Rudnicki and Rice’s Analysis of Strain Localization Revisited

1993 ◽  
Vol 60 (4) ◽  
pp. 842-846 ◽  
Author(s):  
G. Perrin ◽  
J. B. Leblond
Keyword(s):  
Principal Stress ◽  
Strain Localization ◽  
Intermediate Principal Stress ◽  
Pressure Sensitive ◽  
Minimum Principal Stress ◽  
Hardening Modulus ◽  
Special Case

In a celebrated paper published in 1975, Rudnicki and Rice (RR) analyzed the conditions for strain localization in pressure-sensitive dilatant materials. This paper corrects certain results in their work that are relevant in exceptional cases. RR found that the normal to the plane of localization was generally orthogonal to the direction of the intermediate principal stress; however, when a certain inequality was satisfied, it was orthogonal to the direction of the minimum principal stress. In contrast, it is shown here that the normal to the plane of localization is always orthogonal to the direction of the intermediate principal stress; but there is a special case where it is parallel to the direction of either the maximum or the minimum principal stress, and in this case the expression of the critical hardening modulus at localization differs from that given by RR.

The Changing Rule of Rock Strength under True Triaxial Condition

2014 ◽  
Vol 522-524 ◽  
pp. 1410-1413
Author(s):  
Ze Kang Wen ◽  
Ke Min Wei ◽  
Jia Quan Hu ◽  
You Ling Fang
Keyword(s):  
Principal Stress ◽  
Rock Strength ◽  
Quadratic Function ◽  
Intermediate Principal Stress ◽  
Stress Effect ◽  
True Triaxial Test ◽  
True Triaxial ◽  
Minimum Principal Stress ◽  
Stress Coefficient ◽  
Intermediate Principal Stress Effect

The intermediate principal stress effect of the rock has been demonstrated. By analyzing true triaxial test results of Dunham dolomite and Mizuho trachyte, we studied relationship between minimum principal stress and the rock strength under the same intermediate principal stress coefficient, and the relationship between intermediate principal stress and the rock strength under the same minimum principal stress condition. Research shows that the minimum principal stress has a linear relation with the rock strength, the intermediate principal stress coefficient of a quadratic function relation with the rock strength. And the mathematic expression of the intermediate principal stress effect function was calculated.

scholarly journals Seepage Flow Properties of a Columnar Jointed Rock Mass in a True Triaxial Experiment

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Yanxin He ◽  
Zhende Zhu ◽  
Wenbin Lu ◽  
Yunjin Hu ◽  
Xinghua Xie ◽  
...  
Keyword(s):  
Rock Mass ◽  
Principal Stress ◽  
Jointed Rock ◽  
Jointed Rock Mass ◽  
Intermediate Principal Stress ◽  
True Triaxial ◽  
Minimum Principal Stress ◽  
Baihetan Hydropower Station ◽  
Columnar Jointed Rock Mass ◽  
Seepage Characteristics

A columnar jointed rock mass is a type of rock mass with strong geometric anisotropy and high interface permeability. Its seepage characteristics pose new challenges to the construction and maintenance of the Baihetan Hydropower Station on the Jinsha River. The research object in this study is the columnar jointed rock mass (basalt) in the dam area of Baihetan Hydropower Station. Similar-material model samples of the columnar jointed rock mass with different column dip angles ( α = 0 ° ~90°) were prepared following a similar principle. A true triaxial seepage–stress coupling test was conducted to evaluate the seepage characteristics of similar-material samples with different dip angles under intermediate principal stress and minimum principal stress. The experimental results showed that the columnar jointed rock mass exhibited apparent seepage anisotropy. The relationship curve between the volume flow rate Q and the pressure gradient − d P / d L of the samples with different dip angles showed evident nonlinear seepage under intermediate principal stress, which could be well expressed using the Forchheimer equation. It shows the characteristics of a typical linear Darcy flow under minimum principal stress. The law of variations in the permeability of the samples with different dip angles under intermediate principal stress can be well expressed using the one-dimensional quadratic function equation k = a + b σ 2 + c σ 2 2 , and the law of variations in the permeability of the samples with different dip angles under minimum principal stress can be well expressed using the logarithmic function k = a + b ln σ 3 . The permeabilities of the columnar jointed rock mass with dip angles of 0°, 15°, 30°, and 60° were most sensitive to changes in stress, and the seepage characteristics increased in complexity after changes in stress.

