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Critical State Soil Mechanics Phần 5

Tham khảo tài liệu 'critical state soil mechanics phần 5', khoa học tự nhiên, công nghệ môi trường phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 82 Fig. 5.19 Constant-p Test Paths For convenience let Z always be used to denote the point in p v q space representing the current state of the specimen at the particular stage of the test under consideration. As the test progresses the passage of Z on the state boundary surface either from B up towards C or from F down towards C will be exactly specified by the set of three equations pv qs Mps q p r - v - ln p p constant p0. s 0 5.19 bis q 0 5.30bis f 5.33 The first two equations govern the behaviour of all specimens and the third is the restriction on the test path imposed by our choice of test conditions for this specimen. We will find it convenient in a constant-p test to relate the initial state of the specimen to its ultimate critical state by the total change in volume represented by the distance AC or EC in Fig. 5.19 c and define D v0 - vc v0 - r Àlnpữ. 5.34 The conventional way of presenting the test data would be in plots of axial-deviator stress q against cumulative shear strain s and total volumetric strain Av v0 against S and this can be achieved by manipulating equations 5.33 as follows. From the last two equations and 5.34 we have Aq Mp0 v0 - v h-D0 83 and substituting in the first equation ạ M . - q 8 Mạ v - v Do . v A Remembering that 8 Ỗ8 whereas v -ỗv this becomes f1 I. D0 Iv v-v0 D0 J M d8 _ -1 _1 A dv v v- v0 D0 v0 - -1 T_1 Integrating 8 ------- ln A v0 - Do I v ----- r constant v - v0 D0 J and if 8 is measured from the beginning of the test M8 A 1 f Dov ln x r v0 -D0 Iv0 v- v0 D0 J i.e. M v0 - Do A 8 r v0 v - v0 D0 v0 v D0 D0v D0 v v0 which is the desired relationship between v and 8. Fig. 5.20 Constant-p Test Results 5.35 5.36 84 i M v -Dok. exp j-------- s Ả Similarly we can obtain q as a function of s v MMpo -q 5.37 Do Oỹdpto vo - Do ty - ty These relationships for i a specimen looser than critical and ii a specimen denser than critical are plotted in Fig. 5.20 and demonstrate that we have been able to describe a complete .