Report of work carried out January- December 2005 Project Report 1
Microscope Rock Texture Characterization and Simulation of Rock Aggregate Properties SGU project 60-1362/2004
Hongyuan Liu, Shaoquan Kou and Per-Arne Lindqvist
Department of Civil & Environmental Engineering Luleå University of Technology (LTU)
Jan Erik Lindqvist and Urban Åkesson
Department of Building Technology and Mechanics Swedish National Testing and Research Institute (SP)
December 2005
Table of Contents Abstract ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ III 1. Introduction ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 1 2. Literature review on the relationship between the textural and mechanical properties of rock aggregates ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 1 2.1. Assessment of rock aggregate texture properties ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 2 2.2. Assessment of rock aggregate mechanical properties ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 2 2.2.1. Fundamental mechanical tests ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 2 2.2.2. Rock aggregate tests ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 3 2.3. Relationship between texture and mechanical properties of rock aggregates ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 5 2.3.1. Influence of textural properties on the strength of rock aggregates in fundamental mechanical tests ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 6 2.3.2. Influence of textural properties on the fragmentation and abrasion properties in rock aggregate tests ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 18 3. Characterization of rock textures ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅26 3.1. Rock material⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅26 3.2. Sample preparation⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅26 3.3. Grain size distribution⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅26 3.4. Characterization of micro cracks⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅27 3.5. Characterization of perimeters⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅36 4. Mechanical tests of rock properties ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅36 4.1. Fundamental mechanical tests – UCS and BTS ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 36 4.2. Rock aggregate test – DSC ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 38 5. Numerical simulation of rock aggregate breakage properties ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 39 5.1. Microstructural modelling of rock aggregate breakage properties ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 40 5.1.1. Microstructure observation, image analaysis and microstructural modelling ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 40 5.1.2. Calibration of the microstructural modelling ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 45 5.1.3. Modelling of single aggregate breakages under typical loading conditions ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 50 5.2. Micromechanical modelling of rock aggregate breakage properties ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 62 5.2.1. Micromechanical model for characterizing rock aggregate textural properties ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 62 5.2.2. Modelling of single aggregate breakages under typical loading conditions ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 67 5.2.3. Modelling of multiple aggregate breakages in Dutch Static Compressive (DSC) tests ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 76 6. Correlations between the Dutch Static Compression (DSC) test and the Los Angeles (LA) test ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 80 7. Discussion ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 81 7.1. Microstructural modelling VS micromechanical modelling ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 81 7.2. Relationship between textural and mechanical properties of rock aggregates ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 83 7.3. Correlation between the numerical modelling and the standard rock aggregate test ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 85 8. Conclusions ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 86 Acknowledgement ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 88 References ⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅ 89
II
Abstract
The literature review on the relationship between the textural properties and mechanical properties of rock aggregates indicates that most studies investigated the relationship in two separate processes, i.e. microscope observations and mechanical tests, and then correlate the mechanical properties with one of textural properties indirectly using various regression models. Samples of three granites with similar mineral content but varying mechanical properties are investigated by microscope texture quantification including image analysis followed by rock mechanics testing and rock aggregate testing in the laboratory. Computer simulation of rock mechanics properties, of strength of single aggregate particles and fracture of multiple particles in a cylindrical chamber (DSC test) is then made. Finally computer simulations are compared of with tumbling mill tests (LA test) through results from previous research. This study uses numerical modelling as a main tool to directly investigate the relationships, i.e. from the physical mechanisms’ point of view and taking major textural properties into consideration. Two main modelling methods, i.e. microstructural modelling and micromechanical modelling are implemented. In the microstructural modelling, the numerical simulation model is built on the basis of rock microstructure. In the micromechanical modelling, the model is constructed on the basis of the Weibull theory. The modelled results from single particle tests of three granites, i.e. Ävja, LEP and Vändle under BTS, point-to-point, plane-to-plane, point-to-plane and multiple-point loading conditions using microstructural modelling and micromechanical modelling show that Ävja is weaker than LEP and Vändle in terms of the aggregate tensile strength and applied work. The microstructural modelling also reveals that LEP is weaker than Vändle but the micromechanical modelling indicates that LEP and Vändle have similar mechanical properties. From this work it is concluded that microscope texture quantification and computer simulation is a promising approach to analyse mechanical properties of rock aggregates. Numerical modelling of the DSC test shows the potential to simulate multi particle chamber compression tests for assessment of rock aggregate quality. In general, the texture properties work together to influence the mechanical properties of rock aggregates. Computer simulation using a heterogeneous material model provides a valuable tool to investigate the relationship between the textural properties and mechanical properties of rock aggregates by taking main textural properties into consideration. In particular, for the three rocks in this study, micro crack size distribution, grain perimeter and grain size show strong correlations with the mechanical properties, e.g. for DSC strength: cracks and grain size negatively affect the mechanical properties but the perimeter positively influences the mechanical properties.
Keywords: Microstructural modelling, Micromechanical modelling, Rock aggregate, Breakage, Texture property, Mechanical property, Microscopic observation, Image Analysis
III 1. Introduction
Rock aggregate products are essential for our infrastructure and the society as a whole. Rock aggregates are used for road and railroad construction and for the manufacture of asphalt and concrete. In 2003 more than 75 million tons were produced in Sweden to a value of 450 million Euros (Sveriges Bergmaterialindustri, 2004). The availability of high quality, low cost, environmentally friendly rock aggregates and recirculation of materials is important for the development of a sustainable society. The relative amount of crushed bedrock is steadily increasing due to joint efforts by the authorities and industry in order to save natural gravel. During 2004 the amount of crushed bedrock was around 73 % of the total usage of aggregates (Sveriges Geologiska Undersökning, 2004). One activity to increase the use of crushed bedrock is the production of rock quality maps by the Swedish Geological Survey (Persson & Schouenborg, 1996). This study is aimed to support the goal to reduce natural gavel. The literature review, which will be conducted in Section 2, on the relationship between the textural and mechanical properties of rock aggregates, made by previous researchers, indicates that in most studies, the relationship is obtained from two separate processes: on one hand, the textural properties of rock aggregates are gathered through microscopic observations and image analyses, on the other hand, the mechanical properties are measured by laboratory mechanical tests. Finally, the two data groups are correlated using statistical single- or multiple- variable regression analyses. Till this moment, few studies investigated the relationship between the textural and mechanical properties of rock aggregates from the mechanics point of view since the problem is too complicated. Recently, with the rapid development of computing power, interactive computer graphics and topological data structure, a powerful technique, numerical simulation, has made it possible to investigate the relationship from the mechanics point of view. In this study, firstly, samples of three granite rocks are taken with similar mineralogy and grain size but with different mechanical properties. Secondly, the texture of the rocks is characterized using quantitative microscopy and image analysis techniques developed at Swedish National Testing and Research Institute (SP). Thirdly, with the obtained textural parameters as input parameters, the mechanical properties of rocks will be modelled using the rock and tool interaction code (R-T2D) applying a heterogeneous material developed at Luleå University of Technology. The primary goal of the study is to evaluate the approach to use microscope quantification methods and computer simulation. Positive results will hopefully make it possible to improve present geological methods for quality assessment and classification of rocks.
