Microplane damage model for jointed rock masses

Abstract

The paper presents a new microplane constitutive model for the inelastic behavior of jointed rock masses that takes into account the mechanical behavior and geometric characteristics of cracks and joints. The basic idea is that the microplane modeling of rock masses under general triaxial loading, including compression, requires the isotropic rock matrix and the joints to be considered as two distinct phases coupled in parallel. A joint continuity factor is defined as a microplane damage variable to represent the stress-carrying area fraction of the joint phase. Based on the assumption of parallel coupling between the rock joint and the rock matrix, the overall mechanical behavior of the rock is characterized by microplane constitutive laws for the rock matrix and for the rock joints, along with an evolution law for the microplane joint continuity factor. The inelastic response of the rock matrix and the rock joints is controlled on the microplane level by the stress-strain boundaries. Based on the arguments enunciated in developing the new microplane model M7 for concrete, the previously used volumetric-deviatoric splits of the elastic strains and of the tensile boundary are avoided. The boundaries are tensile normal, compressive normal, and shear. The numerical simulations demonstrate satisfactory fits of published triaxial test data on sandstone and on jointed plaster mortar, including quintessential features such as the strain softening and dilatancy under low confining pressure, as well as the brittle-ductile transition under higher confining pressure, and the decrease of jointed rock strength and Young's modulus with an increasing dip angle of the joint.This leads to the following basic relation between the macrocontinuum stress tensor and the microplane stresses of the rock mass: MICROPLANE DAMAGE MODEL FOR JOINTED ROCK MASSES Figure 12. The normal stress on the microplane μ = 7 versus axial strain: (a) p = 10 MPa, (b) p = 30 MPa, (c) p = 60 MPa, and (d) p = 100 MPa. Figure 13. The shear stress on the microplane μ = 7 versus axial strain: (a) p = 10 MPa, (b) p = 30 MPa, (c) p = 60 MPa, and (d) p = 100 MPa. MICROPLANE DAMAGE MODEL FOR JOINTED ROCK MASSES

Spectral stiffness microplane model for damage and fracture of textile composites

“…Since its introduction in the early 1980s, the microplane model for concrete has evolved through 7 progressively improved versions labeled as M1 [29,30], M2 [31], M3 [32], M4 [33,34], M5 [35], M6 [36], M7 [37] and it has been recently adopted for the simulation of concrete at early age [38]. Microplane models have also been developed for other complex materials such as jointed rock [39], sand, clay, rigid foam, shape memory alloys, and unidirectional and textile composites [23,24,[40][41][42][43][44]. A high order microplane model [45] was also derived recently on the basis of an underlying discrete model [46,47].…”

Study on fracture behavior of molars based on three‐dimensional high‐precision computerized tomography scanning and numerical simulation

“…Based on the two‐dimensional numerical model of a digital image, a 3D meshed material structure model was established by superimposing a certain thickness of the representative image identified form each section, as shown in Figure 5A. For the solid continuous heterogeneous material, it has been assumed that an image slice represents the microstructure of the material with a small thickness t 30–33 …”

Spherocylindrical microplane constitutive model for shale and other anisotropic rocks

“…The microplane model has been progressively improved for concrete through versions M1, M2, ...M7 (Bažant and Oh, 1985;Bažant and Prat, 1988;Bažant et al, 1996Bažant et al, , 2000bBažant and Caner, 2005;Bažant, 2011, 2013) and has recently been widely applied in finite element analysis (Bažant et al, 2000a;Caner and Bažant, 2014, e.g.). It was also adapted to other isotropic randomly heterogeneous quasibrittle materials, particularly rocks (Bažant and Zi, 2003;Chen and Bažant, 2014) and clays (Bažant and Kim, 1986;Bažant and Prat, 1987). The thermodynamic restrictions of microplane model M7 have been elucidated in (Bažant and Caner, 2014).…”