Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity

Abstract

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.

Safety Factor of Unsaturated Soil Slopes considering the Intermediate Principal Stress Effect and Different Profiles of Matric Suction

“…where c′ � effective cohesion, c t ′ � unified effective cohesion, c tt � unified total cohesion, φ′ � effective internal friction angle, φ t ′ � unified effective internal friction angle, φ b � friction angle relative to matric suction, φ b t � unified friction angle with matric suction, u a � pore-air pressure, u w � pore-water pressure, u a −u w � matric suction, σ � total normal stress, σ−u a � net normal stress, b � unified strength theory parameter, and 0 ≤ b ≤ 1. e parameter b represents the effect of intermediate principal stress on the strength of unsaturated soils, and it can be calculated by the values of basic mechanical properties (e.g., uniaxial compressive strength, uniaxial tensile strength, and pure shear strength) or comparing the limit loci of equation (1) with true triaxial tests of unsaturated soils on a deviatoric plane. In addition, the friction angle φ b is simply taken as a constant not larger than the effective internal friction angle φ′, and its variation with respect to matric suction can be well addressed by a hyperbolic function similar to that of Zhang et al [29] and Yan et al [30].…”

“…Integrated effects of matric suction and intermediate principal stress on the strength of unsaturated soils are reasonably considered by the unified shear strength equation. Meanwhile, the unified shear strength equation has been successfully applied to typical geotechnical engineering problems [29][30][31][32], such as the Earth pressure of retaining walls, the bearing capacity of strip foundations, and the slope stability with the upper bound theorem of limit analysis. e objective of this study is to present theoretical formulations of safety factor for an infinite unsaturated soil slope under four different profiles of matric suction based on the limit equilibrium method.…”

Ultimate Bearing Capacity of Strip Foundations in Unsaturated Soils considering the Intermediate Principal Stress Effect

“…On the basis of the unified strength theory [30] and the theory of two independent stress state variables [35], Zhang et al [36,37] presented a unified equation for the plane strain shear strength of unsaturated soils to reasonably capture the effect of intermediate principal stress. In addition, the relationship between the unsaturated soil strength and matric suction is nonlinear over a broad range of matric suctions rather than linear ones, and the friction angle related to matric suction (φ b ) varies nonlinearly with increasing matric suction [38][39][40][41][42][43]. A hyperbolic function of the angle φ b was introduced to exhibit strength nonlinearity of unsaturated soils.…”

“…A hyperbolic function of the angle φ b was introduced to exhibit strength nonlinearity of unsaturated soils. Moreover, there are two profiles of matric suction commonly used in engineering practice [9,10,16,40]: one is the matric suction distributing uniformly with depth, and the other is the matric suction decreasing linearly with depth. e primary objective of this study is to present a formulation of the ultimate bearing capacity for strip foundations in unsaturated soils under uniformly and linearly distributed suctions.…”

Boundary Effect and Dynamic Response Study for the Penetration of Rigid Projectiles into Thick, Finite-Radius, Metallic Targets

“…Since the unified strength theory, which considers all the stress components acting on a twin-shear element and their different effects on material failure, can comprehensively reflect the basic strength characteristics of different target materials and the influence of different strength criteria [15,16], it is widely used as a more reasonable strength criterion for solving penetration problems with complex stress states [8][9][10]. Note that the establishment and selection of material strength criteria are crucial when studying the antipenetration performance of targets.…”