The Impact of Strain Amplitude on Young's Modulus in Water-Saturated Sandstone

Strain amplitude, frequency, stress conditions, and fluid saturation influence the stiffness response of rocks. In order to quantify the effect of frequency and strain amplitude, we performed low-frequency measurements on fully saturated Bentheimer sandstone samples to measure the dynamic stiffness at seismic frequencies (0.5 – 143 Hz) with strain amplitudes ranging from 10−7 to 10−5 . In order to quantify the effect of pressure, we increased the effective stress subsequently. The results show that Young’s modulus decreases with increasing strain amplitude even in the seismic-frequency range. The applied wave-stress signal contains the first harmonic at the central frequency, but the measured wave strain rate spectrum contains higher-order harmonics indicating hysteresis in the stress-strain response. The increased signal at higher-order harmonics is only captured for higher strain amplitudes. The general trend shows a decreasing signal with increasing order of harmonics. Remarkable is that the 3rd harmonic indicates a stronger signal than the 2nd harmonic and the 5th harmonic a stronger signal than the 4th. Understanding non-linearities and non-elastic mechanisms and their dependency on the strain amplitude for saturated samples are fundamental for the link between dynamic and static properties of reservoir rocks.