scholarly journals Failure in Confined Brazilian Tests on Sandstone

2021 ◽  
Vol 11 (5) ◽  
pp. 2285
Author(s):  
Tyler Hagengruber ◽  
Mahmoud Reda Taha ◽  
Esteban Rougier ◽  
Earl Knight ◽  
John Stormont
Keyword(s):  
Principal Stress ◽  
Experimental Tests ◽  
Confining Pressure ◽  
Intermediate Principal Stress ◽  
Brazilian Test ◽  
Test Results ◽  
Strong Function ◽  
Strength Data ◽  
Minimum Principal Stress ◽  
Coulomb Criterion

Strength of rocks in the confined tension region, where the minimum principal stress is tensile, has only infrequently been measured and is not well understood. Quasi-static confined Brazilian tests under a range of confining stresses (2.76 to 27.58 MPa) where used to determine the strength of sandstone in the confined tension region. The test results indicate that the strength in the confined tension region was a strong function of the intermediate principal stress: increasing the intermediate principal stress significantly increased the strength of the sandstone. The strength data were well fit by the Mogi–Coulomb criterion, which accounts for the intermediate principal stress. Unconfined Brazilian strength data were not well fit to the Mogi–Coulomb criterion derived from the confined Brazilian test data, consistent with a transition from tensile to shear processes dominating failure with increasing confining pressure. Observations of post-failure fracture surfaces reveal more indication of shear processes with increasing confining pressure. Numerical simulations from combined finite-discrete element method are compared to the experimental results and reflect similar conditions for failure compared to the experimental tests in the confined tension region.

scholarly journals Numerical simulation on the simultaneous stress interference of parallel multiple hydraulic fractures

2021 ◽  
pp. 014459872110019
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Principal Stress ◽  
Hydraulic Fracture ◽  
Stress Ratio ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Fracture Spacing ◽  
Induced Stress ◽  
Minimum Principal Stress ◽  
Fracturing Process ◽  
Stress Ratios

During horizontal well staged fracturing, there is stress interference between multiple transverse fractures in the same perforation cluster. Theoretical analysis and numerical calculation methods are applied in this study. We analysed the mechanism of induced stress interference in a single fracture under different fracture spacings and principal stress ratios. We also investigated the hydraulic fracture morphology and synchronous expansion process under different fracture spacings and principal stress ratios. The results show that the essence of induced stress is the stress increment in the area around the hydraulic fracture. Induced stress had a dual role in the fracturing process. It created favourable ground stress conditions for the diversion of hydraulic fractures and the formation of complex fracture network systems, inhibited fracture expansion in local areas, stopped hydraulic fractures, and prevented the formation of effective fractures. The curves of the maximum principal stress, minimum principal stress, and induced principal stress difference with distance under different fracture lengths, different fracture spacings, and different principal stress ratios were consistent overall. With a small fracture spacing and a small principal stress ratio, intermediate hydraulic fractures were difficult to initiate or arrest soon after initiation, fractures did not expand easily, and the expansion speed of lateral hydraulic fractures was fast. Moreover, with a smaller fracture spacing and a smaller principal stress ratio, hydraulic fractures were more prone to steering, and even new fractures were produced in the minimum principal stress direction, which was beneficial to the fracture network communication in the reservoir. When the local stress and fracture spacing were appropriate, the intermediate fracture could expand normally, which could effectively increase the reservoir permeability.

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