I believe the soil in question is translated elsewhere as 'ground', and is described in Heidegger's 1929 treatise "On the Essence of Ground".
And no, I don't think he intends any reference to the greek circular notion of time.
Attaching a couple of quotes from the beginning and near the end of the above mentioned essay (only 39 pages in its entirety), to give a flavour of the concepts under discussion :-
I. THE PROBLEM OF GROUND
The "principle of reason" as a "supreme principle" seems to preclude
from the very outset anything like a problem of ground. Yet is the
"principle of reason" an assertion about ground as such? As a
supreme principle, does it reveal at all the essence of ground? The
usual, abbreviated version of the principle states: nihil est sine
ratione, nothing is without reason. Transcribing it positively, this
states: omne ens habet rationem, every being has a reason. The
principle makes an assertion about beings, and does so with regard
to something like "ground." Yet what constitutes the essence of
ground is not determined in this principle. It is presupposed for
this principle as a self-evident "idea." However, the "supreme"
principle of reason makes use of the unclarified essence of ground
in yet another way; for the specific character of principle belonging
to this principle as a "grounding" principle, the character of
principle belonging to this principium grande (Leibniz) can after
all be delimited originarily only with regard to the essence of
ground.
... we shall now discuss briefly whether anything, and if so, what,
has been attained with regard to the problem of the "principle of
reason" through our attempt at shedding light upon the "essence" of
ground. The principle means: every being has its reason [ground].
The exposition we have given first of all illuminates why this is
so. Because being, as understood in advance, "intrinsically"
grounds things in an originary manner, every being as a being in its own way announces "grounds," whether these are specifically grasped
and determined in an appropriate way or not. Because "ground" is a
transcendental characteristic of the essence of being in general,
the principle of reason [ground] is valid for beings. Ground,
however, belongs to the essence of being because being (not beings) is
given only in transcendence as a grounding that finds itself in a
projecting of world.
Furthermore, it has become clear with respect to the principle of
reason [ground] that the "birthplace" of this principle lies neither
in the essence of proposition nor in propositional truth, but in
ontological truth, i.e., in transcendence itself.
-- Pathmarks, The Essence of Ground, M. Heidegger, trans. W. McNeill
So in my loose understanding, existential beings transcend the extant being of their component material (which is the ontological difference), and as a property of transcendence they (or somatic bodies in general) need to operate according to reason (or rationality), and it is this principle that is the ground.
