A soil mechanics problem this time. We want to dig a 4m deep trench in very soft clay. Can we do this without support?
Undrained shear strength (Su): 10kPa
Shear modulus (G): 500kPa
Wet weight (Gamma): 20kN/m3
For Tresca material we can translate undrained shear strength into yield strength by simply doubling it. For von Mises material doing so will introduce some error, as I will explain later.
I created the model by extruding a simple sketch. The bottom and left boundaries are fully fixed and the right boundary represents a symmetry plane, so is allowed to slide. The facing boundary and its opposite are fixed out of plane to create the plane strain conditions of a long trench.
The weight load is incremented until failure occurs. The load factor is therefore the proportion of the weight load applied.
As can be seen from the load-deflection curve, the trench will collapse at a load factor of 0.58 and is therefore not safe!
The plastic deformation plot shows a soil wedge sliding into the trench at collapse.
A hand calculation assuming a straight slip surface at 45 degrees shows that collapse occurs at a load factor of 0.5.
So why this 16% error in the analysis? Well part is always related to lack of mesh refinement. However previous analyses showed that even for coarse meshes rather accurate collapse loads can be predicted.
The answer is in the translation of undrained shear strength to yield stress. The von Mises stress (S_vm) for pure shear (Tau) equals S_vm = Sqrt(3) * Tau. So a von Mises material with yield stress Sy has a shear strength of of Sqrt(3) * Sy and not 2 * Sy as is the case with Tresca (= Mohr Coulomb with Phi=0) material. So by simply doubling the undrained shear strength to get a yield stress, we introduce as much as a 2/Sqrt(3) ~ 1.155 (or 15.5%) error in the collapse load.
This simple case study shows that the macro accurately predicts collapse, but that care should be taken with translation of measured soil parameters into model parameters
Last edited by HarryvL
on Sun Mar 24, 2019 5:46 am, edited 3 times in total.