2. Literature review on the relationship between the textural and mechanical properties of rock aggregates
Investigation of the textural properties and mechanical properties of rock aggregates has occupied many researchers in recent years. The relationship between rock textural and mechanical properties has however not received the same prominence in the literature as the engineering aspects. This literature review has been written with a view to gathering together the salient publications regarding the relationship between the textural and mechanical properties of rock aggregates. In this section, firstly the various textural properties likely to influence the aggregate mechanical properties are indicated together with methods used to measure them. Then the
1 methods used to assess the rock aggregate potential performance are described. Finally, the relationship between the textural and mechanical properties of rock aggregates is reviewed.
2.1. Assessment of rock aggregate texture properties
Rock texture has been defined as “the degree of crystallinity, grain size or granularity and the fabric or geometrical relationship between the constituents of a rock” (Williams et al, 1982). Therefore, the texture properties mainly refer to the grain size, grain shape, degree of grain orientation, packing density, relative proportion of grains, texture coefficient, mineral content, matrix material and type, cement type and degree of cementation, porosity, grain boundary or grain contact relationships, and bonding structure (Ersoy and Waller, 1995). The texture properties which affect the performance of rock aggregates are mainly: 1) the type, size, shape and proportions of the mineral grains; 2) the relative orientation and arrangement of the minerals; and 3) the occurrence and distribution of fossils and of metallic ore inclusions within the rock (Hartley, 1974). Therefore, in this study the textural properties of rock are mainly assessed using the following texture parameters: 1) Mineral composition, 2) grain size, 3) grain shape, 4) grain spatial arrangement, 5) porosity and 6) crack. Those texture parameters are usually obtained using quantitative microscopy and image analysis. Lindqvist and Åkesson (2001), Lindqvist et al (2003) and Åkesson (2004) introduced in detail how to assess the textural properties using quantitative microscopy and image analysis. Therefore, the assessment of rock aggregate texture properties will not be reviewed here again.
2.2. Assessment of rock aggregate mechanical properties
Knowledge of the mechanical properties of rock aggregates is essential to the performance of rock aggregates. As the rock aggregates are often obtained from bedrock, mechanical tests on the parent rock can give an indication of the likely mechanical properties of the aggregates. Such mechanical tests of rock are usually determined according to the International Society of Rock Mechanics (ISRM) suggested methods, such as uniaxial compressive test and Brazilian tensile test. However, fundamental mechanical tests such as those described above are not generally used as a method to assess the potential of rock aggregates due to their poor reproducibility (Hartley, 1974). The effects of variability of individually prepared specimens have been reduced by the introduction of aggregate tests using specimens composed of a number of pieces of the aggregate, such as Dutch static compressive test, Los Angeles test and Studded tyre test.
2.2.1 Fundamental mechanical tests
Uniaxial compressive test Uniaxial compressive strength (UCS) is the most widely used index of the strength, deformation and fracture characteristics of rock. The UCS is characterised by loading a cylindrical specimen with a diameter of approximate 54 mm and a length to diameter of 2,5:1 axially until the specimen fails. The strength of the rock is given by ISRM (1979) as following: P σ = max c A where σ c is UCS of the rock, Pmax is the peak load and A is the initial cross-sectional area of specimen. Correspondingly, Young’s modulus can be calculated as the ratio between the axial stress change and the axial strain change. Poisson’s ration is the negative ratio between the slope of axial stress-strain curve and the slope of the diametric stress-strain curve.
2
Brazilian tensile strength test The tensile strength of rock is usually obtained through Brazilian test. The Brazilian test consists of loading a disc with a diameter of approximate 54 mm and a thickness to diameter ratio of 1:2 of the rock using two curved jaws until failure occurs across the diametrical axis (ISRM, 1978). The Brazilian tensile strength of the specimen is calculated from the formula: 2P σ = max t πDt where Pmax is the peak load, D is the diameter of the test specimen and t is the thickness.
Other tests The other fundamental mechanical tests includes point load tests (ISRM, 1985), triaxial compressive test (ISRM, 1978), hardness test (ISRM, 1981) etc. Here just the point load test is introduced since it is a simple and economical index test for predicting the unconfined compressive strength of rock material both in the laboratory and in situ. It induces failure in tension and can be used to obtain a measure of both tensile and uniaxial compressive strength. The point load strength is calculated as (ISRM, 1985) 0.45 ⎛ De ⎞ Pmax I s(50) = F × I s = ⎜ ⎟ × 2 ⎝ 50 ⎠ De where De is the equivalent core diameter and Pmax is the peak load.
2.2.2. Rock aggregate tests
Los Angeles test (LA) The Los Angeles test determines the resistance of an aggregate to fragmentation. According to the EN1097-2 (European Committee for Standardization, 1997) method, the 5000 ± 5g sample (10 to 14 mm fraction) is placed in a steel drum with eleven 45 to 49 mm steel balls (total weight 400-445g). The drum rotates 500 revolutions (31-33 rpm). After the test, the crushed material is sieved through a 1.6 mm sieve and the Los Angeles value is calculated according to the formula: LA = 5000 − m / 50 where m is the weight of the material retained after 1.6 mm sieving.
