Amongst many mechanical properties, cohesion (c) and angle of internal friction (φ) are probably the most widely used rock and rock-like material strength design parameters. However, unlike Mohr-Coulomb (MC) failure criterion that assumes cohesion and friction angle are intrinsic material properties and are not affected by the applied stress level, the Hoek-Brown (HB) criterion predicts a continuous change of apparent cohesion and friction angle if the induced normal stress on the fracture plane changes. That is, at low values of normal stresses, the instantaneous angle of friction will be relatively large, whereas cohesion will be a small value. As the applied normal stress value on the fracture plane increases (moving ‘up’ the non-linear Hoek-Brown strength envelope), the angle of friction reduces, and the cohesion increases. This is an important result from the HB failure model and allows a more realistic estimate of shear strength to be made at low values of normal stress, preventing potential over-design problems. Nevertheless, the HB model neglects the effect of the intermediate principal stress on material properties. Limited studies on the variation of apparent cohesion and friction angle under polyaxial stresses in concrete are available in the literature. Therefore, this paper aims to investigate the effect of true triaxial stresses on concrete cohesion and friction angle using a polyaxial strength criterion developed by Mogi. The results of concrete show that the intermediate principal stress has a pronounced effect on cohesion degradation and the mobilization of internal friction angle as the ratio of the intermediate to the minor principal stress changes. The results are expected to provide a framework for a more realistic design of underground concrete structures at depth.
Proper and reliable estimation of rock, concrete and rock-like material strength and deformation characteristics are necessary to develop a safe and sustainable design for open-pit mines, rock slopes, foundations, tunnels, and underground excavations. The most widely used mechanical parameters to characterize the material strength parameter are cohesion (c) and angle of internal friction (φ). One of the earliest and widely adopted failure criteria in rock mechanics solely based on c and φ is Mohr-Coulomb [1]. In 1776, the basis of Coulomb failure criterion was introduced on the assumption that rock failure in compression occurs when the shear stress (τ) on an arbitrarily oriented failure plane inside the rock mass becomes sufficiently large to overcome the rock cohesion and the frictional force that opposes the sliding motion and shear displacement on that plane [2]. The MC model is simply a linear shear-based strength relationship describing the failure of intact rock (or a smooth joint) under the major (σ1) and minor (σ3) principal stresses, but also has representation in the form of normal (σn) and shear stresses (τ) acting on the fracture plane or the joint surface [3, 4]. Despite the success of the MC criterion in rock engineering, it has several practical shortcomings. For instance, the MC model (i) ignores the non-linear response of rock especially under high confinements, (ii) neglects the effect of the intermediate principal stress (σ2), (iii) assumes that cohesion and friction angle are intrinsic material properties and are not affected by the applied stress level, (iv) postulates that both cohesion and friction angle acts simultaneously during the rock progressive yield process, and (v) overestimates tensile strength of rock and discontinuities [5, 6, 7, 8]. Over the past 250 years or so since the introduction of Coulomb failure theory, many researchers have attempted to develop new rock failure criteria and address the limitations of previously available models. To overcome the above difficulties with the MC model, the well-known Hoek-Brown (HB) failure criterion was introduced in the early 1990s and derived from the results of intact rock failure conducted by Hoek on a model of jointed rock mass studies carried by Brown [9]. [10] suggested that the cohesive strength estimated from the linear MC tends to overestimate the actual rock strength. Unlike the MC failure criterion, the HB criterion predicts a continuous change of apparent cohesion and friction angle as the induced normal stress on the fracture plane changes. That is, at lower normal stresses, the instantaneous angle of internal friction is relatively large. By moving up the HB strength envelope, the applied normal stress value on the fracture plane increases, and therefore the angle of friction reduces while the cohesion increases This is an important result of the HB model which allows a more realistic estimate of rock shear strength to be made at low values of normal stresses, preventing potential over-design problems. Nevertheless, the HB model: (i) neglects the effect of the intermediate principal stress on rock strength properties, (ii) overestimates rock strength at low confinements (usually σ3< 10% UCS) where spalling and rockburst can occur in high-stress deep mines, and (iii) is incapable of capturing strength-hardening at high confinements thus underestimates rock mass strength at confinements above a critical threshold. The fundamental HB assumption of σ2 = σ3 is therefore only valid for a limited range of (rock-dependant) confining stresses between the two critical values above in (ii) and (iii). To resolve the second problem with the HB model, in particular, a non-linear Cohesion Weakening Friction Strengthening (CWFS) model is becoming popular in recent years [11, 12] to capture more reliably the process of brittle failure at laboratory and field scales where cohesion degrades and friction angle mobilizes while damage accumulates in brittle rocks. The CWFS model emphasizes that using straight lines for cohesion degradation and friction mobilization (as a function of plastic strain) can provide an implausible stress-strain curve, hence a smooth curve for the degradation of cohesion and mobilization of friction is suggested where both parameters change simultaneously depending on the loading rate. However, the CWFS model is yet a two-dimensional framework, and one needs to adopt a more appropriate 3D model, e.g. Lade-Duncan, Wiebols and Cook, 3D Hoek-Brown, Mogi–Coulomb, Matsuoka-Nakai, Tridimensional Griffith, von Mises, and Stassi-D’Alia, among others; for the study of cohesion and friction angle variation under true triaxial stresses.