In this work, an experimental study was carried out with the aim of reconciling static and dynamic stiffness of Opalinus Clay. The static and dynamic stiffness of core plugs from a shaly and a sandy facies of Opalinus Clay were characterized at two different stress states. The measurements included undrained quasi‐static loading–unloading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (0.5–150 Hz) and ultrasonic velocity measurements (500 kHz) probing the dynamic stiffness at ultrasonic frequencies. The experiments were carried out in a special triaxial low‐frequency cell. The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non‐elastic effects: Both sandy and shaly facies of Opalinus Clay exhibit large dispersion, that is, a large frequency dependence of dynamic stiffness and acoustic velocities. Especially dynamic Young's moduli exhibit very high dispersion; between seismic and ultrasonic frequencies they may change by more than a factor 2. P‐wave velocities perpendicular to bedding are by more than 200 m/s higher at ultrasonic frequencies than at seismic frequencies. The static undrained stiffness of both sandy and shaly facies is strongly influenced by non‐elastic effects, resulting in significant softening during both loading and unloading with increasing stress amplitude. The zero‐stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness at seismic frequency.

The pioneering work of Mike Batzle and his colleagues has provided a fundamental understanding of mechanisms behind dispersion and attenuation of elastic waves in fluid-saturated rocks. It also has made way for a realization that these phenomena need to be accounted for in a better way when interpreting seismic and sonic data from the field. Laboratory experiments have formed the basis for new insight in the past and will continue to do so. Here, examples of experimental observations that give direct or indirect evidence for dispersion in sand, sandstone, and shale are presented. Ultrasonic data from compaction tests show that Biot flow is the most likely dispersion mechanism in pure unconsolidated sand. Strong shale dispersion has been identified through low-frequency and low-strain quasistatic measurements and through a novel technique based on static loading and unloading measurements. In shale and sandstone containing clay, there is evidence for water weakening. A comparative study shows an example where the stress dependences of P-and S-wave velocities at seismic frequencies exceed those measured by traditional ultrasonic methods.

The relation between static and dynamic stiffness in shales is important for many engineering applications. Dynamic stiffness, calculated from wave velocities, is often related to static stiffness through simple empirical correlations. The reason for this is that dynamic properties are often easier to obtain; however, it is the static properties that define the actual subsurface response to stress or pore pressure changes. Rocks are not elastic media, and stiffness depends on the stress state, stress-change amplitude, loading rate, drainage conditions, fluid saturation, and scale. All these factors require consideration when static and dynamic stiffness properties are to be related. Two mechanisms that may have a strong effect on the stiffness of shales were studied in this experimental work: (i) a reduction of undrained static stiffness with an increase in stress amplitude and (ii) a frequency dependence (or dispersion) of dynamic stiffness. Laboratory tests were performed on four fully brine-saturated undrained field shales from different overburden formations. Experiments were conducted using a low-frequency apparatus-a triaxial loading cell with the ability to measure dynamic stiffness at seismic frequencies (1-150 Hz) and ultrasonic velocities (500 kHz). Shale anisotropy was characterized by testing differently oriented core plugs. Static and dynamic stiffness of shales The results demonstrated that all the tested shales exhibited a dispersion of dynamic stiffness from seismic to ultrasonic frequencies. Young's modulus dispersion for the tested shales ranged from nearly 30% to above 100%. Wave velocity dispersion was on the order of 10-20% for P-waves and 20-40% for S-waves. In static tests, the undrained rock stiffness gradually decreased with increasing stress amplitude. For one shale, the static undrained Young's modulus was reduced by 50% when amplitude of the loading-unloading measurement cycle was increased from 1 MPa to 3 MPa. This finding is explained by non-elastic deformations that increase with the stress level. A method of zero-stress extrapolation of static stiffness was used to obtain the purely elastic response. The stiffness for the limit of zero stresschange amplitude agreed well with the dynamic response at seismic frequency, providing a link between static and dynamic stiffness.

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