The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.
The unified solutions are presented for stresses and displacements around a circular tunnel subjected to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic and governed by the Unified Strength Theory. The displacements are obtained accounting for three different definitions for elastic strains and different Young's modulus in the plastic zone. The unified solutions obtained in this paper are especially versatile in reflecting the intermediate principal stress effect to different extents for different materials. The conventional solutions, based on the Mohr-Coulomb failure criterion and the Generalized Twin Shear Stress yield criterion, are special cases of the present unified solutions. The new unified solutions can compare with those computed by the latest generalized Hoek-Brown failure criterion. The results obtained demonstrate the importance of the intermediate principal stress influence for the stresses and displacements analysis. The effects of different definitions for elastic strains and different Young's modulus in the plastic zone on the displacements are significant. Unified Strength Theory, intermediate principal stress, different definitions for elastic strains, different Young's modulus Citation:Zhang C G, Wang J F, Zhao J H. Unified solutions for stresses and displacements around circular tunnels using the Unified Strength Theory. Sci
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