Studded tyre test (STT) and aggregate abrasion value II (AAV-II) test The studded tyre test measures a rock aggregate’s resistance to abrasion. According to the EN1097-9 (European Committee for Standardization, 1997) method, the samples consisted of approximately 1000g of sieved rock aggregate (depending on the rock density), of which 65% was 11.2-14.0 mm and 35% between 14.0 and 16.0 mm. The samples were placed in a steel cylinder with an inner diameter of 206.5 ± 2 mm and an inner length of 335 ± 1 mm together with 7000 ± 1g of steel bullets (around 500 bullets with a diameter of 15 mm) and 2000 ± 10 ml of water. The cylinder was rotated at a speed of 90 ± 3 r/min for 60 min. The material was then sieved through 14, 8 and 2 mm sieves. The studded tyre test value is calculated according to the formula
STT =100()mi − m2 mi where mi is the weight of the material before analysis and m2 is the part of the analysed material that is larger than 2 mm.
3 In Sweden, the studded tyre test is also called the abrasion value II test according to FAS 259-98 method (Swedish Asphalt Pavement Association, 1998, reported in Miskovsky et al, 2003). Length-thickness (LT) index test and flakiness index test The geometry of the aggregates was determined through the length-thickness index (LT- index) on the crushed material. The LT-3 value was used by Åkesson et al (2003) to measure the shape of the aggregate particles with sizes of 11.2-16.0 mm. The LT-3 value means the percentage of aggregate particles that are less than three times longer than their thickness. The geometry of the aggregates after the rock material has been fragmented can also be determined using the flakiness index test according to the EN933-3 (European Committee for Standardization, 1997) method, which corresponds to the FAS 209-98 (Swedish Asphalt Pavement Association, 1998, reported in Miskovsky et al, 2003) method. The flakiness index varies from 1 to 2 and the low flakiness index refers to cube-like form of the particles. Thin or elongated rock aggregates fragment more easily than cubical aggregates.
Aggregate impact value (AIV) test and brittleness test According to the FAS 210-98 method (Swedish Asphalt Pavement Association, 1998, reported in Huang, 1999 and Miskovsky et al, 2003), a standard sample in size range 5.6-8 mm, 8-11.2 mm, or 11.2-16 mm is subjected to blows from a standardised hammer. The sample suffers degradation to a graded assemblage of fines. A sieve size of the lower fraction limit in the samples above (5.6, 8 or 11.2 mm) is chosen as the diagnostic cut-off level, ad the percentage of material passing, relative to the initial weight, gives the Swedish aggregate impact value. This is used as the measure of resistance to granulation. A low numerical value indicates a more resistant rock. The brittleness test is also a measure of resistance to wear by impact, which gives a good measure of the ability of the rock to resist crushing by repeated impacts. The brittleness test is aggregate impact testing of the fraction 11.2-16 mm (Gertsch et al, 2000). The brittleness value is defined as the percentage of the original test material that passes 11.2 mm mesh after the aggregate has been crushed by 20 impacts of the falling weight. The brittleness value is usually the mean value of 3 to 5 parallel tests and a lower numerical value indicates a more resistant rock to impact.
Aggregate abrasion value I (AAV-I) test Aggregate abrasion value I test provides an estimate of surface wear (Huang, 1999; Miskovsky et al, 2003). Clean 8-11.2 mm material is set into an epoxy backing. The sample is held against a rotating lap for some 500 revolutions. Abrasion power is fed in front of the sample. The weight of the original sample minus the loss in weight during the test, all divided by the density of the sample, gives the Swedish abrasion value I. A lower numerical value indicates a more resistant rock. The aggregate abrasion value I test is somewhat like the sandblast testing (Verhoef, 1987) of rock in rock mechanics.
Other tests Other aggregate tests include the crushing test (Evertsson, 2000), Dutch static compressive test (Ballmann et al, 1997), durability value test (Brattli, 1992), aggregate crushing value (ACV) test (British Standards Institution, 1990, reported in Al-Harthi, 2001), aggregate impact value (AIV) test (British Standards Institution, 1990, reported in Al-Harthi, 2001), polished stone value test (British Standards Institution, 1990, reported in French et al, 2001), etc. Here, just the crushing test developed at Chalmers University of Technology, which is similar to the Dutch static compressive test to be introduced and used in this study
4 later, is introduced. In the crushing test, i.e. single particle breakage test and inter-particle breakage test, the rock materials with a size of 16-19 mm are crushed in a steel cylinder under form conditions. The tests are performed in five to six different series, each with a constant compression ratio (10%, 15%, 20%, 25% and 30% for the single particle breakage test, and 10%, 15%, 20%, 25%, 30% and 35% for the inter-particle breakage test). The first tests in each series are done on a mono-size material of fraction 16-19 mm. The remaining tests are done on the material originating from preceding tests. After every compression test, the material is sieved to obtain the fragment size distribution.
