Date of Award

Spring 1996

Document Type


Degree Name

Doctor of Philosophy in Civil Engineering - (Ph.D.)


Civil and Environmental Engineering

First Advisor

Jay N. Meegoda

Second Advisor

William R. Spillers

Third Advisor

William R. Spillers

Fourth Advisor

Mary M. Eshaghian

Fifth Advisor

Anthony D. Rosato


It is the state-of -the-art within Geotechnical Engineering to model soils as systems of particles rather than using the traditional continuum approach. Simulating these systems of particles for geotechnical boundary value problems results in systems which are of necessity large, motivating the application of massively parallel supercomputers. This thesis pursues such an approach.

The following work describes numerical experiments using a Discrete Element Method (DEM) paradigm for soils (Trubal) together with massively parallel computers with Single Instruction Multiple Data (SIMD) architecture. The discrete element method describes the behavior of granular assemblies using the classical mechanics of discrete bodies. The computational requirements of DEM algorithms introduce time complexities, which mandate a compatible topology for massively parallel machines in order to achieve optimal performance. This thesis demonstrates the compatibility of a Single Instruction Multiple Data (SIMD) topology in performing discrete element simulations for 3-d spherical dry granular media.

The serial algorithm, Trubal, was first modified to run with a parallel data structure on a SIMD architecture. The modified version, known as Trubal for Parallel Machines (TPM), is the data parallel version that was tested on the connection machines (CM-2) and (CM-5), consisting of 32,768 processors and 512 nodes, respectively. The first version of TPM was tested on the CM-2 machine before its use was discontinued. Because the architecture is synchronized at each instruction, elemental data movements reduce the performance of the machine's overall resources and increase the latency of the communication between processors. This issue is addressed within the design of the algorithm so that the SIMD vector processing capability can adapt to a dynamic memory data structure.

A second version of TPM was subsequently designed for the CM-5 machine using a more efficient parallel data structure to improve the performance of the simulations. TPM version 2.0 was able to obtain a speedup in performance by handling all possible contacts within each processor, thereby creating a homogeneous data structure. The overall efficiency is governed by the global communication which is a function of the speed of the interconnection network within the architecture.

TPM's improved performance is demonstrated using two different triaxial simulations. One of them involved a physical triaxial experiment with steel spheres performed by Rowe (1962) and later simulated by Cundall (1979). The remodeling of this numerical simulation validated TPM version 2.0 overall performance where a nine-fold speedup was obtained. TPM's reproduction of these results and its improved speedup encourage further investigations using discrete models on parallel platforms.

This thesis substantiates the use of parallel computing as a technique for geotechnical applications. It is further anticipated that developing and adapting heterogeneous platforms to DEM models will make the application of parallel computing more attractive in geotechnical engineering.