Shear failure in Dense Sand

Question

Hello, I've modeled a square footing with a huge point load at its center (100,000 kN) on Dense Sand in order to assess the bearing capacity of soil by locating the shear failure point from the Load-displacement curve. 
 
 Mstage vs IuI for the loading phase for a pre-cal node at the center of the footing: 
 
 After increasing the max unloading steps, it is predicted that the ultimate load should be taken where the solver finishes the calculation (point 3). However it seems that in points 1 & 2, the curve has gotten flat too, with the number of steps used at each point > the number of unloading steps in point 3, therefore why didn't the calculation stop at either of the first two points? 
 At which point should the ultimate pressure be taken? 
 Can someone explain how the unloading mechanism works in PLAXIS, and specifically at points 1 and 2? 
 Thanks for sharing your thoughts!

Dennis Waterman · Accepted Answer

Dear Mohamad, 
 The calculation didn't stop at 1) and 2) because there was no failure detected yet. Failure is considered if the maximum amount of unloading steps is exceeded while the Current Stiffness Parameter (CSP) < 0.01. Apparently that condition was not met there. With respect to your second question: at none of the 3 points. The load-displacement curve gives no indication that failure is really occurring - the behaviour seems to be almost linear elastic. PLAXIS will try to increase the load and solve the stress increments due the load increase. After doing so, the new stresses must be in equilibrium with the load applied so far. In case this equilibrium cannot be reached, PLAXIS may decide to unload the soil (hence decrease the load a bit) to find equilibrium. If this is necessary for Nmax consecutive steps the calculation stops. If CSP < 0.01 PLAXIS will give the message "Soil body seems to collapse", otherwise the message will be "Load advancement procedure fails". CSP is a measure for how much of the generated strain increment in a load step is elastic. If CSP = 1 the strain increment is fully elastic, if CSP = 0 the strain increment is fully plastic. If strains resulting from a load step are (almost) fully plastic it's likely to assume failure is occurring. 
 With kind regards, 
 Dennis Waterman

Dennis Waterman · Answer

Dear Mohamad, 
 I didn't say anything like that. There is a big difference between soil failing at one single stress point according to the M-C criterion of a whole geotechnical structure failing because there are too many single stress points where the soil fails. The determination of whether the whole geotechnical structure fails is based on Nmax and CSP. 
 If the whole geotechnical structure fails one normally sees excessive displacement increase without load increase, which your graph doesn't demonstrate. Therefore based on your graph it cannot be determined what the ultimate load is. 
 With kind regards, 
 Dennis Waterman

Dennis Waterman · Answer

Dear Mohamad, 
 At 1) and 2) after these small horizontal parts it continues to increase the load again, which clearly indicates that the ultimate load was not reached because if the ultimate load was reached, it couldn't increase the load any further. So how do you know for sure that it won't be able to increase the load further after the small horizontal part at 3 as well? Load-displacement curves are generally curved and flattening whereas in your case it's quite straight and linear and suddenly goes horizontal (3 times, actually). This doesn't look like the typical load displacement curve hence based on just the curve it cannot be decided the ultimate load and thus failure has been reached. Now if you see based on other data that indeed failure was reached, that is different. But you have that data and I don't, I only have the graph and based on the graph it cannot be determined that the failure load was reached. 
 With kind regards, 
 Dennis Waterman

Dennis Waterman · Answer

Dear Mohamad, 
 The Nmax doesn't determine the ultimate load, it only detemines when PLAXIS will stop trying to increase the load. Hence, if you really reached the ultimate load a higher Nmax will only lead to a larger horizontal part, but it will be the same ultimate load as for a lower Nmax. Your graph doesn't look like an ultimate load is reached, but more like there is convergence problem due to the mesh or the model making the calculation stop. But as I mentioned before, graphs may not tell the whole story - based on other results like plots of displacement increments, shear strain increments, plastic points and/or mobilised shear it may become clearer whether the ultimate load has been reached (hence, there is failure or not). I would start checking those results rather than being very fixated on a single graph. 
 With kind regards, Dennis Waterman