Determining the stresses that exist in the rock mass opening has been a significant area of research in mining for a long time. The main reason for this is the concern of roof collapse of the excavation due to overlying pressure from the rock mass. This thesis is concerned with the state of stresses that exist in the rock mass in 2 conditions: 1. Stresses in rock before the mine openings; 2. Altered state of stresses after the excavations are made.
Theories have been formulated to calculate the pre-stressed state of the rock mass. But any sort of measurement invalidates the original condition of the intact rock. There are mainly 3 ways to study these different stress conditions in the rock mass: Analytical solutions using pre-defined mathematical equations; using numerical modelling to predict the stresses by duplicating the in-situ stress conditions; and in-situ measurements of the stress conditions in the rock mass.
One of the first assumptions taken while doing the measurements is assume that the rock mass is elastic and homogenous (single layer). There are also assumptions where the rock is considered viscous, plastic or a combination of these. But for this research project, the first assumption is considered. This is done to ease up the subsequent calculations on the more complex characteristics of the rock mass.
In this research project, the attempt is to do a comparison of the initial and final stressed conditions of the rock mass in a series of square and circular drifts between the analytical and the numerical solutions of the model. It must be noted that a completely accurate picture of the stress phenomena cannot be drawn because of the lack of knowledge of the physical properties of rock under field conditions.
The purpose of the project is to compare numerically calculated loading behavior of rock mass to that of analytical solutions obtained from the same.
Table of Contents
1.0 Pre-stressed state of the rock mass
2.0 Stresses around excavations in solid homogenous materials
2.1 Stresses around single excavations
2.1.1 Circular Excavation
2.1.2 Square excavation
3.0 Analytical solutions around multiple circular and square excavations
4.0 Loading behaviour around circular and square excavations using numerical modelling
4.1 Circular Excavation
4.2 Square Excavation
5.0 Results
5.1 Analytical solution
5.2 Numerical solutions for circular and square excavation
5.3 Comparison of equivalent stresses and strains
6.0 Conclusion
7.0 References
8.0 Appendix
8.1 Appendix A: stress and strain distribution around a square excavation
8.2 Appendix B: stress and strain distribution around a circular excavation
Research Objectives and Key Topics
The primary objective of this research is to evaluate and compare the load-bearing behavior of rock masses in square and circular drift configurations by contrasting analytical calculations with numerical simulation results derived from FLAC 3D software.
- Analysis of pre-stressed conditions in elastic, homogenous rock masses.
- Application of analytical solutions for stress and strain distribution.
- Implementation of numerical modeling to simulate load behavior in multiple excavations.
- Comparison of stability and stress concentration between circular and square geometries.
- Evaluation of analytical model accuracy through regression analysis.
Excerpt from the Book
2.1 Stresses around single excavations
As the starting point of any calculation, we must first consider the effect of a single excavation on the underground and then move on to multiple excavations. This is of paramount importance as the pressure redistribution changes in different shapes as well as the number of excavations and the circular excavation seems like the most basic shape to start the analysis with.
The main objective of these problems is to achieve:
Effect of different shapes in stress concentrations around the boundary of the excavation.
The most stable shape to perform the excavation to avoid failure of the rock
Determine in situ stress around the mine openings
Summary of Chapters
1.0 Pre-stressed state of the rock mass: Discusses the factors influencing initial rock stress, such as overburden weight and depth, and introduces Mindlin’s hypothesis for pressure states.
2.0 Stresses around excavations in solid homogenous materials: Outlines the project’s scope regarding coal seam homogeneity and details the dome theory used for initial stress analysis.
3.0 Analytical solutions around multiple circular and square excavations: Details the mathematical assumptions and initial conditions, such as support resistance and elastic properties, for calculating stresses.
4.0 Loading behaviour around circular and square excavations using numerical modelling: Describes the methodology of using FLAC 3D and the FISH programming language to model and simulate excavation stress distribution.
5.0 Results: Presents the findings from analytical and numerical models, including data comparisons and regression statistics to evaluate correlations.
6.0 Conclusion: Summarizes that circular excavations are more stable than square ones and that analytical solutions are highly accurate for circular but not for square shapes.
7.0 References: Lists the academic literature and foundational works used to support the research methodology.
8.0 Appendix: Provides detailed visual documentation of stress and strain distributions derived from the numerical simulations.
Keywords
Mining Engineering, Rock Mechanics, FLAC 3D, Numerical Modelling, Analytical Solutions, Stress Distribution, Circular Excavation, Square Excavation, Load-bearing Behaviour, Elastic Model, Poisson Ratio, Strain, Pillar Stability, Coal Seam, Regression Analysis
Frequently Asked Questions
What is the core focus of this research project?
The project investigates the stress and strain behavior of rock masses surrounding underground excavations, specifically comparing the load-bearing characteristics of square and circular drift shapes.
Which primary themes are addressed in this study?
The work covers theoretical stress calculation, the influence of excavation geometry on stability, numerical simulation of multiple tunnels, and the accuracy validation of analytical solutions.
What is the ultimate goal of the investigation?
The goal is to determine the most stable excavation shape by comparing numerical data from FLAC 3D software against traditional mathematical analytical solutions.
Which scientific methodology is employed?
The study utilizes both analytical equations for elastic rock mass behavior and numerical modeling software (FLAC 3D) to simulate stress redistribution after excavations are made.
What topics are covered in the main body?
The main body treats the pre-stressed state of rock, the specific stress profiles of single and multiple excavations, the simulation setup, and the final comparative results of stresses and strains.
Which keywords define this research?
Key terms include Rock Mechanics, Numerical Modelling, Stress Distribution, Circular/Square Excavation, and Pillar Stability.
Why are square excavations considered less stable in this study?
Numerical modeling indicates that square excavations exhibit higher stress concentrations in the pillar and roof compared to circular designs, leading to greater instability.
How is the accuracy of the analytical solutions assessed?
The author performs a regression analysis comparing analytical results with numerical simulation outputs; an adjusted R-square value is calculated to verify the degree of correlation.
What role does the FLAC 3D software play?
It is used as the numerical tool to simulate the stress and strain conditions within the rock mass around multiple tunnels, providing empirical data for comparison with the analytical models.
- Quote paper
- Arijit Ghosh (Author), 2017, Stresses in Multiple Excavations. A Comparative Study, Munich, GRIN Verlag, https://www.grin.com/document/380431
