Inertial flow in porous media, governed by the Forchheimer equation, is affected by domain heterogeneity at the field scale. We propose a method to derive formulae of the effective Forchheimer coefficient with application to a perfectly stratified medium. Consider uniform flow under a constant pressure gradient $$\Delta P/L$$Δ P / L in a layered permeability field with a given probability distribution. The local Forchheimer coefficient $$\beta$$β is related to the local permeability k via the relation $$\beta =a/k^c$$β = a / k c , where $$a>0$$a > 0 being a constant and $$c\in [0,2]$$c ∈ [ 0 , 2 ] . Under ergodicity, an effective value of $$\beta$$β is derived for flow (i) perpendicular and (ii) parallel to layers. Expressions for effective Forchheimer coefficient, $$\beta _e$$β e , generalize previous formulations for discrete permeability variations. Closed-form $$\beta _e$$β e expressions are derived for flow perpendicular to layers and under two limit cases, $$F\ll 1$$F ≪ 1 and $$F\gg 1$$F ≫ 1 , for flow parallel to layering, with F a Forchheimer number depending on the pressure gradient. For F of order unity, $$\beta _e$$β e is obtained numerically: when realistic values of $$\Delta P/L$$Δ P / L and a are adopted, $$\beta _e$$β e approaches the results valid for the high Forchheimer approximation. Further, $$\beta _{e}$$β e increases with heterogeneity, with values always larger than those it would take if the $$\beta - k$$β - k relationship was applied to the mean permeability; it increases (decreases) with increasing (decreasing) exponent c for flow perpendicular (parallel) to layers. $$\beta _{e}$$β e is also moderately sensitive to the permeability distribution, and is larger for the gamma than for the lognormal distribution.

In this work, we design an experimental campaign to assess the attenuation performance of a medium-scale resonant wave barrier operating within the frequency range of 50–100 Hz. In particular, the dispersive properties of (i) bare soil, (ii) a configuration of “dead masses” placed over the soil surface, and (iii) a locally resonant barrier, also known as metabarrier, are compared numerically. The resonant barrier introduces a significant amplitude reduction of the surface waves in a narrow frequency range around the resonant frequency of the resonators. Multiple-frequency barriers are designed with increasing and decreasing resonant frequencies to enlarge the attenuation frequency band.