Closed-Form Solution for Cavity Expansion in Strain-Softening and Undrained Soil Mass Based on the Unified Strength Failure Criterion

Large‐strain analysis for cylindrical cavity contraction in strain‐softening geomaterials

“…The values of the parameters of geomaterial are taken mainly from Zhao et al 15 . and Zou and Xia, 28 $$G = 10{p}_0$$, the Poisson's ratio $$\nu = 0.3$$, $$c = 0.175{p}_0$$, the internal friction angle $$\varphi = {20}^0$$,$${\sigma }_c = 0.5{p}_0$$.…”

“…Here, the elastic strains are assumed to be constant and equal to the elastic strains at EP boundary 28 . Combining Equations (32) and (31), the tangential plastic strain in the softening region can be obtained as, $$\begin{equation}\varepsilon _\theta ^p = {\varepsilon }_\theta - \varepsilon _\theta ^e = - \ln \left\{ {\frac{r}{{{r}_b\centerdot {{\left[ {{{({r}_{b0}/{r}_b)}}^{\beta + 1} + \frac{{\beta + 1}}{{\chi (R - 1)}}\int_{1}^{\ell }{{\exp (\xi \ell ){\ell }^\gamma d\ell }}} \right]}}^{1/(\beta + 1)}}}} \right\} + \frac{{1 + v}}{E}\left( {{p}_y - {p}_0} \right)\end{equation}$$…”

“…For $$r = {r}_f,\,{\sigma }_0 = {\sigma }_{cr}$$, and $$\lambda = \frac{{{\sigma }_c - {\sigma }_{cr}}}{{{A}_0( {\varpi - 1} )}}$$ at the boundary of the softening and plastic flow regions, 28–30 and combined with the Equation (36), $$\begin{equation}{r}_f = {r}_b\centerdot \exp \left[ {{A}_0\left( {\varpi - 1} \right)\beta + \frac{{1 + v}}{E}\left( {{p}_y - {p}_0} \right)} \right]\centerdot {\left[ {{{({r}_{b0}/{r}_b)}}^{\beta + 1} + \frac{{\beta + 1}}{{\chi (R - 1)}}\int_{1}^{\ell }{{\exp (\xi \ell ){\ell }^\gamma d\ell }}} \right]}^{1/(\beta + 1)}\end{equation}$$…”

“…Here, the elastic strains are assumed to be constant and equal to the elastic strains at EP boundary. 28 Combining Equations ( 32) and (31), the tangential plastic strain in the softening region can be obtained as,…”

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

“…Extensive true triaxial test results of unsaturated soils [27,28] and predictions of the Drucker-Prager criterion [29] and the unified strength theory [30,31] have confirmed that a conservative result is obtained by utilizing the Mohr-Coulomb criterion without reflecting the influence of intermediate principal stress. Meanwhile, the intermediate principal stress has a marked impact on the strength of saturated soils [32][33][34]. e unified strength theory proposed by Yu [30] is a set of failure criteria including or approximating various conventional ones, and the intermediate principal stress effect can be reasonably reflected.…”