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 groundwith any orientation would behave identically. However, we know that soilshave been deposited in som
2、e way for example, sedimentary soils will knowabout the vertical direction of gravitational deposition. There may in additionbe seasonal variations in the rate of deposition so that the soil contains moreor less marked layers of slightly different grain size and/or plasticity. The scaleof layering m
3、ay be suffciently small that we do not wish to try to distinguishseparate materials, but the layering together with the directional depositionmay nevertheless be suffcient to modify the properies of the soil in differentdirections in other words to cause it to be anisotropic. We can write the stiffn
4、ess 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. Fora completely general anisotropic elastic material utrokftsqnjerqpmidonmlhckjihgbfedcbaD 1)37.3( whereeachlettera,b,. is,inprinciple
5、,anindependentelasticpropertyandthenecessary symmetry of the sti?ness matrix for the elastic material has reducedthe maximum number of independent properties to 21. As soon as there arematerial symmetries then the number of independent elastic properties falls(Crampin, 1981). For example, for monocl
6、inic symmetry (z symmetry plane) the compliancematrix has the form: migdlkkjihfcgfebdcbaD00000000000000001)38.3( and has thirteen elastic constants. Orthorhombic symmetry (distinct x, y andz symmetry planes) gives nine constants: ihgfecedbcbaD0000000000000000000000001)39.3( whereas cubic symmetry (i
7、dentical x, y and z symmetry planes, together withplanes 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 and set Ea /1 an
8、d 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 elasticproperties, it has to be expected that in general materials which have be
9、enpushed around by tectonic forces, by ice, or by man will not possess any ofthese symmetries and, insofar as they have a domain of elastic response, weshould expect to require the full 21 independent elastic properties. If we chooseto model such materials as isotropic elastic or anisotropic elastic
10、 with certainrestricting 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 andsymmetry of deposition is essentially vertical. All horizontal directions look thesame bu
11、t 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 hhhhvhvhvvhvvhvvhhhhhvvhhhhhEvGGEEvEvEvEEvEvEvE/12000000/100000
12、0/1000000/1/000/1/000/1)42.3( This is described as transverse isotropy or cross anisotropy with hexagonal symmetry. There are 5 independent elastic properties: vE and hE are Youngsmoduli for unconfined compression in the vertical and horizontal directions respectively； hvG is the shear modulus for shearing in a vertical plane (Fig 3.9a).Poissonsratios hhV and hvV relatetothelateralstrainsthatoccurinthehorizontal direction orthogonal to a horizontal direction of compression and a verticaldirection of compression respectively (Fig 3.9c, b).
