弹性模型外文翻译

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1、附录 1 外文翻译原文 3.2 Elastic models 3.2.1 Anisotropy An isotropic material has the same properties in all directions we 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 s

2、ome 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 laye

3、ring 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 t

4、he stiffness relationship between elastic strain increment e and stress increment compactly as eD )36.3( whereD is the stiffness matrix and hence 1D is the compliance matrix. For a completely general anisotropic elastic material utrokftsqnjerqpmidonmlhckjihgbfedcbaD 1)37.3( whereeachlettera,b,. is,i

5、nprinciple,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 examp

6、le, for monoclinic symmetry (z symmetry plane) the compliance matrix has the form: migdlkkjihfcgfebdcbaD00000000000000001)38.3( and has thirteen elastic constants. Orthorhombic symmetry (distinct x, y and z symmetry planes) gives nine constants: ihgfecedbcbaD0000000000000000000000001)39.3( whereas c

7、ubic symmetry (identical x, y and z symmetry planes, together with planes joining opposite sides of a cube) gives only three constants: cccabbbabbbaD0000000000000000000000001)40.3( Figure 3.9: Independent modes of shearing for cross-anisotropic material If we add the further requirement that )(2 bac

8、 and set Ea /1 and Evb / ，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 independent elastic properties, it has to be expected that in general mater

9、ials 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 properties. If we choose to model such materials as isotropic elastic

10、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 and symmetry of deposition is essentially vertical. All horizontal di

11、rections look the same but horizontal sti?ness is expected to be di?erent from vertical stiffness. The form of the compliance matrix is now: feedcccabcbaD0000000000000000000000001)41.3( and we can write： :/)1(2)(2/1,/1,/,/,/1 hhhvhvvvhhhhh EvbafGeEdEvcEvbEa 和 1D hhhhvhvhvvhvvhvvhhhhhvvhhhhhEvGGEEvEv

12、EvEEvEvEvE/12000000/1000000/1000000/1/000/1/000/1)42.3( This is described as transverse isotropy or cross anisotropy with hexagonal symmetry. There are 5 independent elastic properties: vE and hE are Youngs moduli for unconfined compression in the vertical and horizontal directions respectively； hvG

13、 is the shear modulus for shearing in a vertical plane (Fig 3.9a).Poissons ratios hhV and hvV relate to the lateral strains that occur in the horizontal 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