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1、附录1 外文翻译原文3.2 Elastic models3.2.1 AnisotropyAn isotropic material has the same properties in all directionswe cannot dis-tinguish 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 w
2、ayfor 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 m
3、ay 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 directionsin other words to cause it to be anisotropic. We can write the stif
4、fness relationship between elastic strain increment and stress increment compactly as whereis the stiffness matrix and henceis the compliance matrix. For a completely general anisotropic elastic material whereeachlettera,b,. is,inprinciple,anindependentelasticpropertyandthe necessary symmetry of the
5、 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 compliance matrix has
6、 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 3.9: Independent mo
7、des of shearing for cross-anisotropic materialIf we add the further requirement that and set and ，then we recover the isotropic elastic compliance matrix of (3.1).Though it is obviously convenient if geotechnical materials have certain fabric symmetries which confer a reduction in the number of inde
8、pendent 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 of these symmetries and, insofar as they have a domain of elastic response, we should expect to require the full 21 independent elastic
9、 properties. If we choose to model such materials as isotropic elastic or anisotropic elastic with certain restricting symmetries then we have to recognise that these are modelling decisions of which the soil or rock may be unaware.However, many soils are deposited over areas of large lateral extent
10、 and symmetry of deposition is essentially vertical. All horizontal directions look the same but horizontal sti?ness is expected to be di?erent from vertical stiffness. The form of the compliance matrix is now: and we can write： This is described as transverse isotropy or cross anisotropy with hexag
11、onal symmetry. There are 5 independent elastic properties: andare Youngs moduli for unconfined compression in the vertical and horizontal directions respectively; is the shear modulus for shearing in a vertical plane (Fig 3.9a).Poissons ratios and relate to the lateral strains that occur in the hori
12、zontal direction orthogonal to a horizontal direction of compression and a vertical direction of compression respectively (Fig 3.9c, b). Testing of cross anisotropic soils in a triaxial apparatus with their axes of anisotropy aligned with the axes of the apparatus does not give us any possibility to
13、 discover ，since this would require controlled application of shear stresses to vertical and horizontal surfaces of the sampleand attendant rotation of principal axes. In fact we are able only to determine 3 of the 5 elastic properties. If we write (3.42) for radial and axial stresses and strains fo
14、r a sample with its vertical axis of symmetry of anisotropy aligned with the axis of the triaxial apparatus, we find that： The compliance matrix is not symmetric because, in the context of the triaxial test, the strain increment and stress quantities are not properly work conjugate. We deduce that w
15、hile we can separately determineand the only other elastic property that we can discover is the composite stiffness.We are not able to separateand (Lings et al., 2000).On the other hand, Graham and Houlsby (1983) have proposed a special form of (3.41) or (3.42) which uses only 3 elastic properties b
16、ut forces certain interdependencies among the 5 elastic properties for this cross anisotropic material. This is written in terms of a Youngs modulus,the Youngs modulus for loading in the vertical direction, a Poissons ratio ,together with a third parameter . The ratio of stiffness in horizontal and vertica
