I am not an expert in soil, but, from reading in Bowles' book " foundation analysis and design", there is a table giveing qu versus ks such as
clayey soil:
qu less than 200 kPa ; ks =12000-24000 kN/m3
200 <qu< 400 kPa; ks=24000-48000 kN/m3
So the ratio you metioned...