## Correction for hydrodynamic pressure

To the extent that the water level is within or above the backfill, the software applies a correction factor to Westergaard's hydrodynamic pressure for water volumes within the backfill (Matsuzawa et al. 1985). Since the water is partially trapped, the generated hydrodynamic pressures are consequently reduced by a factor (1 – m) expressed by the following equation:

; ( 0 > m > 1 )

Where n = backfill porosity

γw = weight of water (9.807 kN/m³)

Hw = height between water surface and bedrock (in m)

Ew = water compressibility modulus (2.2 x106 kN/m²)

k = permeability coefficient (in m/s)

T = fundamental period of the earthquake (in s)

Figure 217 shows the variation of the factor (1-m) as a function of the permeability coefficient (hydraulic conductivity) of the backfill.

Figure 217 Evolution of the correction factor for hydrodynamic water pressure as a function of the permeability coefficient of the backfill (porosity, n=0.4)

The hydrodynamic pressures corrected by the factor (1 - m) correspond to the volume of water that is free to move through the pores of the backfill. However, to account for the volume of water that is trapped in the pores, CADAM3D uses the m-factor as a multiplier factor for the inertia force stemming from this trapped mass of water.