Water weakening of chalk shear modulus and mechanical strength of chalk can be described as a consequence of solid liquid interaction at the pore level. When pores are narrow, deformation of the chalk not only depends on stiffness of the solid frame, but also on the kinematic viscosity of the pore fluid, because the pore fluid has to give way. Atmospheric air has a higher kinematic viscosity than water, so chalk saturated with dry air is stiffer than chalk saturated with water. The effect of this viscous air becomes significant when pore radius is close to or is smaller than the mean free path of atmospheric air molecules. In order to quantify this fluid effect on frame stiffness I model a vacuum state Biot’s coefficient, which is higher than that calculated from velocity and density of air saturated samples. This also involves the modeling of a Biot’s coefficient of the water imbedded frame. This Biot’s coefficient is lower than for the frame in vacuum but higher than for the frame in air. Biot’s coefficient for the frame in a given liquid may be calculated from Biot’s coefficient in vacuum and Biot’s frequency ratio for the liquid in question. Bulk modulus of the frame in vacuum may be calculated from Biot’s coefficient. When this vacuum frame bulk modulus is used for Gassmann substitution between bulk modulus calculated from density and velocity of elastic waves for air saturated chalk and for water saturated chalk, the good match between measured and calculated data indicate that the frame bulk modulus changes with the pore fluid in a predictable way.
Gassmann (1951) found that provided fluid-solid interaction can be disregarded, shear modulus is independent of saturating pore fluid. A significant systematic difference between shear moduli of chalk in the dry state and in the water saturated state was first noticed by Japsen et al. (2002) and documented by Røgen et al. (2005) (Figure 1a). This would indicate that Gassmann’s equations are only applicable to chalk with some approximation. Andreassen and Fabricius (2010) found that also mechanical strength of weakly cemented chalk depend on pore fluid and is directly related to the reference frequency. Apparent water weakening of not only the shear modulus but also the bulk modulus of the chalk frame was observed by Fabricius et al. (2010) (Figure 2a).
The presented theory implies that for rocks with small pore size such as chalk, velocities of elastic waves in air saturated samples do not give information on the frame elasticity directly. It should be noted, that if the rock remains wetted with the same fluid but only the movable fluid is exchanged, then Gassmann’s equations may be used with no modifications. For frequency ratio of water saturated samples above 10-2, the difference between shear moduli of air saturated and water saturated chalk becomes small, and the difference between bulk modulus of air saturated chalk and chalk in vacuum becomes small (Figure 5).
