Based on the dynamic tri-axial experiments and series trials about the Nanning expansive soils，the strength and deformation characteristic of unsaturated expansive soils are analyzed under the conditions of different compactness，different confining pressures and different saturations. And a mathematical relationship of single log-hyperbolic equation 1/Sr-lg c is derived to predict the cohesive force c of unsaturated expansive soils. The experiments prove the applicability and effectiveness of this mathematical relationship under definite range.