  The breakdown of Efimov universal relations between resonances and
interference features in ultracold $^{40}$K-$^{87}$Rb mixtures has sparked much
discussion. In this study, we investigate the atom-dimer elastic scattering and
three-body recombination (TBR) rates with $J=0$ symmetry for a
$^{87}$Rb-$^{87}$Rb-$^{40}$K system to understand the mechanisms underlying
this breakdown. We use the R-matrix propagation method in a hyperspherical
coordinate frame with the Lennard-Jones model potential describing the
interactions between atoms. We extract the atom-dimer scattering length, cross
sections and three-body recombination rates with a finite intraspecies
scattering length. An atom-dimer elastic scattering resonance at negative
interspecies scattering length is found, which is due to the presence of the
near-threshold trimer state at the atom-dimer threshold ($^{40}$K +
$^{87}$Rb$^{87}$Rb). In addition, we predict an Efimov recombination minima at
positive interspecies scattering length, which is outside the range of previous
measurements. Our calculations show that the breakdown of the universal
relations predicted by zero-range theory can be attributed to the effective
range corrections and finite intraspecies scattering length. The present
results help elucidate the universal relations between Efimov features as well
as the importance of finite-range corrections for mixed systems.
