Prestress significantly influences the mechanical properties of fractured rocks due to stress-induced anisotropy in the surrounding matrix and the stress-induced closure of cracks. Understanding the stress-dependent elastic moduli and anisotropic properties is crucial for various geoscience applications. The theory of acoustoelasticity only accounts for weak nonlinear elasticity with finite strains through the third-order elastic constants (3oECs) that are strictly valid for an isotropic homogeneous medium. Incorporating the David-Zimmerman (DZ) and Mori-Tanaka (MT) models into the theory of acoustoelasticity leads to an acoustoelastic DZ-MT model of fractured rocks. In this study, we extend the isotropic acoustoelastic DZ-MT model to address anisotropic conditions by examining two scenarios: one involving isotropic prestress applied to rocks with aligned cracks, and the other involving uniaxial prestress applied to rocks with isotropic cracks. The resulting anisotropic acoustoelastic DZ-MT model of fractured rocks is validated by experiment data measured from an artificial sample with aligned cracks and three isotropic sandstones (Massilon, Portland, and Berea). For the artificial sample, applying isotropic pressure will reduce the crack-induced anisotropy due to crack closure, leading in turn to increase the acoustoelastic effect on the background matrix as well as the effective elastic moduli of rocks. Aligned cracks primarily reduce the P-wave modulus for waves propagating perpendicular to the crack surfaces, making the P-wave modulus undergo significant changes because of its sensitivity to crack closure. For the natural sandstones with isotropic cracks subjected to uniaxial prestress, some existing cracks are closed, strongly depending on the relativity between crack orientation and loading direction. The P-wave modulus normal to the loading direction exhibits a slight increase, indicating the integrated effect of both acoustoelasticity and crack deformation. The complex microstructural changes in the case of uniaxial loading influence the application of acoustoelasticity and crack-closure model, potentially reducing the accuracy of the proposed DZ-MT model.

中文翻译：

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用于裂隙岩石应力相关弹性模量的各向异性声弹性有效介质模型


由于周围基质中应力诱导的各向异性和应力诱导的裂纹闭合，预应力显着影响裂隙岩石的力学性能。了解应力依赖性弹性模量和各向异性特性对于各种地球科学应用至关重要。声弹性理论仅通过三阶弹性常数 （3oEC） 来解释具有有限应变的弱非线性弹性，这些弹性常数对各向同性均质介质严格有效。将 David-Zimmerman （DZ） 和 Mori-Tanaka （MT） 模型纳入声弹性理论，可以得到裂隙岩石的声弹性 DZ-MT 模型。在本研究中，我们通过研究两种情况来扩展各向同性声弹性 DZ-MT 模型以解决各向异性条件：一种涉及施加到具有对齐裂纹的岩石上的各向同性预应力，另一种涉及施加到具有各向同性裂纹的岩石上的单轴预应力。由此产生的裂隙岩石各向异性声弹性 DZ-MT 模型通过从具有对齐裂纹和三种各向同性砂岩（Massilon、Portland 和 Berea）的人工样品中测量的实验数据得到验证。对于人工样品，施加各向同性压力将减少由于裂纹闭合引起的裂纹诱导的各向异性，进而增加对背景基体的声弹性效应以及岩石的有效弹性模量。对齐的裂纹主要降低了垂直于裂纹表面传播的波的 P 波模量，由于 P 波模量对裂纹闭合敏感，因此发生了显著变化。 对于具有各向同性裂缝的天然砂岩，在单轴预应力作用下，一些现有的裂缝被封闭，这在很大程度上取决于裂缝方向和加载方向之间的相对性。垂直于加载方向的 P 波模量略有增加，表明声弹性和裂纹变形的综合效应。单轴加载情况下复杂的微观结构变化影响声弹性和裂纹闭合模型的应用，可能会降低所提出的 DZ-MT 模型的准确性。