2.3. Relationship between textural and mechanical properties of rock aggregates
In recent years, many researchers have focused on the relationship between textural and mechanical properties of rocks. The mechanical properties of rock aggregates are a function of the textural properties. In other words, the textural properties of rock aggregates significantly affect their mechanical performance. Early works on texture properties that affect the mechanical properties have been presented by a great number of authors (Brace, 1961; Mendes et al, 1966; Willard and McWilliams, 1969; Merriam et al, 1970; Smordinov et al, 1970; Ehrlich and Weinberg, 1970; Dube and Singh, 1972; Dunn et al, 1973; Hoshino, 1974; Olsson, 1974; Bell, 1978; Fahy and Irfan and Dearman, 1978; Guccione, 1979; Hugman and Friedman, 1979; Onodera and Asoka, 1980; Barret, 1980; West, 1981 and 1986; Kendall et al, 1983; Alm et al, 1985; Kelsall et al, 1986; Howarth and Rowlands, 1986 and 1987). Most of the studies above investigated the influence of textural properties including mineral composition, porosity, grain shape and size on the strength of rock. For example, Brace (1961) found that the strength of rocks was greater for finer grained rocks. Mendes et al (1966) proposed that quantitative micropetrographic data could be used to formulate rock quality indices, which could be closely correlated with mechanical characteristics. They made a modal analysis of the mineralogical composition of the granite samples, together with an analysis of their texture and microstructure, and demonstrated that petrographic characteristics had a good correlation with the mechanical properties. Willard and McWilliams (1969) developed a number of petrofabric techniques in an attempt to gain a better understanding of the mechanical behaviour of rocks in relation to their micro-structure. They reported that microfractures, grain boundaries, mineral cleavages and twinning planes influence the ultimate strength of a rock and may act as surfaces of weakness, which control the direction in which failure occurs. Merriam et al (1970) found a definite relationship between the quartz content and the tensile strength of granitic rocks they investigated. Olsson (1974) studied the yield stress of marble and showed that it increases linearly with the inverse square root of the mean grain size. Irfan and Dearman (1978) developed a quantitative method of assessing the grade of weathering of granite in terms of its microscopic petrography. They proposed a micropetrographic index as a percentage ratio of sound constituents to unsound constituents. They found good correlation between the micropetrographic index and the geomechanical properties of granitic rocks. Hugman and Friedman (1979) found that weighted mean grain size (in carbonates) and micrite content (in limestones) have the highest linear correlation coefficient with ultimate strength. Onodera and Asoka (1980) reported that the strength decreased significantly as the grain size increased in igneous rocks. They determined a linear relationship between the grain size and strength, that is, as the grain size of the granite decreased, the strength increased. The early studies on the influence of texture properties on the mechanical properties, especially the strength and the resistance to fragmentation and abrasion, of rock aggregates are reviewed by Hartley (1974) in a general way. The purpose of this section is to review the
5 specific investigations on the relationship between the textural properties and mechanical properties conducted recently, especially after 1990s.
2.3.1 Influence of textural properties on the strength of rock aggregates in fundamental mechanical tests
Strength is one of the most important mechanical properties of rock aggregates evaluated in rock mechanics and in building-stone testing.
Fig. 1 Relationships between: a) the uniaxial compressive strength and quartz to feldspar ratio, and b) the tensile strength and the quartz to feldspar ratio in the granitic rocks (Tugrual and Zarif, 1999)
Tugrul and Zarif (1999) determined the relationship between the mineral composition and the uniaxial compressive strength as well as the tensile strength of the granitic rocks using simple regression analyses. The relationship and the correlation coefficient are shown in Fig. 1. According to the figure, there is a linear relationship between the quartz to feldspar ratio and uniaxial compressive strength, as well as tensile strength of the granitic rocks. Because the degree of alteration of feldspar affects this ratio, these relationships are not significant at a 95% confidence level. The relationship between the percentage of the main minerals (quartz, plagioclase, K-feldspar, biotite and amphibole) in the granitic rocks and the uniaxial compressive strength is given in Fig. 2. As can be seen from the figure, in many samples of the granitic rocks, the feldspars have a very important role in strength reduction. The presence of mineral cleavage and microfissures in feldspars within the intact specimen also lowers the tensile strength as it lowers the compressive strength (Onodera and Asoka, 1980). Moreover, according to Fig. 1, the strength increases as the quartz content increases, except in some samples, although quartz rich rock texture is characterized by little intergrowth or interlocking of grains. The reason why the abundance of quartz can result in higher strength is that as much as quartz has little or no cleavage and quartz fills the spaces between the other constituents. However, there have been conflicting results about the effect of mineral composition on rock strength (Howarth and Rowlands, 1986). Some researchers (Gunsallus and Kullhawy, 1984; Tugrul and Zarif, 1999) found a strong positive correlation between quartz content and compressive strength. In contrary to this, other researchers (Bell, 1978; Fahy and Guccione, 1979; Shakoor and Bonelli, 1991) did not find any significant relationship between the quartz content and the strength of different sandstones. Therefore,
6 the types of grain contact are more important than the total amount of quartz, which will be discussed later.
Fig. 2 Relationship between the percentage of minerals and the uniaxial compressive strength of the granitic rocks (Tugrul and Zarif, 1999)
Fig. 3 Relationship between the uniaxial compressive strength and the average grain size for Yuen Long marbles (Wong et al, 1996)
Fig. 4 Relationship between the maximum7 grain size and the uniaxial compressive strength of granitic rocks (Tugrul and Zarif, 1999)
Fig. 5 Uniaxial compressive strength versus mean grain size of granitic rocks (Tugrul and Zarif, 1999) a) Quartz b) Plagioclase c) K-Feldspar
Fig. 6 Relationship between strength (stress difference in triaxial tests) and grain size: ◊ = stress different at crack initiation; □ = peak stress difference, a) maximum grain size measured using petrographic microscope, b) mean grain size measured using SEM (Hatzor et al, 1997)
The Griffith’s fracture criterion forms the theoretical basis for the correlation between strength and grain size, which can be generalized in the following form (Atkinson, 1987)
