The equations for a vertical cut in cohesive material are given in several publications including Heyman (1973): The stability of a vertical cut (see attachment Equations1.jpeg) and Verruijt (2001) Soil mechanics (see attachment Equations2.jpeg). I would like to try to replicate this analytical example as closely as possible using FEM. I am using Plaxis2D and the results for vertical and horizontal stress are given in Result1.jpeg and Result2.jpeg respectively. The material defined is Mohr-Coulomb with Undrained C material type. The parameters are as follows:
gamma_sat = 18 kN/m3 E_undr = 5000 kN/m2 nu_undr = 0.495 su (undrained shear strength) = 1000 kN/m2
The geometry is 20 meters high (total) and 40 meters long (total).
The vertical stresses (Result1.jpeg) look promising, since at the bottom of the left part (zone 3 according to Equations2.jpeg) we have a value nearing 180 kN/m3 and at the right part (zone 2 according to Equations2.jpeg) we have a value nearing 360 kN/m3. The horizontal stresses (Result1.jpeg) however look completely wrong. I was expecting the right top part (zone 1 according to Equations2.jpeg) to show a value of 0 kN/m3 throughout and the bottom part (zones 2 and 3 according to Equations 2.jpeg) to show a minimum of 180 kN/m3 throughout. The bottom right part (zone 2 according to Equations2.jpeg) shows decent values which correspond to the minimum result of 360 kN/m3 but the bottom left part (zone 3 according to Equations2.jpeg) does not.
Why are the horizontal stresses deviating from the analytical result? How can I replicate the distributions predicted by the publications on an FEM program?
Equations 1 and 2 show hydrostatic stress condition, i.e. hor to vert stress ratio of 1.
Horizontal stress near vertical excavation boundary is zero (second Newton`s law).
How did you model initial stress state in Plaxis (gravity loading or k0 procedure) for undrained material?
What is the ratio of hor to vert stress in your case?
Equations 1 and 2 are a form of limit analysis solution (upper or lower bound) as far as I recall and you are using complete stress-strain method to try to replicate vertical cut example..?
Does the software accounts for the value of shear stress during calculation of horizontal stress?
Maybe this link could help to clarify answer to your question..
https://www.google.rs/amp/s/www.researchgate.net/post/How_does_Plaxis_calculate_stresses/amp
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