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7.3. Experimental section 99[ ( ) ( )]2 θ 0.5 − θ 2.094S 2 (θ) ≈ exp − √π . (7.6)1 − θ 0.670In case the beam consists of rock, which has a much higher modulus than gel, the compressibilityeffects have to be taken into account. The parameter A is then replaced by[129]( ) ( 1 − 2νp1 − K ) 2p3 K SA =1 − K pK S+ (1 − ρ)(KpK L− K pK S), (7.7)in which K p is the bulk modulus of the drained network, K S is the bulk modulus of thesolid constituting the porous network, K L is the bulk modulus of the pore fluid, and ρ isthe volume fraction of the solid content. The hydrodynamic relaxation time τ R is relatedto the permeability D and the viscosity of the pore fluid η L by [129]{ 2(1 + νp )τ R =3K p+ 1 − ρ + 1 [ρ − 4(1 + ν p)−K L K S 3( 1 − 2νp3) ( )]} ( )Kp ηL a 2. (7.8)K S DThe bulk modulus K L is known for most common liquids, and the bulk modulus K p equalsE p /3(1 − 2ν p ). The approximation K p /K S ≈ ρ 2 can be used to estimate K S [129].Many materials, including aged gels that still contain a certain amount of water,show viscoelastic (VE) behavior. When the characteristic time of viscoelastic relaxationis at least an order of magnitude longer than the characteristic time of hydrodynamicrelaxation, the total load relaxation W (t)/W (0) is adequately represented by the productof the hydrodynamic relaxation function R(t), as described above, and an uniaxial stressrelaxation function, Ψ V E : [133]W (t)W (0) = R(t)Ψ V E(t). (7.9)The function Ψ V E is essentially an empirical function and can be inferred from experimentaldata. However, for many systems the VE relaxation can be adequately describedby a stretched exponential:[ ( ) α ] tΨ V E = exp − , (7.10)τ V Ewhere τ V E is the VE relaxation time and α is a parameter (0 ≤ α ≤ 1).7.3 Experimental section7.3.1 MaterialsThe Bentheim sandstone was obtained from a Bad-Bentheim quarry in Germany. Rectangularplates were sawed from a single block. The length and the width of the plateswere 160 ± 5 mm and 25.2 ± 0.4 mm, respectively. The thickness of the plates varied