Based on non-Darcian flow law described by exponent and threshold gradient within a double-layered soil, the classic theory of one-dimensional consolidation of double-layered soil was modified to consider the change of vertical total stress with depth and time together. Because of the complexity of governing equations, the numerical solutions were obtained in detail by finite difference method. Then, the numerical solutions were compared with the analytical solutions in condition that non-Darcian flow law was degenerated to Dary's law, and the comparison results show that numerical solutions are reliable. Finally, consolidation behavior of double-layered soil with different parameters was analyzed, and the results show that the consolidation rate of double-layered soil decreases with increasing the value of exponent and threshold of non-Darcian flow, and the exponent and threshold gradient of the first soil layer greatly influence the consolidation rate of double-layered soil. The larger the ratio of the equivalent water head of external load to the total thickness of double-layered soil, the larger the rate of the consolidation, and the similitude relationship in classical consolidation theory of double-layered soil is not satisfied. The other consolidation behavior of double-layered soil with non-Darcian flow is the same as that with Darcy's law.
BISHOP’s effective stress or two state stress variables are unsatisfactory for unsaturated soils where one of fluid phases is discontinuous, so new expressions of effective stress should be founded. The approach for derivation was according to the principle of equilibrium of forces (i.e., the stress-sharing principle), and it was firstly validated by demonstrating TERZAGHI’s principle of effective stress. And then, the derivations were subdivided into four parts according to different pore air states: 1) air bubbles were spherical and suspended in pore water; 2) air bubbles were bound on soil skeleton; 3) air bubbles held almost the single section of pore; 4) air phase was continuous. The different formulae of effective stress were presented. Conclusions are drawn as follows: 1) For nearly-saturated soils, the "real" effective stress would be a little smaller than TERZAGHI’s effective stress; 2) For soils in which air phase is discontinuous in the form of bubbles, a new concept of pore air elastic pressure is put forward, and the total stress can be constituted by effective stress, pore water pressure and pore air elastic pressure; 3) For soils in which air phase is continuous, effective stress is equal to the value of the total stress plus suction; 4) Suction can be divided into two parts: one is the effect caused by additional pressure, and the other is the contract action by the "skin".
