Rock Mechanics

Course Description
Rock mechanics is a fundamental branch of a great variety of engineering and geoscience disciplines, mainly in mining, geology, and civil among others. The rock mechanics course has been structures focusing in the mining engineering students so they can develop an understanding of the basic principles of applied rock mechanics. The application of these principles on the design of excavations that ensure the objectives of safety and economic feasibility are also covered.

The course starts with an introduction of the concepts of stress, strain, elasticity, strength and plasticity which are fundamental to the understanding of the principles that govern the behavior of rock masses. Part of the objectives of this course is to provide the students with the necessary tools to formulate the framework required to solve a wide range of rock mechanic problems, from the stand point of view of the load and deformation that take place within the rock masses. The course also cover most of the rock mechanics laboratory tests commonly performed to determine crucial parameters applied to solve rock mass stability problems.

The next section starts with a description of the rock masses as an engineering material where is covered the methods to determine their most relevant characteristics from a stability stand point. It also covers the most relevant rock mass classification systems available to date. The stress redistribution around underground excavations and the deformation that the rock is subjected to due to the stress redistribution to is also discussed in this section. A field trip will be done in order to complement the course material and to exercise the field data collection.

The following section will make use of the field data collection which is then applied to the design of underground stopes, support requirements, maximum stable excavation spans among others. The stability analysis and the design principles both for slope stability in open pit excavations and stopes and pillars in underground excavations will be discussed in terms of safety and economic principles. Multiple practical design exercises will be performed with the use of rock mechanics computer programs aiming to provide the students with a realistic perception of the engineering process required for the design of stable excavations in rock.

General and Specific Objectives
The main objective of the course aim at the students to develop an understanding of the principles of rock mechanics applied to the design of stable surface and underground excavations in rock.

The specific objectives of the course aim at the students to be able to design in a safe and cost effective manner, stable slopes in surface mining and pillars and stopes in underground mining.

Other specific objectives can be summarized as follows:
- Understand the concept of factor of safety,
- Understand the implications that the factor of safety has on the design of an excavation, and its economic impact,
- Identify and mitigate the potential causes of rock instabilities, such as wedge, planar and rotational failures,
- Apply empirical tools towards the design of cost effective underground excavations,
- Learn the use of rock mechanic software to solve a wide range of geomechanical problems.

Course Contents
1. Introduction to rock mechanics

• General concepts in rock mechanics
• Path to the solution of rock mechanics problems
• Stability in surface excavations
• Stability in underground excavations
• Surface and underground instability examples

2. Stress, Strength, Strain and Displacement

• Concept of force and stress
• Concept of strain and displacement
• Concept of strength and factor of safety

3. Pre mining stress state

• Specifications of the state of pre mining stresses
• Factors that influence the in situ state of stresses
• Methods to determine the in situ state of stresses
• Presentation and results of in situ stress measurements
• Mining induced stresses

4. Rock mass structure and geotechnical characterization

• Types of structures present in the rock mass
• Geomechanic classification using Bieniawski’s RMR system
• Geomechanic classification using Barton’s Q system
• Geomechanic classification using Hoek’s GSI system

5. Slope stability

• Schmidt stereographic projection
• Cinematic wedge stability analysis
• Cinematic planar stability analysis
• Rotational failure stability analysis

6. Stability of underground excavations

• Induced stress in pillars
• Empirical design for stability of underground excavations
• Maximum stable span for tunnels and drifts
• Stability of open stopes

7. Ground support systems

• Types of support
• Support design of underground wedges

8. Geomechanic instrumentation to control and monitor rock mass instabilities

• GMM´s
• Instrumented rock bolts
• Instrumented cable bolts
• Robotic total stations
• Radar

Evaluations
Nota de presentación a examen NPE
The course considers two “pruebas” with grades P1 and P2 with equal ponderation towards the final grade.

It also contemplates a number of activities (tareas y laboratorios) to be developed during the term. The average of all the “tareas y laboratorios” will give the grade of “Tareas y Laboratorios (TyL)”

The final exam presentation grade (NPE) is the result of the following weighted average:
NPE = 0.3 x P1 + 0.3 x P2 + 0.4 x TyL

Each averaged grade is calculated rounding to one decimal place.
Nota final NF

The objective of the final exam (EX) is to evaluate the main contents of the course. The final exam covers all the course notes and is mandatory for all students.

The final grade (NF) will be calculated using the following formula: 𝑵𝑭=0.7 𝑥 𝑁𝑃𝐸+0.3 𝑥 𝐸𝑋

Students which final grade (NF) is equal or higher than 4.0 will pass the course.

Bibliography
The course notes of each class will be provided after each class in electronic format (pdf) through webcurso. These will be the material used for the evaluations during the term. More information about the concepts and subjects viewed during the classes can be reviewed and downloaded from the following web page: https://www.rocscience.com/education/hoeks_corner. Also, books such as Rock Mechanics for Underground Mining de B H G Brady and E T Brown, 3ª edition, George Chapman and Hall and Rock Slope Engineering de E Hoek and J W Bray (2ª edition), will be part of the literature that the students are invited to read.