In numerical analyses involving multiple geological materials, predicted stress distributions, deformation patterns, and failure mechanisms depend on the ratios of the Young?s moduli for the different materials, a detailed often overlooked. Using two simple examples this paper demonstrates the wide range of behaviours that can accompany different Young?s modulus ratios in problems involving multiple materials.
The complex and wide-ranging behaviours of geological materials, the great variability in material properties, and the intricacies of numerical analysis methods, such as the finite element and finite difference methods, often combine to make the modelling of geotechnical problems a challenge. An important and difficult aspect of such modelling is the specification of constitutive models that best describe the stress-strain behaviour of soil and rock materials.
Full description of the constitutive behaviour of a material requires specification of deformation and strength parameters. Upon initial loading a material responds elastically; deformations are reversible when loading is removed. After a certain level of stress is attained plastic deformations (permanent deformations that are not reversed when loading is removed) begin to occur. In general, after yielding, deformations occur at significantly reduced material stiffness.
From the authors? interactions with various users of the finite element program Phase2, it appears to them that many geotechnical engineers pay more attention to the specification of the strength component of constitutive behaviour than to the deformation aspect. This may stem from the fact that it is generally easier to estimate or measure the strength envelopes of soil and rock masses than it is to measure their in situ deformation properties. Notwithstanding, in numerical models of geotechnical problems engineers must endeavour to specify deformations properties (primarily values of Young?s modulus) characteristic of the materials. Failure to do so often leads to ?surprises?, especially in problems involving more than one material. The ratios of the different Young?s moduli in a multiple material model can significantly alter overall model response, including induced failure mechanisms. This paper will demonstrate the impact of the ratios of material stiffness (Young?s modulus) on behaviour, using two problems involving linear elastic materials. These examples, although quite simple, will underline the need to pay attention to material stiffness if one desires to properly capture the physics of geotechnical problems.