This posted article from May 2019 discusses the claim and its origins.
The idea that there are only 100 harvests left is just a fantasy
Despite dozens of headlines quoting these predictions, surprisingly
only one peer-reviewed paper from a scientific journal is ever cited
as evidence to back them up. This 2014 study from the University of
Sheffield compared the soil quality of a range of sites in the English
city, including agricultural, garden and allotment soils.
Now, before we question whether the results of this single, small
study can be extrapolated to represent all of England, let alone the
whole UK or even the whole world, let us take a look at their
findings: basically, some urban soils in Sheffield are higher in
carbon and nitrogen than some nearby agricultural ones. OK, but where
is the 100-year statistic? It turns out that nowhere in the study was
there any calculation, prediction or even passing reference to the
claim. None whatsoever. Perhaps not so much shaky evidence to support
this assertion as much as non-existent.
The article goes on to say:
Maybe this is the result of a typo and the work is in another research
paper? After an 8-hour trawl through the academic journals failed to
pull up a single study that even attempted to make this calculation, I
contacted six leading soil scientists across the world to ask if they
had ever come across such a prediction in either the published
literature or their work. Not a single one had.
In fact, the words they used to describe this claim were “bold”, “too
Malthusian”, “hardly useful”, “almost insulting” and “I have used this
in my soil science lectures to show the students to be wary of
headlines!”. Ouch.
Does that mean there aren’t real threats to some agricultural soils
around the world? Absolutely not. Indeed, all the scientists I spoke
to went to great lengths to point these out, where they exist.
However, they also highlighted how incredibly complex the calculations
needed to make such predictions would be, based on myriad factors,
only some of which can be predicted with any reliability, with
generalisations almost impossible. The boring reality is that while
soils in some parts of the world might be in decline, others are not.
Then there is this article, Borrelli, Pasquale et al. “An assessment of the global impact of 21st century land use change on soil erosion.” Nature communications vol. 8,1 2013. 8 Dec. 2017, doi:10.1038/s41467-017-02142-7, whose abstract is:
Human activity and related land use change are the primary cause of
accelerated soil erosion, which has substantial implications for
nutrient and carbon cycling, land productivity and in turn, worldwide
socio-economic conditions. Here we present an unprecedentedly high
resolution (250 × 250 m) global potential soil erosion model, using a
combination of remote sensing, GIS modelling and census data. We
challenge the previous annual soil erosion reference values as our
estimate, of 35.9 Pg yr−1 of soil eroded in 2012, is at least two
times lower. Moreover, we estimate the spatial and temporal effects of
land use change between 2001 and 2012 and the potential offset of the
global application of conservation practices. Our findings indicate a
potential overall increase in global soil erosion driven by cropland
expansion. The greatest increases are predicted to occur in
Sub-Saharan Africa, South America and Southeast Asia. The least
developed economies have been found to experience the highest
estimates of soil erosion rates.
However see as well these articles describing soil degradation due to industrial agricultural practices which is disrupting the soil.
From POLITICO Sep-2017 Can American soil be brought back to life?
Now, some farmers and soil scientists are realizing that for the
health of both people and farms, the most important thing you can do
is look at soil differently—seeing topsoil as a living thing itself,
which can be tended and even improved. Good soil is alive with a host
of delicate organisms, many of them microscopic, producing structure
and nutrients. As long as they’re thriving, soil can better absorb and
retain water and feed plants and control pests. But when they die off,
because they’ve been churned up and exposed to the sun and air or
smothered with chemicals, the soil gradually becomes little more than
powdered minerals.
As well see this Corteva Agriscience article published on the BBC, Why soil is disappearing from farms which describes a number of different ways that soil health is degraded as well as ways that farming practices are changing to reduce those negative effects on soil health.