Undrained strength for a 3D spatially variable clay column subjected to compression or shear

• Mobilized shear strengths of 3D spatially variable clay columns are simulated.
• The 3D results can be effectively predicted by 2D equations and 2D models.
• The 3D results exhibit stronger spatial averaging effect and weaker critical SOF phenomenon than 2D.

The mobilized shear strength (τfm) of a soil is the most important design parameter governing ultimate limit states. The authors have proposed some models and equations to characterize several useful aspects of the mean, variance, and probability density function of τfm for a two dimensional (2D) spatially variable clay specimen. This paper demonstrates that the models and equations developed for 2D can be extended to three-dimensional (3D) cases. An important class of 3D cases are examined in detail: two horizontal scales of fluctuation (SOF) are equal, and both are larger than the vertical SOF. A key observation for 3D cases is that the averaging effect over the potential slip planes is significantly stronger than that for 2D cases. The upshot is that the phenomenon of the critical SOF (e.g., SOF producing the lowest mean value of τfm) is less clear for 3D cases.