Theoretical solution for drained cylindrical cavity expansion in clays with fabric anisotropy and structure

Abstract

This paper presents a novel, exact, semi-analytical solution for the quasi-static drained expansion of a cylindrical cavity in soft soils with fabric anisotropy and structure. The assumed constitutive model is the S-CLAY1S model, which is a Cam clay-type model that considers fabric anisotropy that evolves with plastic strains, structure and gradual degradation of bonding (destructuration) due to plastic straining. The solution involves the numerical integration of a system of eight first-order ordinary differential equations, three of them corresponding to the effective stresses in cylindrical coordinates, other three corresponding to the components of the fabric tensor and one corresponding to the amount of bonding and another corresponding to the specific volume. The solution is validated against finite element analyses. When destructuration is considered, the solution provides slightly lower values of the effective radial and mean stresses near the cavity wall. Besides, the specific volume is further reduced due to loss of bonding. Parametric analyses and discussion of the influence of soil overconsolidation, expansion of the cavity and initial amount of bonding are presented.

Revisiting undrained cavity expansion problem in critical state soils: A simple graph‐based approach

“…and for the ultimate total pore pressure 𝑢 𝑢 𝑢 𝑢 = 𝜎 𝑢 − 𝑝 ′ 𝑢 − 𝑠 ru (27) where 𝑝 ′ 𝑢 = e −Λ 𝑝 ′ 𝑒 , which is obvious from Equation ( 12); and 𝑠 𝑟𝑢 can be determined by substituting 𝜃 = , respectively, into Equation (1a) for the spherical and cylindrical cases, in conjunction with the critical state conditions, giving…”

“…While the total and excess pore pressures at the cavity wall, 𝑢 𝑎 and Δ𝑢 𝑎 , and the ultimate pore pressure value 𝑢 𝑢 may be evaluated by means of the same Equations ( 25), (27), and (28) as used for the OCC model, with the only exception that the ultimate mean effective stress now should be replaced by 𝑝 ′ 𝑢 = 2 −Λ 𝑝 ′ 𝑒 . Equations ( 24) and (33) indicate that the internal cavity pressure 𝜎 𝑎 for both OCC and MCC models can be obtained through relatively simple numerical integration, for any given value of 𝑝 ′ (or 𝑝 ′ 𝑎 ) in the inclusive interval of [𝑝 ′ ep , 𝑝 ′ 𝑢 ].…”

“…[13][14][15][16][17][18][19] The approaches commonly adopted for the solutions of cavity expansion problems, especially in the critical state soils, appear to be the similarity method (and its variants) proposed by Collins and his co-workers 4,20,21 and the rigorous Lagrangian-based solution procedure developed by Chen 22 and Chen & Abousleiman. 7,8 These two methodologies have been extensively employed and successfully expanded by many researchers to derive new analytical cavity solutions over recent years, to investigate the impacts of the particle crushing/damage, [23][24][25] material anisotropy, 15,[26][27][28][29] and partial saturation [30][31][32] on the cavity expansion behavior.…”