in engineering practice, which is quite challenging. With the development of human engineering activities, the issues surrounding rock engineering are becoming more and more prominent, and the problems encountered are becoming more and more complex. In the practice of solving complex rock engineering, human beings have summarized many topics that are difficult to explain or solve with classical mechanics

Wave propagation through discontinuous media in rock engineering

The analysis of wave propagation in jointed rock masses is of interest for solving problems in geophysics, rock protective engineering, rock dynamics and earthquake engineering. At present, more than in the past, analyses of underground structures in seismic conditions need be considered. The aim of the present thesis is to contribute to the understanding of wave propagation in rock masses and of its influence on the stability of underground structures. The research is focused first on the analysis of the phenomenon through analytical, numerical and experimental methods. Then, static and dynamic stability analyses of a real case study such as the water storage cavern of the Tel Beer Sheva archaeological site in Israel (Iron age 1200-1700bc) are carried out. An analytical method such as the Scattering Matrix Method (SMM) is developed for the study of wave propagation through rock masses. This method (SMM) is based on the scattering matrix and is borrowed from electromagnetic wave propagation theory of transmission lines such as coaxial cables, optical fibres, strip-lines, etc. The scattering matrix is composed of reflection and transmission coefficients of a single joint or a set of parallel joints. Dry, fluid filled or frictional joints are considered. The computation can also be performed with material damping. Both P, SV or SH-waves can be applied to the model with any oblique angle of incidence. The analytical solution is obtained in the frequency domain and allows one to consider multiple wave reflections between joints. The analytical results obtained with the SMM are compared with other analytical methods and with the Distinct Element Method (DEM) by using the UDEC and 3DEC codes (from Itasca Consulting Group). The results obtained with the SMM applied to different joint models are compared with those obtained experimentally with the Hopkinson pressure bar (SHPB) tests. Resonant column laboratory tests are also performed to investigate the effects of fractures on wave propagation in a soft rock. A three-dimensional DEM model is implemented to simulate the resonant column test. Numerical and experimental results are compared. The stability of the water storage cavern of the Tel Beer Sheva archaeological site in Israel, excavated in a jointed chalk is assessed by means of static and dynamic DEM analyses in two and in three dimensional conditions. A back analysis of both the roof collapse during construction and of the cavern in its present configuration with a pillar installed in the centre is also carried out. Finally dynamic analyses are performed to evaluate the influence of wave propagation on the stability of the cavern with a deconvoluted motion produced by the Nuweiba earthquake (1995) being applied as input. Additional numerical analyses are performed to evaluate the dependence of the damage on the amplitude, duration, frequency and direction of the input wave

Wave propagation through discontinuous media in rock engineering

The analysis of wave propagation in jointed rock masses is of interest for solving problems in geophysics, rock protective engineering, rock dynamics and earthquake engineering. At present, more than in the past, analyses of underground structures in seismic conditions need be considered. The aim of the present thesis is to contribute to the understanding of wave propagation in rock masses and of its influence on the stability of underground structures. The research is focused first on the analysis of the phenomenon through analytical, numerical and experimental methods. Then, static and dynamic stability analyses of a real case study such as the water storage cavern of the Tel Beer Sheva archaeological site in Israel (Iron age 1200-1700bc) are carried out. An analytical method such as the Scattering Matrix Method (SMM) is developed for the study of wave propagation through rock masses. This method (SMM) is based on the scattering matrix and is borrowed from electromagnetic wave propagation theory of transmission lines such as coaxial cables, optical fibres, strip-lines, etc. The scattering matrix is composed of reflection and transmission coefficients of a single joint or a set of parallel joints. Dry, fluid filled or frictional joints are considered. The computation can also be performed with material damping. Both P, SV or SH-waves can be applied to the model with any oblique angle of incidence. The analytical solution is obtained in the frequency domain and allows one to consider multiple wave reflections between joints. The analytical results obtained with the SMM are compared with other analytical methods and with the Distinct Element Method (DEM) by using the UDEC and 3DEC codes (from Itasca Consulting Group). The results obtained with the SMM applied to different joint models are compared with those obtained experimentally with the Hopkinson pressure bar (SHPB) tests. Resonant column laboratory tests are also performed to investigate the effects of fractures on wave propagation in a soft rock. A three-dimensional DEM model is implemented to simulate the resonant column test. Numerical and experimental results are compared. The stability of the water storage cavern of the Tel Beer Sheva archaeological site in Israel, excavated in a jointed chalk is assessed by means of static and dynamic DEM analyses in two and in three dimensional conditions. A back analysis of both the roof collapse during construction and of the cavern in its present configuration with a pillar installed in the centre is also carried out. Finally dynamic analyses are performed to evaluate the influence of wave propagation on the stability of the cavern with a deconvoluted motion produced by the Nuweiba earthquake (1995) being applied as input. Additional numerical analyses are performed to evaluate the dependence of the damage on the amplitude, duration, frequency and direction of the input wav