Mechanics of Using 3DEC

Projects and Files

See Projects.

Commands and FISH

For 3DEC commands and FISH functions (blocks, joints, block zones, etc.), see 3DEC Commands and FISH. For commands and FISH functions common to 3DEC, FLAC3D, PFC (model commands, program commands, geometry commands, etc.) see i Common Model Objects.

For information on how commands work (issuing commands, command syntax, principles governing their use, etc.), see i How Commands Work. For all general information about the FISH scripting language, see i FISH Scripting Reference in the i Scripting section.

Plotting and the Graphical User Interface

See i Plotting for complete information on plotting. The information in this section is applicable to 3DEC, FLAC3D, and PFC.


The nomenclature used in 3DEC is similar, for the most part, to that used in continuum stress analysis programs. In addition, though, special terminology is used to describe the discontinuum features in a 3DEC model. The basic definitions are given here for clarification. The figure below illustrates 3DEC terminology.


Figure 1: Example of a 3DEC model (not to scale)

3DEC model

The 3DEC model is created by the user to simulate a physical problem. When referring to a 3DEC model, we imply a sequence of 3DEC commands (see 3DEC Commands and FISH) that define the problem conditions for numerical solution.


The block is the fundamental geometric entity for the distinct element calculation. The 3DEC model is created by either “cutting” a single block into many smaller blocks, or creating separate blocks and joining them together. Each block is an independent entity that may be detached from other blocks, or may interact with other blocks via surface forces. Another term for block is polyhedron.


Each block is connected to adjacent blocks via point contacts. A contact may be considered a boundary condition that applies external forces to each block.


Each contact is divided into sub-contacts for both rigid and deformable blocks. Interaction forces between blocks are applied at sub-contacts.


A discontinuity is a geologic feature that separates a physical mass into distinct parts. Discontinuities, for example, include joints, faults and fractures, and other discontinuous features in a rock mass.

To be represented in 3DEC, a discontinuity must have a trace length scale that is approximately of the same order as the engineering structure being analyzed. A discontinuity in 3DEC is defined by at least one contact between blocks.


Deformable blocks are composed of tetrahedral finite-difference zones. Mechanical changes (e.g., stress/strain) are calculated within each zone. Mixed-discretization (m-d) zones are special zones that are composed of two overlays of five tetrahedral subzones. m-d zones provide accurate solutions for block plasticity analysis.


Gridpoints are associated with the corners of the tetrahedral finite-difference zones (or subzones of m-d zones). There are always four gridpoints associated with each zone. A set of x-, y-, z-coordinates is assigned to each gridpoint, thus specifying the exact location of the finite-difference zones. Other terms for gridpoint are nodal point and node.

Model boundary

The model boundary is the periphery of the 3DEC model. Internal boundaries (i.e., holes within the model) are also model boundaries.

Boundary condition

A boundary condition is the prescription of a constraint or controlled condition along a model boundary (e.g., a fixed displacement or force for mechanical problems).

Initial conditions

This is the state of all variables in the model (e.g., stresses) prior to any loading change or disturbance (e.g., excavation).

Null block

Null blocks are blocks that represent voids (i.e., no material present) within the model. Null blocks can be made “real” later in an analysis – for example, to simulate backfilling. (Once a block is deleted from a model, it cannot be restored.)

Block constitutive model

The block constitutive (or material) model represents the deformation and strength behavior prescribed to the zones of deformable blocks in a 3DEC model. Several constitutive models are available in 3DEC to simulate different types of behavior commonly associated with geologic materials.

Joint constitutive model

The joint constitutive model represents the normal and shear interaction between blocks at their contact (sub-contact) points. The joint model includes normal and shear elastic stiffness components, and limiting shear and tensile strength components. The basic joint model is the Coulomb-slip model.

Structural element

Structural elements are one-dimensional elements that represent the interaction of structures (such as rock bolts or cable bolts) with a rock mass. Material nonlinearity is possible with structural elements. Geometric nonlinearity occurs as a result of the large-strain formulation.


Because 3DEC is an explicit code, the solution to a problem requires a number of computational steps. During computational stepping, the information associated with the phenomenon under investigation is propagated across the blocks in the model. A certain number of steps is required to arrive at an equilibrium (or steady-flow) state for a static solution. Typical problems are solved within 2000 to 4000 steps, although large, complex problems can require tens of thousands of steps to reach a steady state. When using the dynamic analysis option, model step model cycle refers to the actual timestep for the dynamic problem. Other terms for step are timestep and cycle.

Static solution

A static or quasi-static solution is reached in 3DEC when the rate of change of kinetic energy in a model approaches a negligible value. This is accomplished by damping the equations of motion. At the static solution stage, the model will either be at a state of force equilibrium or a state of steady flow of material if a portion (or all) of the model is unstable (i.e., fails) under the applied loading conditions.

Unbalanced force

The unbalanced force indicates when a mechanical equilibrium state (or the onset of joint slip or plastic flow) is reached for a static analysis. A model is in exact equilibrium if the net nodal force vector at each block centroid or gridpoint is zero. The maximum nodal force vector is monitored in 3DEC, and printed to the screen when the model step or model cycle command is invoked. The maximum nodal force vector is also called the “unbalanced” or “out-of-balance” force. The maximum unbalanced force will never exactly reach zero for a numerical analysis; the model is considered to be in equilibrium when the maximum unbalanced force is small compared to the representative forces in the problem. If the unbalanced force approaches a constant nonzero value, this probably indicates that joint slip or block failure and plastic flow are occurring within the model.

Dynamic solution

For a dynamic solution, the full dynamic equations of motion (including inertial terms) are solved; the generation and dissipation of kinetic energy directly affect the solution. Dynamic solutions are required for problems involving high frequency and short duration loads (e.g., seismic or explosive loading). The dynamic calculation is an optional module to 3DEC (see i :re:`dynamic_3dec`).


This is specifically used to describe the corners of rigid blocks. However in 3DEC, the terms vertex and gridpoint are sometimes used interchangeably when referring to the gridpoints on the surface of blocks. Each vertex will be connected to a gridpoint when the blocks are zoned.

Sign Conventions

See the topic Sign Conventions.

System of Units

See the topic System of Units.