Should all the levels of a fixed factor be present in all the experimental trials? I would like to analyze the output of 11 field trials dealing with the disturbance to soil after logging operations. The goal is to check if there are significant differences between two machinery: skidder and forwarder in comparison to control soil not affected by machinery passage (so three treatments skidder, forwarder and control). The idea is to use GLMM using treatment as a fixed factor with three levels (skidder; forwarder and control) and other parameters like study area, soil texture and kind of intervention as random factors. The problem is that in all the field trials I don't have data on both skidder and forwarder but just on one machinery (5 study areas skidder and 6 study areas forwarder). Is it possible to apply the approach mentioned above or the fact that the two levels of the fixed factor are not present in all the study areas does not allow to conduct such kind of analysis?

Technically this is doable - a model will give you some results, the real question is if this is sensible. The issue is the same as for control vs. any treatment, that is an area was either left alone (control) or was logged (any treatment), you can't have both at the same location.
So the question boils down to if these areas are comparable, are the control and treatment sites more or less the same? And were the machines used in more or less the same environments? If the answer is yes then this analysis makes sense, otherwise it doesn't.
For ex. if you were to select what kind of machine you were going to use based on the site (a machine better suited to that environment) then you could not realistically compare these machines, as the differences could be attributed more to the environment type rather than the machine.
