Page 194 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

8.2 Some Numerical Simulation Issues Associated with the Particle Simulation Method 185

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(A) A four-node element in the mesh (B) A particle with its neighbors

Fig. 8.4 Comparison of a four-node element with a particle

the nodal mechanical property is called the consistent mechanical property of the
element. On the other hand, a particle used in the distinct element method is assumed
to be rigid and therefore, the mechanical property at a contact between the particle
and its neighboring particle is called the lumped mechanical property. Due to this
difference, the consistent mechanical properties (i.e. stiffness matrix) of an element
are directly calculated from the macroscopic mechanical properties and constitutive
law of the element material. This means that once the macroscopic mechanical prop-
erties and constitutive law of the element material are available from a laboratory
test or a field measurement, the finite element analysis of a deformation problem
can be straightforwardly carried out using these macroscopic mechanical proper-
ties and constitutive laws of the material. On the contrary, because the particle-scale
mechanical properties of materials, such as particle stiffness and bond strength, are
used in the distinct element method but are not known apriori, it is important
to deduce these particle-scale mechanical properties of materials from the related
macroscopic ones measured from both laboratory and field experiments. This indi-
cates that an inverse problem needs to be solved through the numerical simulation
of a particle system. Thus, the numerical simulation question introduced by the dif-
ference between an element used in the continuum-mechanics-based finite element
method and a particle used in the discrete-block-mechanics-based distinct element
method is how to determine particle-scale mechanical properties from macroscopic
mechanical properties available from both laboratory and field experiments. Clearly,
the problem associated with this numerical simulation issue cannot be effectively
solved unless the required particle-scale mechanical properties of particles can be
directly determined from laboratory tests in the future.
As an expedient measure, primitive trial-and-error approaches can be used to
solve any inverse problems. For the above-mentioned inverse problem, input param-
eters are the macroscopic mechanical properties of materials, while the particle-
scale mechanical properties of materials, such as the particle stiffness and bond
strength, are unknown variables and therefore, need to be determined. Due to the
difficulty in directly solving this inverse problem, it is solved indirectly using a trial-
and-error approach, in which a set of particle-scale mechanical properties of mate-
rials are assumed so that the resulting macroscopic mechanical properties can be