8 K = Yσ πc where K is a general stress intensity factor, σ is the remote applied stress, Y is a numerical modification factor which accounts for crack geometry, loading conditions and edge effects, and c is half crack length. In this criterion stress intensity is directly proportional to the square root of the initial flaw size, and hence the expected correlation between strength and grain size. The relationship is validated by a lot of experimental studies conducted by numerous researchers in various kinds of rocks, for example, by Brace (1961) for quartzite, Brace (1964) for delomite and limestone, by Olsson (1974) for marble, and Fredrich et al (1990) for calcite marble and limestone. Recently, Wong et al (1996) experimentally and theoretically investigated the grain size effect on the peak strength of Yuen Long marbles, as shown in Fig. 3. It is evident that the UCS decreases inversely with the square root of the average grain size. The correlation coefficient is as high as 0.98. In the figure, the experimentally observed UCS is denoted by “□” and the solid line is an inverse-square-root-fit of the experimental data. Moreover, in their study, the inverse-square root relationship between the UCS and the average grain size is also theoretically predicted using a sliding shear crack model proposed by Ashby and Hallam (1986), which is denoted by “*” and the dashed curve in Fig. 3. Tugrul and Zarif (1999) investigated granitic rocks from Turkey and found that there is a good relationship between the uniaxial compressive strength and the maximum grain size (quartz, plagioclase and K-feldspar), as shown in Fig. 4. As seen in the figure, grain size is the primary strength factor in granitic rocks. Fig. 5 records the correlation between the uniaxial compressive strength and the mean grain size determined by Tugrul and Zarif (1999). The smaller grain size is a primary reason for the higher mean strength of particular granitic rocks. The correlation between the uniaxial compressive strength and the size of K-feldspar for the granitic rocks is more significant ( r = 0.91) than the other mineral constituents. However, Hatzor et al (1997) found that the peak and crack initiation stresses are independent of the maximum grain size captured using petrographic microscope for dolomites, as shown in Fig. 6 a). A week dependence of crack initiations and peak stresses on the mean grain size captured by SEM observations is indicated by Hatzor et al’s (1997) result, as shown in Fig. 6 b). Therefore, it means that the mean grain size is more likely to function as critical cracks in Griffith’s fracture criterion. The weak correlation suggests that additional texture factors must be considered, which will be discussed later. It should be noted that better correlation exists between mean grain size and crack initiation stress ( R 2 = 0.09 , power law) than between mean grain size and ultimate stress (R 2 = 0. 02 , power law). Those results consist with the Griffith’s fracture criterion since the criterion is formulated for crack initiation, a process that has been shown to take place before the maximum stress level. The ultimate stress level must be influenced by fracture growths and interaction processes. Eberhardt et al (1999) conducted a laboratory investigation into the effects of grain size on the initiation and propagation thresholds of stress-induced brittle fracturing in crystalline rocks with similar mineralogical compositions, but with three different grains sizes. As shown in Table 1, the crack initiation
σ ci and secondary cracking σ ci2 thresholds for the granodioriate were the same as those for the grey granite, which would seem to suggest that the initial stages of cracking are not strongly dependent on grain size, but are more related to the feldspar and quartz mineralogy. However, grain size did affect the number of AE events recorded. Fig. 7 shows that the number of detected AE events decreases markedly with decreasing grain size. The granodiorite produced approximately 90% fewer total AE events than the pegmatite, and 60% fewer total events than the grey granite. Accordingly, the grey granite produced approximately 60% fewer total events than the pegmatite. According to Griffith’s theory larger grain boundaries critically aligned to the direction of loading should initiate before smaller ones. It then follows that the overall increase in the number of detected events with
9 increasing grain size is due to the increasing number of cracks originating along grain boundaries. Thus, the grain size effect was seen to play a secondary role to the mineralogy in terms of the initial generation of propagating cracks. The effects of grain size were seen to be most significant in terms of the crack coalescence σ cs and crack damage σ cd thresholds. The values in Table 1 show that the crack coalescence values for the grey granite and pegmatite decreased by 23% and 36%, respectively when compared to values for the granodiorite. Values for the crack damage threshold decreases by 21% and 42% respectively when comparing grey granite and pegmatite values to the granodiorite. Therefore, according to Eberhardt et al (1999), the grain size had a minimal effect in terms of when intergranular cracking began, but the behaviour of the cracks during propagation was highly influenced by grain size. Prikryl (2001) found a non-linear negative correlation between uniaxial compressive strength of granites and average grain size of all rock-forming minerals, as shown in Fig. 8 and the following equation: Y = alog()X + b where Y is strength, X is the mean grain diameter and a < 0 < b . This type of relationship is valid for all major rock-forming minerals but is most pronounced when considering the strongest mineral phase – quartz and the weakest phase – mica. According to his experimental results as well as data from other studies, Prikryl (2001) suggested that the relationship between grain size and uniaxial compressive strength is the universal property of all rock like materials. Moreover, according to Hareland et al (1993), the confined compressive strength obtained in triaxial compressive tests is also a function of grain size:
σ = σ 0 + a()μ {}1− exp[]− b ()u P where σ is the confined compressive strength, σ 0 is the unconfined compressive strength, P is the confining pressure, μ is the mean grain size, a(μ) =10()1.948+4.009μ and b()μ =101.982−1.4log a .
Table 1 Relationship between the grain size and crack thresholds of crystalline rocks: standard deviation in parentheses (Eberhardt et al, 1999)
Strength parameters Granodiorite Grey granite Pegmatite Number of tests 5 5 5 Average grain size (mm) 1 3 20
Crack closure, σ cc (MPa) 45,6 (±3,4) 55,6 (±1,5) 45,2 (±2,7)
Crack initiation, σ ci (MPa) 79,6 (±2,7) 79,6 (±2,3) 72,0 (±5,9)
Secondary cracking, σ ci2 (MPa) 102,8 (±4,5) 102,8 (±4,3) 96,0 (±4.4)
Crack coalescence, σ cs (MPa) 164,7 (±9,0) 127,6 (±14,2) 104,8 (±6,4)
Crack damage, σ cd (MPa) 194,0 (±2,8) 147,4 (±9,1) 113,2 (±6,8)
Prikryl (2001) found that the shape-preferred orientation of rock-forming minerals affected the strength anisotropy of granitic rocks. As shown in Fig. 9, the highest strength anisotropy was observed for granites exhibiting well-pronounced shape-preferred orientation of minerals expressed as orientation of long axis of each grain. The maximum uniaxial compressive strength was oriented parallel to the lineation and to the preferential shape orientation of rock-forming minerals (Gottschalk et al, 1990; Dobereiner et al, 1993; Prikryl, 2001). Rocks exhibit the minimum strength when the plane of weakness is oriented at a
10 certain degree (30-45 degrees) to the loading direction (Gottschalk et al, 1990; Rammamurthy, 1993; Kwasniewski, 1993).
