The Hoek–Brown failure criterion and GSI – 2018 edition

The Hoek–Brown criterion was introduced in 1980 to provide input for the design of underground excavations in rock. The criterion now incorporates both intact rock and discontinuities, such as joints, characterized by the geological strength index (GSI), into a system designed to estimate the mechanical behaviour of typical rock masses encountered in tunnels, slopes and foundations. The strength and deformation properties of intact rock, derived from laboratory tests, are reduced based on the properties of discontinuities in the rock mass. The nonlinear Hoek–Brown criterion for rock masses is widely accepted and has been applied in many projects around the world. While, in general, it has been found to provide satisfactory estimates, there are several questions on the limits of its applicability and on the inaccuracies related to the quality of the input data. This paper introduces relatively few fundamental changes, but it does discuss many of the issues of utilization and presents case histories to demonstrate practical applications of the criterion and the GSI system.     

Study of failure mechanisms of rock under compressive–shear loading using real-time laser holography

Failure of rock is quite commonly induced by compressive and shear coupling loading. The knowledge of the mechanism and process of deformation and failure of rock under compressive–shear loading condition is an important basis for the study of stability of rock engineering. Based on the principles of laser holographic interferometry, an experimental system with high precision has been established. Through the experiment, the real-time laser holographic interferential fringes under compressive–shear loading are simultaneously observed and recorded. The active fringes can visually display the distribution, mode, moving path and dynamic evolution of deformation and cracking in rock. On the basis of interpretation and quantitative analysis of the active fringes, the whole process of deformation and failure of rock, including time–spatial evolution law of initiating, propagating, growing and closing of cracks in rock, is quantitatively described. From the experimental results, some conclusions on the mechanism and characters of deformation and failure of rock under compressive–shear loading condition are drawn out.     

Correlation of the Hoek–Brown failure criterion for a sparsely jointed rock mass with an extended plane of weakness theory

An appropriate estimate of rock mass strength is necessary for the design of civil and mining structures built in or on rock. Rock mass is an inhomogeneous and anisotropic material with complex behaviour, which contains random planes of discontinuities that tend to reduce its strength. The direct estimation of this strength is practically unfeasible, due to difficulties in sampling and testing. This has led to the development of empirical failure criteria. These, express the strength of the rock mass in terms of properties of the intact rock and the discontinuities. The Hoek–Brown criterion is the most widely accepted one. However, albeit its use for many years, no experimental in situ validation with the actual rock mass strength has been demonstrated. Therefore, the Hoek–Brown criterion is investigated analytically through an extended plane of weakness theory, already validated with experimental evidence on physical specimens. Various intact rock qualities with blocky and very blocky structure are examined. The results indicate deviations in the rock mass strength predicted by the two approaches, especially when the intact rock strength is low.     

Sand–concrete interface response: The role of surface texture and confinement conditions

Sand–concrete interface direct shear tests were used to investigate the effects of surface roughness, surface waviness, mean sand diameter and relative density on interface strength and behavior under different confinement conditions. Extreme concrete surface textures, including smooth, rough and rough–wavy textures, were reproduced. Surface plowing was assessed via image analysis, laser scanning and extended multifocal micrographs. The experimental results showed that smooth concrete surfaces exhibited high values of interfacial–to–internal friction angle ratios, ranging 88–90%, due to the angular shape of sand particles. The rough concrete surfaces generated higher interface strength than smooth concrete surfaces; however, the interface strength was still inferior to the surrounding sand strength. Surface plowing, which identified a mixed shear plane at the sand–concrete interface, was developed as particles were detached from the surface, thus inhibiting the interface friction angle from reaching the sand friction angle. Higher sand–concrete interface strength was achieved as surface waviness increased, and interface friction angles greater than the surrounding sand friction angle were reached. Under a constant normal stiffness condition, significantly high interface strength is achieved due to the increase of the current normal stress, which was directly influenced by the initial normal stress, stiffness, surface roughness, mean sand diameter and relative density; surface waviness did not have a marked effect on the normal stress variation. Based on these results, multiple regressions were proposed to estimate the sand–concrete interface strength by the interfacial–to–internal friction angle ratio and the effect of the constant normal stiffness condition.     

Behavior and strength of steel reinforced concrete beam–column joints with single-side force inputs

Five large-scale beam–column subassemblies were fabricated and tested under cyclic loading to investigate the behavior of SRC Type I exterior and Type II corner beam–column joints. In addition, the applicability of strength superposition method on joint shear strength was assessed. It was found that: (1) the strength superposition method was able to estimate the SRC beam–column joint shear strength with reasonable accuracy; (2) the anchorage position of beam longitudinal bars has an obvious influence on the joint shear strength and crack pattern; (3) increased depth of cross-sectional steel leads to a higher shear strength for the beam–column joint; and (4) a combination of corner stirrups and shaped steel cross-sections was able to provide sufficient lateral support to longitudinal steel bars and adequate confinement to the concrete in the joint to replace the need for closed hoops.     

Structural behavior and m–k value of composite slab utilizing concrete containing crumb rubber

Many research works have been conducted to study the fresh and hardened properties of concrete containing crumb rubber as replacement to fine aggregate. The outcome of these researches indicated that though the compressive and flexural strength of crumb rubber concrete (CRC) decreased as percentage of fine aggregate replacement increased; the CRC has lower unit weight, better slump values, better toughness and absorb more energy before failure. In view of the fact that the main strength of composite floor slab lies within the bond between the concrete and the profiled steel sheeting, therefore the using of more ductile concrete such as CRC to toping the profiled steel sheeting could produce a new composite slab system. Two sets of slabs; each set comprising three CRC composite slabs and one conventional concrete slab has been tested with two shear span (450 and 900 mm). The results showed that the CRC slabs behavior could be characterized as ductile, while the m–k value has been found to be 80.7 and 0.037, respectively.     

Numerical integration of a class of 3d plastic-damage concrete models and condensation of 3d stress–strain relations for use in beam finite elements

This paper presents a method for the integration of a class of plastic-damage material models. The integration of the evolution equations results in a nonlinear problem, which is linearized and solved with the Newton–Raphson method using a sub-stepping strategy. The consistent tangent matrix can be formulated either in terms of the stress components in a general reference system or in terms of the principal stress and strain components with the former then transformed to the general reference system. In order to account for plane stress conditions, the stress–strain relations of the 3d material model are then condensed out. Plane stress conditions are imposed by the linearization of the stresses that need to be set equal to zero; thus the strain fields are updated in the corresponding directions. This solution method is extended to include transverse pressure and the effect of transverse reinforcing steel for a 3d concrete material model. The equilibrium of the stresses in the reinforcing steel and concrete is linearized and the strain fields are updated until the residual satisfies a specified tolerance. The consistent tangent matrix due to the condensation process is derived. The proposed algorithms are tested at the material and element level by comparison of numerical solutions with available experimental data.     

Investigation into the effects of grain size on strength and failure behaviors of granites using a breakable polygonal grain–based model

Bulletin of Engineering Geology and the Environment - The microstructure of rock is one of the most important factors that affect its mechanical behaviors. In order to study the effects of grain...