  In the context of design studies for future $pp$ colliders, we present a set
of predictions for average soft-QCD event properties for $pp$ collisions at
$E_\mathrm{CM} = 14$, $27$, and $100$ TeV. The current default Monash 2013 tune
of the PYTHIA 8.2 event generator is used as the baseline for the
extrapolations, with uncertainties evaluated via variations of cross-section
parametrisations, PDFs, MPI energy-scaling parameters, and colour-reconnection
modelling, subject to current LHC constraints. The observables included in the
study are total and inelastic cross sections, inelastic average energy and
track densities per unit pseudorapidity (inside $|\eta|\le 6$), average track
$p_\perp$, and jet cross sections for 50- and 100-GeV anti-$k_T$ jets with
$\Delta R=0.4$, using aMC@NLO in conjunction with PYTHIA 8 for the latter.
