The evolution of the muon content of very high energy air showers ( EAS ) in the atmosphere is investigated with data of the KASCADE-Grande observatory .
For this purpose , the muon attenuation length in the atmosphere is obtained to \Lambda _ { \mu } = 1256 \pm 85 ^ { +229 } _ { -232 } ( \mbox { syst } ) \mbox { g / cm } ^ { 2 } from the experimental data for shower energies between 10 ^ { 16.3 } and 10 ^ { 17.0 } \mbox { eV } .
Comparison of this quantity with predictions of the high-energy hadronic interaction models QGSJET-II-02 , SIBYLL 2.1 , QGSJET-II-04 and EPOS-LHC reveals that the attenuation of the muon content of measured EAS in the atmosphere is lower than predicted .
Deviations are , however , less significant with the post-LHC models .
The presence of such deviations seems to be related to a difference between the simulated and the measured zenith angle evolutions of the lateral muon density distributions of EAS , which also causes a discrepancy between the measured absorption lengths of the density of shower muons and the predicted ones at large distances from the EAS core .
The studied deficiencies show that all four considered hadronic interaction models fail to describe consistently the zenith angle evolution of the muon content of EAS in the aforesaid energy regime .