Fig. 7 Relationship between AE events count and grain size of crystalline rocks (Eberhardt et al, 1999)
Fig. 8 Correlation between uniaxial compressive strength of granites and average grain size of all rock-forming minerals11 (Prikryl, 2001)
Fig. 9 Relationship between shape-preferred orientation, expressed as the orientation of grains’ long axes, and position of strength extremes in granitic rocks (Prikryl, 2001)
The inverse relationship between bulk porosity and ultimate strength has been noted by many studies (Dunn et al, 1973; Scott and Nielsen, 1991; Vernik and Nur, 1992; Vernik et al, 1993) for reservoir source rocks: siliciclastics and pure sandstones. Hatzor et al (1997) studied the influence of porosity on crystalline dolomites with varying microstructures. Fig. 10 shows two representative stress-strain curves of triaxial tests under equal confining pressure (10 MPa) for two dolomites of similar mean grain size but different bulk porosity. The influence of bulk porosity on strength is evident from inspection of these two curves since all other parameters are equal. In Fig. 11, the relationship between the stress difference and porosity is shown at crack initiation and ultimate stress. As can be seen from the figure, there is an inverse relationship between the strength and ultimate stress of dolomites. The data set for crack initiation stress yields a higher correlation coefficient ( R 2 = 0.53) for exponential fit than the σ i ultimate stress (R 2 = 0. 41). Moreover, Hatzor et al (1997) found that the ultimate strengths σ p in triaxial compressive tests were also related to the porosity, as shown in Fig. 12. The data are clustered into four groups of similar porosity values and two linear regression lines are plotted, for medium porosity (6.6% 12 to both mean grain size and porosity for monomineralic dolomite. The three-dimensional relation is represented by a surface of fracture initiation stress which concavely declines from low porosity-low grain size to high porosity-high grain size coordinate, as shown in Fig. 13. The influence of grain size on crack initiation stress is more pronounced in low porosity than in higher porosity rocks. The influence of porosity on crack initiation stress is more pronounced in rocks with small grain size. It is further shown that only at extreme case of low porosity-low mean grain size, the initial flaw length in Griffith fracture criterion approaches the mean grain size length (Fig. 14). Hence, the conventional rock mechanics assumption that grain size is a suitable scale for initial flaw length is in fact erroneous in the general case and is only correct in the restricted case of low porosity-small grain size textural arrangements. In low porosity rocks, crack initiation stress is extremely sensitive to mean grain size and initial flaw length is shown to approach the mean grain size value. These findings confirm that in low porosity textures, the effect of individual grains on fracture initiation stress is very significant, probably because individual grain boundaries function as true initial flaws. In higher porosity textures, crack initiation stress is much less sensitive to mean grain size and initial flaw length is shown to be higher by up to two orders of magnitudes than the mean grain size value. These findings suggest that the effect of individual grain boundaries in high porosity textures is less significant, rather, the union of several individual grain boundaries may function as the initial stress concentrator. Tugrul and Zarif (1999) found inverse relationships exist between the uniaxal compressive strength and both the effective and total porosity, as shown in Fig. 15. Therefore, the porosity is an important factor in rock strength in that voids reduce the integrity of the material. A small change in pore volume can produce an appreciable mechanical effect (ISRM, 1981) and the influence of porosity cannot be underestimated as well (Prikryl, 2001). It is normally believed that failure of rock specimens under compression is caused by unstable growth and coalescence of microcracks (Wong, 1982; Kranz, 1983). Consequently, it seems reasonable to believe that the peak uniaxial compressive strength of rocks should, more and less, decrease with the initial degree of microcracks in the rocks (Alm, et al, 1985). Wong et al (1996) adopt the concept of crack density to quantify the degree of cracking in Yuen Long marbles and found that the peak strength drops with the crack density in fine grain Yuen Long marbles but remains roughly constant in coarse marbles through experimental studies and theoretical analyses using a sliding crack model originally proposed by Ashby and Hallam (1986). In coarse marbles, the grain size of marbles seems to play an important but subtle role in affecting the peak strength. Chen et al (1999) clarified the correlation between the splitting planes and the distribution patterns of microcracks in granitic rock: in the Inada granite, the rift plane, i.e. the plane of least rock cleavage resistance, was dominated by inter- granular cracks that the total length of which was shorter than that of intra-granular cracks and grain boundary cracks. On the other hand, the grain plane, i.e. the second weakest cleavage plane, coincided with the orientation of the intra-granular cracks. The grain boundary cracks showed no leading orientation. In the Kurihashi granodiorite, there was no preferential orientation of cracks since Kurihashi granodiorite showed no characteristic splitting planes. Thus, in granitic rocks, the splitting planes and the anisotropy were mainly caused by microcracks (Schedl et al, 1986; Kudo et al, 1986). In above, the correlation between a single parameter of rock texture, such as mineral composition, grain size, grain shape, grain spatial arrangement, porosity and crack, and mechanical properties in the literatures are reviewed. Here the relationship between the whole rock texture (as a single parameter) and the mechanical properties is discussed although little attention has been given to assess this kind of relationship. Ersoy and Waller (1995) used a texture coefficient (Howarth and Rowlands, 1986 and 1987) to represent the principal texture characteristics of rocks, such as grain size, grain shape, grain orientation, relative proportion 13 of grains and matrix material and then correlated the texture coefficient with the mechanical properties of rocks, as shown in Table 2. A relationship between strength properties and texture coefficient was in evidence (R=0.62) from Table 2. There is a good correlation between texture coefficient and abrasivity factor F (R=0.83) because the average grain size is included in the derivation of factor F. Cerchar abrasivity index is not influenced by texture to the same degree as the abrasivity factor F since mineral content, mineral hardness, bonding structure and type and degree of cementation all influence the Cerchar index as well as the grain characteristics. There are also some correlation between texture coefficient and Shor hardness (R=0.69). Hecht et al (2005) applied the principle of “geomechanical order” to relate textural properties to mechanical properties of coarse grained sedimentary rocks of Permocarboniferous age. The geomechanical order, which is the summary of geomechanically relevant textural elements