At present, there is no clear understanding of the influence of differences in soil mineral composition, particle size grading, and hydraulic paths on the shear strength of unsaturated soil, and the related strength models are not applicable. The shear strength characteristics of different saturation specimens under different hydraulic paths were studied on two granite weathered soils. The experimental results show that the shear strength index of the prepared specimen is “arched” with the increase of saturation, and the dehydration specimen decreases linearly with the saturation. As considering the cementation of free oxides in soils and the interaction among soil particles at different saturations, it is assumed that there are three different contact modes among soil particles: direct contact, meniscus contact, and cement contact. The difference in contact modes will reflect the different laws of shear strength. A shear strength model capable of distinguishing between the capillary effect and the adsorptive effect was established. The model predicted and verified the shear strength data of granite weathered soil under different hydraulic paths well, and then theoretically explained the evolution law of the shear strength of granite weathering soil under the change of saturation.

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With homogenization theory developing, solving some properties of a rough surface becomes more and more simple. What we studied was a two-dimensional perfectly conducting periodic rough surface with a thin cover layer. This allows for the development of an isovalent boundary condition for the effective fields at such a surface. It is shown that the coefficients in this isovalent boundary condition can be expressed as electric and magnetic polarizability densities. And at last we got the simplification of boundary problem for a rough surface.

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