The stress-dilatancy equations which relate principal strain increment ratio with principal stress ratio in the previous studies are first reviewed and shown is the necessity to investigate the relationship between the stress-dilatancy equation for axisymmetric deformation and that for general stress condition and to clarify the effect of inherent anisotropy on the stress-dilatancy equations. Then, in summary form, three fundamental postulates are introduced as the bases on which a theory to investigate above mentioned two problems is to be established. The stress-dilatancy performance of sands predicted by the proposed theory were compared with several experimental data obtained by other investigators. These data include those of triaxial compression and extension tests, general stress condition tests (σ₁>σ₂>σ₃) and plane strain tests. This comparison disclosed the relevence of the theory in spite of its simplicity.

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Statistical techniques are used to analyze and evaluate experimental data from more than 700 consolidation tests on a large variety of undisturbed soils, and regression equations are developed to estimate the compression index and the compression ratio from classification or index data. These regression equations are then examined within the framework of a variety of similar, but more restricted, empirical relationships that have been reported by other investigators. It is found that both the compression index and the compression ratio can be reasonably well approximated by use of a simple linear regression model involving only the initial void ratio.

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Two main assumptions in Marston-Spangler theory on vertical earth pressure on a buried pipe, which are two vertical planes (a pair of vertical slide lines) and a plane of equal settlement are discussed by the use of X-ray film analysis.Sand surrounding a pipe fixed in a small sand bin is forced to settle by lowering a trap door, and just after lowering the trap door by a controlled amount, vertical earth pressure on the pipe is measured (see Fig. 4) and an X-ray film is taken (see Appendix).According to X-ray pictures which show slide lines, settlement of sand particles (small lead balls instead of sand particles) and location of the pipe, two vertical planes could not be signified and could not reach vertically the top of the embankment, but the plane of equal settlement could be suggested. Propagation of slide lines can be considered to depend upon H/D ratio (H : height of the sand layer above the pipe, D : pipe diameter). In the experiments, the ratio was 6.3∼15.4. Only when the ratio is very small, a pair of slide lines will be supposed to reach vertically the top of the embankment.On the other hand, characteristic correlation between vertical pressure and settlement by lowering the trap door was obtained. Further analyses on the relation between the slide lines around a pipe and measured vertical earth pressure are necessitated to calculate vertical earth pressure on a pipe including the conditions which govern Marston-Spangler theory.

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This paper discusses two elastic-plastic soil models--an elastic-perfectly plastic model (extended von Mises model or Drucker-Prager model) and an elastic-plastic strain hardening model (Cambridge model). Both theories incorporate a yield surface or loading surface, which is dependent on the mean normal stress, and on the normality of the deformation rate vector to these surfaces. Analytical forms of stress-strain relationships for these soil models are stated in incremental form, suitable for use in numerical analysis.

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