Experimental study of stress direction dependence of sand under biaxial rotation of principal stress

Abstract

The principal stress rotation is often studied by considering the uniaxial rotation of principal stress. In this paper, the stress path on biaxial rotation of principal stresses is considered. The hollow cylindrical apparatus was used to achieve the principal stress rotation around the second stress principal axis. A novel specimen preparation device was developed, which was used to achieve the principal stress rotation around the third principal stress axis. The influence of principal stress biaxial rotation on the dense sand behavior was investigated under undrained conditions. The results revealed that the deformation properties of dense sand were closely associated with the stress direction dependence of the soil. An increase in the inherent anisotropy changed the slope of the effective stress path and the phase transition pore pressure, influenced the shear dilatancy and shear shrinkage characteristic of sand. Likewise, an increase in the stress-induced anisotropy changed the shape of the effective stress path, the development of pore pressure, the shear dilatancy and shear shrinkage characteristic of sand. More importantly, deformation properties of sand were affected by the coupling of the two factors, which was predominantly controlled by stress-induced anisotropy.

Appendix

According to the conversion relationship between the principal stress force system ($\sigma_{1}$,$\sigma_{2}$,$\sigma_{3}$) and the general stress force system(Hight et al. [20]), the relationship between the principal stress force system and the four load parameters can be obtained as follows:

$$\sigma_{{1}} = \frac{W + 2D - B}{{2A}} + \left [ {\frac{{\left( {W + B} \right)^{2} }}{{4A^{2} }} + \frac{{9M_{{\text{T}}} }}{{4C^{2} }}} \right]^{\frac{1}{2}}$$

(9)

$$\sigma_{2} = \frac{{p_{{\text{o}}} r_{{\text{o}}} + p_{{\text{i}}} r_{{\text{i}}} }}{{r_{{\text{o}}} + r_{{\text{i}}} }}$$

(10)

$$\sigma_{3} = \frac{W + 2D - B}{{2A}} - \left [ {\frac{{\left( {W + B} \right)^{2} }}{{4A^{2} }} + \frac{{9M_{{\text{T}}} }}{{4C^{2} }}} \right]^{\frac{1}{2}} .$$

(11)

The deviatoric stress force system contains the average stress $p$, deviatoric stress $q$, intermediate principal stress coefficient $b$, and principal stress direction $\alpha_{{2}}$, which can be as follows:

$$p = \frac{{\sigma_{1} + \sigma_{2} + \sigma_{3} }}{3}$$

(12)

$$q = \frac{1}{\sqrt 2 }\sqrt {\left( {\sigma_{1} - \sigma_{2} } \right)^{2} + \left( {\sigma_{2} - \sigma_{3} } \right)^{2} + \left( {\sigma_{3} - \sigma_{1} } \right)^{2} }$$

(13)

$$b = \frac{{\sigma_{2} - \sigma_{3} }}{{\sigma_{1} - \sigma_{3} }}$$

(14)

$$\alpha_{2} = \frac{1}{2}\arctan \left( {\frac{{2\tau_{z\theta } }}{{\sigma_{z} - \sigma_{\theta } }}} \right) .$$

(15)

Adopting Eqs. (9) to (15) into the deviatoric stress force system, the relationship between the deviatoric stress force system and the load parameters can be derived as follows:

$$p = \frac{W + 3D}{{3A}}$$

(16)

$$q = \left [ {\frac{{W^{2} + 3B^{2} }}{{A^{2} }} + \frac{{27M_{{\text{T}}}^{{2}} }}{{4C^{2} }}} \right]^{{\frac{{1}}{{2}}}}$$

(17)

$$b = \left [ {\left( {W + B} \right)^{2} + \frac{{9A^{2} M_{{\text{T}}}^{{2}} }}{{C^{2} }}} \right]^{{\frac{{1}}{{2}}}}$$

(18)

$$\alpha_{2} = \frac{1}{2}\arctan \frac{{3AM_{{\text{T}}} }}{{C\left( {W + B} \right)}} + \left( { - 1} \right)^{n} \frac{n\pi }{2} ,$$

(19)

where $A = \pi \left( {r_{{\text{o}}}^{2} - r_{{\text{i}}}^{{2}} } \right)$,$B = \pi r_{{\text{o}}} r_{{\text{i}}} \left( {P_{{\text{i}}} - P_{{\text{o}}} } \right)$,$C = \pi \left( {r_{{\text{o}}}^{3} - r_{{\text{i}}}^{3} } \right)$, and $D = \pi \left( {P_{{\text{o}}} r_{{\text{o}}}^{2} - P_{{\text{i}}} r_{{\text{i}}}^{2} } \right).$

Accordingly, the expressions of load parameters (Eqs. 1 to 4) can be inverted according to the deviatoric stress force system.