and mineral compositions, is defined as a function of structural order, which is the summary of quantitative structural properties like grain size distribution, grain shape, packing density and cementation grade, and compositional order, which is the summary of qualitative compositional properties like mineral composition, types of single grains, types of cement, as shown in Fig. 17. Apparently, the concept of geomechanical order provides a general way to characterize textural rock properties for the correlation with any mechanical rock properties without the postulation of one general formula. The concept is variable and one can select the right description methods for correlation purposes with certain parameters. Fig. 10 Influence of bulk porosity on the stress-strain curves of dolomite obtained in triaxial tests under equal confining pressure (10MPa): a) Sample with low porosity (n=3.6%) and high mean grain size (dm=67.5 um), and b) Sample with medium porosity (n=10%) and low mean grain size (dm=25.4 um) (Hatzor et al, 1997) Fig. 11 Relationship between the porosity and the stress difference at crack initiation and the 14 peak stress difference: ◊ = stress different at crack initiation; □ = peak stress difference (Hatzor et al, 1997) Fig. 12 Mohr-Coulomb failure envelope for dolomites of varying porosity: low porosity (n<6.6%), medium porosity (6.6% Fig. 13 Three dimensional representation of the relationship between the mean grain size, porosity and crack initiation stress for dolomites (Hatzor and Palchik, 1997) 15 Fig. 14 Three dimensional representation of the relationship between the mean grain size, porosity and the length of the critical flaw size for dolomites (Hatzor and Palchik, 1997) Fig. 15 Relationship between the uniaxial compressive strength and both a) the effective porosity and the total porosity of granitic rocks (Tugrul and Zarif, 1999) 16 Fig. 16 Relationship between the uniaxial compressive strength and crack density for Yuen Long marbles (Wong et al, 1996) Table 2 Correlation between the textural coefficient and the mechanical properties of rocks (Ersoy and Waller, 1995) Fig. 17 Graphical illustration of the relations of the concept of geomechanical order to the mechanical behaviour of rocks (Hecht et al, 2005) 17 2.3.2 Influence of textural properties on the fragmentation and abrasion properties in rock aggregate tests The quality of aggregates is to a large extent related to mechanical properties such as fragility and resistance to abrasion. Mineral composition, grain size, grain shape, grain spatial arrangement, porosity, crack, etc have an effect on an aggregate’s resistance to fragmentation and abrasion. Table 3 Simples correlation coefficients for textural parameters (the mineral composition and mean grain size) and the mechanical parameters of basic igneous rocks (Brattli, 1992) Indep. Var. Grain size Feldspar Pyroxene Mica Amphibole Dep. Var. Impact value 0.704 0.333 -0.580 0.160 0.115 Abrasion value 0.556 0.183 -0.613 0.309 0.207 Durability value 0.637 0.231 -0.614 0.270 0.186 It is commonly thought that the mineral content is of great important for the degree of fragmentation and abrasion. Brattli (1992) investigated the causality between the mineral composition and the mechanical properties of basic igneous rock aggregates using multiple- regression analysis. In the regression models the impact value (KS-value), abrasion value (Abr-value), and the durability value (Sa-value) are dependent variables, while the compositions of the rock are independent variables, as shown in Table 3. It is evident from Table 3 that apart from mean grain size, the variation in pyroxene content is the most important factor affecting the mechanical parameters. Thin section studies show that amphibole in general is an alteration product of pyroxene and when the amphibole content increases, the pyroxene content decreases. Therefore, the variation in amphibole is also an important factor affecting the mechanical parameters. According to Brattli (1992), the strength reduction of the dependent parameters (KS-value, Abr-value, and Sa-value) is a function of a decrease in pyroxene content or a function of an increase in amphibole content. The reasons are 1) the mechanical strength of the amphibole seems to be lower than for pyroxene. 2) The amount of amphibole correlates positively with the degree of metamorphic alteration in the rocks. A high content of amphibole indicates a high grade of metamorphic alteration while a high content of pyroxene indicates a high degree of preservation of the primary magmatic texture. 3) The metamorphic texture has poorer qualities with respect to strength properties than the primary magmatic according to Haraldsson (1984), who found both impact and abrasion strength, durability and other strength properties diminished rapidly with increasing alteration. The other minerals in the basic igneous rock have little influence upon the strength parameters. This may be due to a small variation in the amounts of the minerals and the mechanical properties of the minerals themselves. However, the variation in feldspar content has a greater impact on the KS-value than on the Abr-value. This is probably a consequence of the relatively weak bonding along the cleavage planes in feldspars which presumably has a greater negative effect upon the brittleness of the rock than on the abrasion resistance. The opposite effect is seen for the variation in mica content. Because mica is a soft mineral, it is likely that an increase in the content will have a stronger negative effect unpon the abrasion resistance than on the brittleness of the rock. Lundqvist and Göransson (2001) evaluated the mechanical properties of Precambrian rocks from the Stockholm region, Sweden and found that the mica content (biotite + muscovite) shows a distinct negative correlation with the LAV/STTV ratio, as shown in Fig. 18. Moreover, the Fe-Mg-rich rocks such as basic rocks are more ductile and therefore more resistance to brittle fragmentation. 18 They seem though to have almost the same abrasion properties as Fe-Mg-poor rocks with the same grain size. High mica content, especially combined with an anisotropic structure, yields very high values (poor) of abrasion resistance. This argument is not valid for the brittle behaviour. An even distribution of mica in non-continuous arrangements is armouring the stone even in anisotropic rocks. Accordingly, mica-poor rocks exhibit higher brittleness. The mica is thus affecting the brittleness properties of a rock in a similar way as the basic mineralogy. French et al (2001) examined about 40 aggregates and formulated the following relationships between the mechanical properties and mineral composition of rock aggregates: AAV = 21.6 − 2.7NH AIV = 13.5GS − 7.1NH + 55.5 PSV = 8.75NH + 2.31 Fig. 18 Relationship between the LAV/STTV ratio and the mica content of Precambrian rocks (Lundqvist and Göransson, 2001) where AAV is the aggregate abrasion value, AIV is the aggregate impact value, PSV is the polished stone value, NH is the normative hardness index of the aggregate, which is calculated from the volume proportions and normative hardness values of the minerals (Verhoef, 1987) and the Mohs hardness data of minerals is taken from a mineralogical source, and GS is the grain size. Räisänen et al (2003) studied