  As the end products of the hierarchical process of cosmic structure
formation, galaxy clusters present some predictable properties, like those
mostly driven by gravity, and some others, more affected by astrophysical
dissipative processes, that can be recovered from observations and that show
remarkable "universal" behaviour once rescaled by halo mass and redshift.
However, a consistent picture that links these universal radial profiles and
the integrated values of the thermodynamical quantities of the intracluster
medium, also quantifying the deviations from the standard self-similar
gravity-driven scenario, has to be demonstrated. In this work, we use a
semi-analytic model based on a universal pressure profile in hydrostatic
equilibrium within a cold dark matter halo with a defined relation between mass
and concentration to reconstruct the scaling laws between the X-ray properties
of galaxy clusters. We also quantify any deviation from the self-similar
predictions in terms of temperature dependence of a few physical quantities
such as the gas mass fraction, the relation between spectroscopic temperature
and its global value, and, if present, the hydrostatic mass bias. This model
allows to reconstruct both the observed profiles and the scaling laws between
integrated quantities. We use the Planck-selected ESZ sample to calibrate the
predicted scaling laws between gas mass, temperature, luminosity and total
mass. Our universal model reproduces well the observed thermodynamic properties
and provides a way to interpret the observed deviations from the standard
self-similar behaviour. By combining these results with the constraints on the
observed $Y_{SZ}-T$ relation, we show how we can quantify the level of gas
clumping affecting the studied sample, estimate the clumping-free gas mass
fraction, and suggest the average level of hydrostatic bias present.
