There are many theories to calculate the vertical pressure on the top slab or lining of the tunnel, the simplest theory was developed by Terzaghi,
Pv=(unit weight of soil above the slab * the span of the tunnel)/ ( 2*k*tan phi), where k is lateral earth pressure and phi is the angle of internal pressure. Best regards, Younis
I have provided an equation in my answer and it includes the reduction factor, please check the equation. Also, more details can be obtained via the following link: