The section of NEN 3650-1:2003/A1:2006 concerning the horizontal soil stiffness kh is based on the Delft Cluster document "Intergraal ontwerp leidingen en riolen, Grondmechanische randvoorwaarden" dated January 2001.

The formula for kh,30 has been derived from a paper by Audibert and Nyman. The kh1 (and kh2 and kh3) formula is based on full scale loading tests on pipelines (Kesteren) and Plaxis calculations. See figure below.

It turns out that for deeper situated pipelines Audibert and Nyman predict a too weak spring behaviour (see graph Audibert/Nyman diep).

That's why it is recommended to use the formula kh1 = 33 qhe/D (graph trilineiar zand). For clay the same formula is proposed.

This can be demonstrated further by calculating the kh,30 values for varying values of Z/D. Say kh,30 = F qhe/D, then (for drained situation):

Z/D F
1 54

2 41

3 33

4 28

This shows that the formula Kh1 is more accurate than the formula kh,30 especially for Z/D > 3.

The remark in the NEN 3650 code only states that the Kesteren tests have been performed up to a Z/D value 3. It does not say that for higher values the formulae do not hold.