  We study spectral properties and geometric functional inequalities on
Riemannian manifolds of dimension $\ge3$ with (finite or countably many)
conical singularities $\{z_i\}_{i\in\mathfrak I}$ in the neighborhood of which
the largest lower bound for the Ricci curvature is \begin{equation}\label{d2}
k(x)\simeq K_i-\frac{s_i}{d^2(z_i,x)}. \end{equation} Thus none of the existing
Bakry-\'Emery inequalities or curvature-dimension conditions apply. In
particular, $k$ does not belong to the Kato (or (extended Kato) class, and
$(M,g)$ is not tamed. Manifolds with such a singular Ricci bound appear quite
naturally., e.g. as cones over spheres of radius $>1$
  For such manifolds with conical singularities we will prove
  * a version of the Bakry-\'Emery inequality
  * a novel Hardy inequality
  * a spectral gap estimate.
