Degradation of rock fracture asperities in unloading,reloading, and reversal

Among the constitutive models for rock fractures developed over the years, Barton's empirical model has been widely used. Although Barton's failure criterion predicts peak shear strength of rock fractures with acceptable precision, it has some limitations in estimating the peak shear displacement, post‐peak shear strength, dilation, and surface degradation. The first author modified Barton's original model in order to address these limitations. Barton proposed his model for degradation of fracture asperities in unloading, reloading, and shear displacement reversal based on just one cyclic direct shear test. In this study, a database of results of 18 cyclic direct shear tests available in the literature was collected and analyzed. Modifications were made to Barton's original model (in terms of fracture cyclic shearing) to make it consistent with the modified model proposed by the first author. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental Validation of Modified Barton’s Model for Rock Fractures

Among the constitutive models for rock fractures developed over the years, Barton’s empirical model has been widely used. Although Barton’s failure criterion predicts peak shear strength of rock fractures with acceptable precision, it has some limitations in estimating the peak shear displacement, post-peak shear strength, dilation, and surface degradation. The first author modified Barton’s original model in order to address these limitations. In this study, the modified Barton’s model (the peak shear displacement, the shear stress–displacement curve, and the dilation displacement) is validated by conducting a series of direct shear tests.     

Influence of geochemistry on toughening behavior of organic-rich shale

Our research objective is to understand the influence of geochemistry on the fracture behavior of organic-rich shale at multiple length-scales. Despite an increasing focus on the fracture behavior of organic-rich shale, the relationships between geochemistry and fracture behavior remain unclear and there is a scarcity of experimental data available. To this end, we carry out 59 mesoscale scratch-based fracture tests on 14 specimens extracted from 7 major gas shale plays both in the USA and in France. Post-scratch testing imaging reveals fractures with a small crack width of about 411–660 nm. The fracture toughness is evaluated using the energetic size effect law, which is extended to generic axisymmetric probes. A nonlinear anisotropic and multiscale fracture behavior is observed. In addition, a positive correlation is found between the fracture toughness and the presence of kerogen, clay and calcite. Moreover, the geochemistry is found to influence the timescale and the regime of propagation of the hydraulic fracture at the macroscopic length-scale. In particular, shale systems rich in total organic content, clay and calcite are more likely to exhibit high values of the fluid lag and a low hydraulic crack width. Our findings highlight the need for advanced constitutive models for organic-rich shale systems and advanced hydraulic fracturing solutions that can fully integrate the complex fracture response of organic-rich shale materials.

     

Coupling of BEM with a large displacement and rotation algorithm

In stability analysis of rock blocks, the deformability of the blocks can conveniently be simulated using the boundary element method (BEM). However, all boundary conditions are given as stresses. Thus, the displacement solution is not unique. In this paper, an algorithm is proposed to remove rigid body motions in the solution of the boundary form of Somigliana identity discretized by the direct BEM formulation. The algorithm is applied to the calculation of the normal stiffness of rock blocks and coupled with BS3D, large displacement and rotation algorithm for the general stability of rock blocks. Copyright © 2010 John Wiley & Sons, Ltd.     

Limiting equilibrium versus BS3D analysis of a tetrahedral rock block

In order to analyze the stability of a 3D rock block using a limiting equilibrium method, some simplifications must be introduced, such as neglecting the effects of deformability of the rock block, fractures, and the surrounding rock mass, the progressive failure and the mobilization of shear strength of fractures, and changes in in situ stresses with block displacement. These limitations may cause some errors when calculating the factor of safety of the block. This paper quantifies the error caused by these simplifications comparing the results against those obtained with a numerical method (BS3D). In addition, the effects of the normal stiffness of the fractures, dilatancy, the tunnel radius, and the block size on stability of the tetrahedron are investigated using the numerical tool to demonstrate the importance of the effects eliminated by the limiting equilibrium approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Assessment of Soil Erosion Susceptibility Using Empirical Modeling

Soil erosion is one of the most serious land degradation problems all over the world,causing irreversible land quality reduction.In this paper,we modify the Revised Universal Soil Loss Equation(RUSLE) model by replacing the factors of slope length and gradient with Sediment Transport Index(STI).The Digital Elevation Model,terrain parameters,Normalized Difference Vegetation Index(NDVI),and rainfall data are used as inputs to the model.Along with the application of remote sensing techniques and ground survey measurements,erosion susceptibility maps are produced.The revised models are then used to obtain the optimal estimate of soil erosion susceptibility at Alianello of southern Italy,which is prone to soil erosion.The soil loss estimated from the modified RUSLE model shows a large spatial variance,ranging from 10 to as much as 7000 ton ha 1 yr 1.The high erosion susceptible area constitutes about 46.8% of the total erosion area,and when classified by land cover type,33% is "mixed bare with shrubs and grass",followed by 5.29% of "mixture of shrubs and trees",with "shrubs" having the lowest percentage of 0.06%.In terms of slope types,very steep slope accounts for a total of 40.90% and belongs to high susceptibility,whereas flat slope accounts for only 0.12%,indicating that flat topography has little effect on the erosion hazard.As far as the geomorphologic types are concerned,the type of "moderate steep-steep slopes with moderate to severe erosion" is most favorable to high soil erosion,which comprises about 9.34%.Finally,we validate the soil erosion map from the adapted RUSLE model against the visual interpretation map,and find a similarity degree of 71.9%,reflecting the efficiency of the adapted RUSLE model in mapping the soil erosion in this study area.     

Rate-independent fracture toughness of gray and black kerogen-rich shales

The objective of this investigation is to characterize the influence of the loading rate, scratch speed, mineralogy, morphology, anisotropy, and total organic content on the scratch toughness of organic-rich shale. We focus our study on a gray shale, Toarcian shale (Paris basin, France) and a black shale, Niobrara shale (northeastern Colorado, USA). Microscopic scratch tests are performed for varying scratch speeds and loading rates. We consider several orientations for scratch testing. For all gas shale specimens, the scratch toughness is found to increase with increasing scratch speed. In the asymptotic regime of high speeds, there is a convergence toward a single constant value irrespective of the loading rate. To understand this evolution of the scratch toughness, a nonlinear fracture mechanics model is built that integrates fracture dissipation with the various forms of viscous processes. In particular, a coupling is shown between the fracture energy and the viscoelastic characteristics. An inverse approach which combines scratch and indentation testing makes it possible to represent all tests in a single curve and retrieve the rate-independent fracture toughness of kerogen-rich shale materials. The presence of organic matter drastically alters the creep and fracture properties at the microscopic length-scale. The fracture behavior is anisotropic with the divider orientation yielding the highest fracture toughness value and the short transverse orientation yielding the lowest fracture toughness. Elucidating the fracture-composition-morphology relationships in organic-rich shale will promote advances in science and engineering for energy-related applications such as hydraulic fracturing in unconventional reservoirs or \(\hbox {CO}_2\) sequestration in depleted reservoirs.