【正文】 nonlinearity in soils es exclusively from soil plasticity—as will be discussed in the subsequent sections—we have seen that with care it may be possible to describe some elastic nonlinearity in a way which is thermodynamically acceptable. Equally, most elasticplastic models will contain some element of elasticity—which may often be swamped by plastic deformations. It must be expected that the fabric variations which acpany any plastic shearing will themselves lead to changes in the elastic properties of the soil. The formulation of such variations of stiffness should in principle be based on the differentiation of some serendipitously discovered elastic strain energy density function in order that the elasticity should not violate the laws of thermodynamics. Evidently the development of strain energy functions which permit evolution of anisotropy of elastic stiffness is tricky. Many constitutive models adopt a pragmatic, hypoelastic approach and simply define the evolution of the moduli with stress state or with strain state without concern for the thermodynamic consequences. This may not provoke particular problems provided the stress paths or strain paths to which soil elements are subjected are not very repeatedly cyclic. HeterogeneityAnisotropy and nonlinearity are both possible departures from the simple assumptions of isotropic linear elasticity. A rather different departure is associated with heterogeneity. We have already noted that small scale heterogeneity—seasonal layering—may lead to anisotropy of stiffness (and other) properties at the scale of a typical sample. Many natural and manmade soils contain large ranges of particle sizes (167。附錄1 外文翻譯原文 Elastic models AnisotropyAn isotropic material has the same properties in all directions—we cannot distinguish any one direction from any other. Samples taken out of the ground with any orientation would behave identically. However, we know that soils have been deposited in some way—for example, sedimentary soils will know about the vertical direction of gravitational deposition. There may in addition be seasonal variations in the rate of deposition so that the soil contains more or less marked layers of slightly different grain size and/or plasticity. The scale of layering may be suffciently small that we do not wish to try to distinguish separate materials, but the layering together with the directional deposition may nevertheless be suffcient to modify the properies of the soil in different directions—in other words to cause it to be anisotropic. We can write the stiffness relationship between elastic strain increment and stress increment pactly as whereis the stiffness matrix and henceis the pliance matrix. For a pletely general anisotropic elastic material whereeachlettera,b,... is,inprinciple,anindependentelasticpropertyandthe necessary symmetry of the sti?ness matrix for the elastic material has reduced the maximum number of independent properties to 21. As soon as there are material symmetries then the number of independent elastic properties falls (Crampin, 1981).For example, for monoclinic symmetry (z symmetry plane) the pliance matrix has the form: and has thirteen elastic constants. Orthorhombic symmetry (distinct x, y and z symmetry planes) gives nine constants: whereas cubic symmetry (identical x, y and z symmetry planes, together with planes joining opposite sides of a cube) gives only three constants: Figure : Independent modes of shearing for crossanisotropic materialIf we add the further requirement that and set and ，then we recover the isotropic elastic pliance matrix of ().Though it is obviously convenient if geotechnical materials have certain fabric symmetries which confer a reduction in the number of independent elastic properties, it has to be expected that in general materials which have been pushed around by tectonic forces, by ice, or by man will not possess any o