# Methods

## Block Theory

Block Theory is one of the most important analysis methods in computational rock mechanics, and is also the basis of discontinuous deformation computation. The fundamental purpose of block theory is to analyse the finiteness, removability and mechanical stability of various blocks under different engineering conditions according to the analysis of dip angles, dip direction angles of discontinuities, frictional angles and the direction of the active resultant force, Then reasonable opinions and suggestions are proposed for the design and construction of rock engineering.

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### Softwares

- Standard KBT: The original implementation provided by Dr. Gen-hua Shi.
- easyKBT: A software with GUI for Key Block Theory, developed by Engineering Computing Center, UCAS.
- VisKBT: A software for 3D visualization of Key Block Theory, developed by Engineering Computing Center, UCAS.

## DDA

**Discontinuous Deformation Analysis (DDA)** is a type method for resolving discontinuous problems in engineering originally proposed by Dr. Gen-hua Shi in 1988. DDA is somewhat similar to the finite element method for solving stress-displacement problems, but accounts for the interaction of independent particles (blocks) along discontinuities in fractured and jointed rock masses. DDA is typically formulated as a work-energy method, and can be derived using the principle of Minimum Potential Energy or by using Hamilton's principle. Once the equations of motion are discretized, a step-wise linear time marching scheme in the Newmark family is used for the solution of the equations of motion. The relation between adjacent blocks is governed by equations of contact interpenetration and accounts for friction. DDA adopts a stepwise approach to solve for the large displacements that accompany discontinuous movements between blocks. The blocks are said to be "simply deformable". Since the method accounts for the inertial forces of the blocks' mass, it can be used to solve the full dynamic problem of block motion.

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### Softwares

- DDA 2D: The original implementation provided by Dr. Gen-hua Shi.
- easyDDA: An easy-to-use GUI software developed by Engineering Computing Center, UCAS.
- UC Berkeley DDA: The DDA software developed by UC Berkeley (only for Windows platform).

## NMM

*Numerical Manifold Method (NMM)*

### Softwares

- NMM 2D: The original implementation provided by Dr. Gen-hua Shi.