Optimizing the Terzaghi Estimator of the 3D Distribution of Rock Fracture Orientations

Tang, Huiming; Huang, Lei; Juang, C. Hsein; Zhang, Junrong

doi:10.1007/s00603-017-1254-7

Cited by 20 publications

(5 citation statements)

References 31 publications

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“…Although they provided deep insight into the mechanical behaviors of rocks, these studies mainly focused on the intact rocks without any defects. However, natural rock masses consist of the intact rock matrix and multiple fractures, resulting in strong mechanical anisotropies [1,[18][19][20]. The transversely isotropic rocks, such as the stratified sedimentary rocks and foliated metamorphic rocks, are common rock types containing parallel bedding planes, and they present orientation-dependent behaviors due to the presence of bedding planes.…”

Section: Introductionmentioning

confidence: 99%

A Parabolic Failure Criterion for Transversely Isotropic Rock: Modification and Verification

Wang

Tang

Shen

et al. 2019

Mathematical Problems in Engineering

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It is of great significance to develop a failure criterion that can describe the orientation-dependent behavior of transversely isotropic rocks. This paper presents a simplified parabolic model that is successful in predicting the strengths of rocks under different confining pressures and bedding angles. The model is a modified version of the normal parabolic criterion for intact rocks. The two orientation-dependent parameters (σcβ and kβ) in the model show trigonometric relationships with the bedding angle, and they can be readily determined through uniaxial and triaxial compression tests. The shape of the failure envelope is determined by kβ, and σcβ only affects the level of rock strength. With application to 446 experimental data, the predicting results by the parabolic criterion are highly consistent with the experimental data, and the predictive capacity of the proposed criterion is better than those of the McLamore-Gray and Tien-Kuo criteria. Besides, the prediction errors for the high confining pressure condition and the bedding-sliding failure mode are smaller than those for the low confining pressure and the non-bedding-sliding failure. Moreover, the prediction error almost remains steady with the decrease of data set, indicating that the proposed criterion is of high precision even if the experimental data are limited.

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Section: Introductionmentioning

confidence: 99%

A Parabolic Failure Criterion for Transversely Isotropic Rock: Modification and Verification

Wang

Tang

Shen

et al. 2019

Mathematical Problems in Engineering

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“…First, the sampling bias of the observed orientations was corrected according to the conventional and the modified Terzaghi methods. A cell size of 2°× 2°was selected for the conventional Terzaghi method because Tang [15] concluded that this size optimizes the accuracy. e result corrected by the conventional Terzaghi method is shown in Figure 6(a) and the result corrected by the modified Terzaghi method is shown in Figure 6(b).…”

Section: Application Of the Modified Terzaghi Methodsmentioning

confidence: 99%

Correction of Line‐Sampling Bias of Rock Discontinuity Orientations Using a Modified Terzaghi Method

Tang

Zhang

Huang

et al. 2018

Advances in Civil Engineering

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The Terzaghi method is widely used to correct the line-sampling bias of rock discontinuity orientations. The method includes four procedures, one of which is meshing the stereographic projection diagram into cells. The method is based on the bias-compensatory factor, 1/sin θ, where θ is the angle between the scanline and the discontinuity defined at each cell center. This paper presents a modified Terzaghi method that eliminates meshing, thereby reducing the method to three steps that (1) count the frequencies, (2) weigh the frequencies by the bias-compensatory factor, and (3) round the weighed frequencies to the nearest integer. Due to the elimination of the mesh, the counting object has changed to the frequency at each pole, and θ in the bias-compensatory factor is redefined as the angle between the scanline and the discontinuity at each pole. The applicability of the redefined bias-compensatory factor is verified through a mathematical logical deduction. The accuracy of the conventional and the modified Terzaghi methods are compared using a case study in Wenchuan, China, revealing improved accuracy for the latter.

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“…According to the linear elasticity theory, under the action of distal stress, in the polar coordinate system near the fracture tip of the TF, the polar coordinate expression of stress at the circumferential angle (θ) (corresponding to point M) in the unit circle with the radius (r) is as follows [16]:…”

Section: Calculation Of Multi-fracture Stress Interferencementioning

confidence: 99%

“…The central question to be answered is the extension angle at the crack tip and the mechanical conditions. Brittle failure includes two main forms, shear and tension [15][16][17]. In this paper, the shear failure theory is used to analyze the initiation law of natural cracks.…”

Section: Introductionmentioning

confidence: 99%

Analytical Investigation on the Shear Propagation Mechanism of Multi-Cracks in Brittle Tight Rocks under Compressive and Shear Loading Conditions

Luo

et al. 2023

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There is abundant shale oil in the ocean and on land. Due to the tight lithology of the reservoir, volume fracturing technology is needed to improve the oil and gas productivity. It is very important to study the expansion law of multiple natural fractures in rock masses and its influencing factors in the process of volume fracturing for the formation of fracture networks. Based on the theory of online elastic fracture mechanics, the calculation method of the stress intensity factor at the end of any I–II composite fracture is established by using effective shear stress and considering the influence of T-stress. The calculation model of the stress intensity factor of any fracture on the main fracture wall or the horizontal section of the main fracture wall is established according to the concrete stress conditions in the process of hydraulic fracturing. Based on the principle of stress superposition, the combined interference stress calculation model of fracture ends is established for the case of multiple penetrating cracks in infinite-plane rock masses. Based on the theory of shear failure and plane strain, a model of the initiation direction and condition of natural cracks on the horizontal section of the main fracture wall and both sides of the main fracture in brittle rock is established when there are many coaxial natural cracks under the action of remote site stress and water pressure on the fracture surface. According to the simulation results, on the main fracture wall, when σH > σv > σh or σH > σh > σv, when the crack angle (CA) is within a certain range and multiple natural cracks (MNC) exist, the required pressure for shear failure decreases. When the fracture angle exceeds a certain size, the required pressure increases. When there are MNC in the horizontal or perpendicular sections of the rock mass on both sides of the main fracture, the required net pressure for shear failure decreases within a certain CA range. When the CA exceeds a certain range, it increases or remains basically unchanged. On the whole, the presence of MNC reduces the net pressure for shear failure, which is conducive to the formation of fracture networks.

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Optimizing the Terzaghi Estimator of the 3D Distribution of Rock Fracture Orientations

Cited by 20 publications

References 31 publications

A Parabolic Failure Criterion for Transversely Isotropic Rock: Modification and Verification

A Parabolic Failure Criterion for Transversely Isotropic Rock: Modification and Verification

Correction of Line‐Sampling Bias of Rock Discontinuity Orientations Using a Modified Terzaghi Method

Analytical Investigation on the Shear Propagation Mechanism of Multi-Cracks in Brittle Tight Rocks under Compressive and Shear Loading Conditions

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