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Abstract
This paper presents a mathematical model that reflects the nature of the dynamic Young’s modulus of a dry sedimentary rock during nonstationary uniaxial loading. The model is based on an idealized model of a system suggested by Jaeger J.C. A rock sample is considered as a spring with stiffness, the bottom point of which is fixed, while the upper point carries a mass. A sample experiences dynamic load and the rock matrix response. Displacement of the mass from the equilibrium state sets the variation of the sample’s length. Displacement of all the sample’s points goes according to the same law regardless of the point location. The response of a rock to a disturbing nonstationary load is selected based on the combination of conditions of each experiment, such as the load frequency and amplitude and the mass, length, and diameter of a sample. The mathematical model is consistent with experimental data, according to which an increase in load frequency leads to an increase in the dynamic Young’s modulus for each value of the load. The accuracy of the models is evaluated. The relations underlying the model can be used as a basis to describe the Young’s modulus dispersion of sedimentary rocks under the influence of nonstationary loads.
Highlights
The elastic characteristics of sedimentary rocks change under the influence of nonstationary loads [1,2,3]
The techniques based on a hysteresis loop during cyclic loading [18,19] allow us to calculate the dynamic Young’s modulus using the conventional formulas given in [20]
The studies that we present in this paper are based on the results of experiments on a dry sandstone
Summary
The elastic characteristics of sedimentary rocks change under the influence of nonstationary loads (e.g., vibrations) [1,2,3]. The most common technique for estimation of the dynamic Young’s modulus of sedimentary rocks is the elastic wave theory, which is grounded in the principles of acoustic wave propagation through a porous rock [5,6,7,8,9,10,11,12,13,14,15] According to such an approach, the dynamic Young’s modulus is estimated using the velocity of waves, elastic constants, and rock density [16]. The other techniques, such as that used in [17], are based on dynamic uniaxial loading (sinusoidal cyclic compression) and consider the dependence of the dynamic component of the Young’s modulus as an approximation function of the frequency ω and amplitude A of a periodic load. Despite the fact that the existing techniques are able to calculate the dynamic component of the Young’s modulus
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