---
title: "Short note: Discrete element method"
subject: "Computational Techniques in Civil Engineering"
chapter: 1
key: "semester_8/computational_techniques_in_civil_engineering:short-note-discrete-element"
source: https://www.bctengineer.com/q/semester_8/computational_techniques_in_civil_engineering/short-note-discrete-element
site: BCT Engineering
---

# Short note: Discrete element method

Computational Techniques in Civil Engineering · Chapter 1: Introduction

- Asked in: 2078 Kartik, 3 marks
- Video: [DEM Part 1 #Discrete element modeling](https://www.youtube.com/watch?v=Jj8fd9fNhto) — Dr. Alphonce Owayo
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/computational_techniques_in_civil_engineering/short-note-discrete-element
- Whole chapter: https://www.bctengineer.com/md/semester_8/computational_techniques_in_civil_engineering/chapter-1

## Question

Write a short note on the discrete element method.

## Short answer

DEM, introduced by Cundall, models material as separate particles or blocks interacting through contacts. It computes contact forces from force-displacement laws and integrates Newton's second law explicitly, handling large displacements and discontinuities naturally. It is computationally expensive and contact parameters need calibration, but suits granular soils, jointed rock and rockfall.

## Answer

The **discrete element method (DEM)**, introduced by Cundall (1971), models a material as an assembly of separate rigid or deformable blocks or particles that interact at contacts. It is suited to discontinua where displacement and rotation are large and contacts open and close.

**Working**
1. Define the particles/blocks and their initial positions.
2. Detect contacts between neighbours.
3. Compute contact forces from a force-displacement law, for example normal force $F_n=k_n\,\delta_n$ and a friction-limited shear force.
4. Sum forces on each particle and apply Newton's second law $m\ddot{x}=\sum F$.
5. Integrate in time with an explicit scheme, update positions and repeat (the time step must be small).

**Advantages:** handles fracture, sliding, rotation and large displacements naturally; no continuity assumption.

**Disadvantages:** computationally expensive; contact parameters (stiffness, friction, damping) need calibration.

**Applications:** granular soils and silo flow, jointed rock slopes, masonry and rockfill, landslides and rockfall.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does DEM represent a material?
   A. As an assembly of separate blocks or particles interacting at contacts
   B. As a continuum divided into elements
   C. As boundary elements
   D. As a regular grid of points
   Answer: A. DEM models discontinua as particles or blocks with contacts that can open and close. (Key point: DEM model)

2. How are contact forces computed in DEM?
   A. From shape functions and [B]^T[D][B]
   B. From a boundary integral
   C. From kernel function sums
   D. From a force-displacement law, e.g. Fn = kn * delta_n, with friction-limited shear
   Answer: D. Contacts use a force-displacement law, then Newton's second law gives particle motion. (Key point: DEM contact)

3. What small requirement does the explicit time integration in DEM have?
   A. A symmetric positive definite matrix
   B. A regular grid
   C. A small time step
   D. A fundamental solution
   Answer: C. The explicit scheme needs a small time step for stability. (Key point: DEM time integration)