# Analysis Method

In the Project Settings dialog you can choose one of the following analysis methods for rockfall simulation:

• Lumped Mass
• Rigid Body

The Lumped Mass and Rigid Body analysis options use different analysis engines within the RocFall program.

## Lumped Mass Approach

In the Lumped Mass approach:

• Each rock is modeled as a very small spherical particle.
• The rocks are not considered to have any size, only mass (used to calculate the kinetic energy for graphs and results).

The Lumped Mass approach is detailed in the RocFall Lumped Mass Theory document. The Lumped Mass engine uses a particle analysis with three sections: the particle algorithm, the projectile algorithm, and the sliding algorithm.

The particle algorithm makes sure that the simulation parameters are valid, sets up the initial conditions, and starts the projectile algorithm. The projectile algorithm is used to calculate the movement of the rock while it is in the air. The sliding algorithm is used to calculate the movement of the rock while it is in contact with the slope.

### FRICTION ANGLE

If the Lump Mass engine is used, you have three options for the Friction Angle.

• Use the friction angle from the RocFall Slope Material Library.
• Calculate the friction angle from Rt (coefficient of tangential restitution).
• Set friction angle to zero (rolling).

If Calculate friction angle from Rt is selected, the equation used is:

Phi = arctan [ ( 1 – Rt ) / Rt ]

### CONSIDER ROTATIONAL VELOCITY

This option is only applicable for the Lump Mass analysis method and allows you to simulate the effect of rotational velocity on point mass rocks. If the check box is turned off, rotational velocity will not be considered.

For Rigid Body analysis rotational velocity is always considered.

## Rigid Body Approach

In the Rigid Body Approach:

• The shape of the rocks is accounted for by selecting from a wide variety of pre-defined smooth or polygonal shapes in the RocFall Rock Type Library dialog. The shapes are two-dimensional and extruded in the third dimension to account for the three-dimensional size and mass.
• The mass of the rock determines the actual size of the rock shape, assuming that the out-of-plane dimension of each rock is approximately equal to the average in-plane dimensions of the rock shape. See the Rock Shape and Size document for details.

The rigid body approach used in RocFall is detailed in the RocFall Rigid Body Theory document.

The Rigid Body approach considers the impulse reaction of the rock during the instantaneous contact period with the slope to determine the critical events of the rock (slip, sticking, reversal behaviour during compression and restitution phase). The normal coefficient of restitution is used during the two phases of the contact period to calculate the terminal impulse. With the terminal impulse, the outgoing velocities at the contact point can be calculated.

### USE TANGENTIAL CRSP DAMPING

If this check box is turned ON, the coefficient of tangential restitution (Rt) is enabled in the RocFall Slope Material Library dialog for all materials. If the check box is turned OFF, Rt is disabled and NO tangential damping is applied to rigid body rock shapes.

## Comparison of Lumped Mass vs. Rigid Body Methods

The Lumped Mass and Rigid Body analysis options use completely separate analysis engines within RocFall. A comparison of the main features of each method is summarized in the table below. For a comparison that shows that the two methods can give equivalent results if the rock shape is modeled as a very small sphere, see the Collision Analysis Verification document.

 Lumped Mass Rigid Body Rock Modeled as a particle Actual rock shape is modeled Normal coefficient of restitution Velocity based Energy based Tangential coefficient of restitution (Rt) Used. Not used unless "Use Tangential CRSP Damping" option is selected Dynamic friction Enter as an angle. Applied when rock is sliding. Enter as a coefficent. Applied during impact and when rock is sliding. Rolling friction Not used. Used. Applied when rock is rolling Special Options Consider rotational velocity • Use Tangential CRSP Damping •Advanced friction parameters (scarring) •Viscoplastic ground drag •Forest Damping