the effect of mineralogy, texture and mechanical properties of anti-skid and asphalt aggregates on urban dust and pointed out the STT value depended on the mineralogy: aggregate consists of hard mineral has a high STT value. Miskovsky et al (2003) investigated 17 samples of granitoid rocks from the Swedish part of the Baltic shield to study the influence of mineralogical composition of granitoid rocks on the quality of coarse aggregates, as shown in Fig. 19 and 20. It was found that a rising content of quartz and feldspar causes diminishing of abrasion value I, as shown in Fig. 19, which means that the resistance of the granitoid rocks to abrasion increases with increasing amount of quartz and feldspar. Moreover, there is a slight indication that an increasing content of mica causes slight deterioration of the rock resistance against abrasion. It is evident from Fig. 20 that an increasing amount of mica (0 to 35, vol. %) improve the resistance of granite to the effects of impact while an increasing of feldspar has the opposite influence. Räisänen (2004) investigated the relationships between mineral composition and resistance to fragmentation of rock aggregate raw materials from the hybridised, subvolcanic Jaala-Iitti complex, southeastern Finland. The rock aggregates have similar compositions of feldspar, quartz, biotite and accessory minerals but different hornblende contents. As shown in Fig. 21, the amount of hornblende has a positive impact on LA values, i.e. more hornblende content, higher resistance to fragmentation the hybrid is. The increase in resistance to fragmentation can be explained by the complex grain boundaries of hornblende. However, Åkesson et al (2001 and 2003) recently argued that there are no such relationships between mineral content and abrasion resistance and between mineral content and fragmentation resistance. In this case, 19 the grain spatial arrangement is more important than the actual mineral content, which will be discussed later. For example, the mica content itself has no direct influence on the resistance to fragmentation. But if micas form plane foliation, they can interact as a large flaw and cause fracture propagation (Åkesson et al, 2003). Fig. 19 Linear correlation between the mineral composition and abrasion value I: a) quartz, Abrasion value I (%) = 3.07-0.032*X, R = -0.64, p = 0.005; b) Feldspar, Abrasion value I (%)= 3.0006 – 0.0137*X, R = -0.52, p = 0.04 (Miskovsky et al, 2003) Fig. 20 Linear correlation between the mineral composition and impact value: a) Feldspar, Impact value (%) = 27.63+0.36*X, R = 0.60, p = 0.0114; b) Mica, Impact value (%) = 55.13+0.50*X, R = -0.73, p = 0.001 (Miskovsky et al, 2003) Fig. 21 Relationship between LA value and amount of hornblende: Hbl-Q-F PORF is hornblende- quartz-feldspar porphyry, Hbl GR is hornblende granite, Hybrid is hybrid rock and Bt GR is biotite granite (Räisänen, 2004) 20 Fig. 22 Relationship between the impact value (KS) and the mean grain size of basic igneous rock aggregates (Brattli, 1992) Fig. 23 Relationship between the abrasion value (Abr) and the mean grain size of basic igneous rock aggregates (Brattli, 1992) Fig. 24 Relationship between the durability value ( S = Abr KS ) and the mean grain a size of basic igneous rock aggregates (Brattli, 1992) According to Table 3 (Brattli, 1992) and other study (Gosawami, 1984), the mean grain size is the most important texture property acting upon the mechanical strength indices of rock aggregates. Fig. 22, 23 and 24 present the scatter plots (the left side) for the investigated impact value, abrasion value and durability value of basic igneous rocks, respectively, with the fitted lines superimposed. The relationship between the mechanical parameters and the mean grain size follows nonlinear trends. Fig. 22, 23 and 24 (the right side) show the same parameters plotted against the transformed values of mean grain size with fitted lines and two- tailed confidence band for prediction of a future value of the mechanical parameter for a given value of mean grain size. It can be seen that the association between mechanical parameters in 21 the rock aggregate tests and the mean grain size is positive. It means that the strength parameters are improving as the mean grain size decreases. The impact is strongest for mean grain size smaller than 1 mm, but decreases for sizes over 1 mm, which indicates a non-linear mathematical relationship between the parameters. The causality between the mechanical strength parameters and the mean grain size is related to how penetrative fractures develop as a function of the length-to-width ratio of so called microcavities in the material. When the grain size increases, the length-to-width ration of the micro-cavities also increases and the stress at the crack tip increases. This in turn favours microcracks to grow and become penetrative. Lundqvist and Göranssion (2001) found that decreasing grain size improves the resistance of Precambrian rocks from the Stockholm region, Sweden, to both wearing and impact forces. Moreover, they pointed out that mechanical properties are controlled by the finest fraction. It is therefore not the grain size per se that is important but rather the amount of fine-grained matrix. Even small quantities of a fine-grained matrix dramatically improve the material’s resistance to both wearing and impact forces. Consequently, the total grain size distribution is the controlling factor. Miskovsky et al (2003) studied the influence of mineralogical composition and textural properties of the 17 granitoid rocks on the quality of coarse aggregates and found that there is an indication that diminishing grain size causes the slight diminishing of impact values, which means that the resistance of granitoid rocks to the effects of impact slightly increases with the decreases of grain sizes. Räisänen (2004) investigated the relationship between texture and mechanical properties of hybrid rocks and found that the average grain size (Fig. 25) and especially the amount of fine-grained matrix (Fig. 26), affect the resistance to fragmentation (LA) and abrasion (AN) values of most hybrid rock aggregates. It is found that better correlation is found between the AN values and grain size than between the LA values and grain size. Thus, the AN value is mainly dependent on grain size properties. The reason for this is that finer mineral grains have a smaller surface to abrade (Åkesson et al, 2001) and that the length-to-width ratio of micro cavities or cracks increases as grain size increases (Brattli, 1992). Fig. 25 Relationship between the average grain size of rock and a) LA value, and b) AN value of rocks (Räisänen, 2004) Grain shape is one of the most important textural parameters affecting the mechanical properties of rock aggregates. Lundqvist and Göransson (2001) pointed out a high complexity of grain shape, produces increased abrasive and brittle resistance of Precambrian rocks from Sweden. Åkesson et al (2001) used a perimeter to describe the shape of a mineral phase and correlated the grain shape with the resistance to fragmentation and abrasion of rock aggregates. The perimeter is the circumference of an object and includes some kinds of information of grain boundaries, grain sizes and grain spatial arrangement (Åkesson et al, 22 2003; Lindqvist et al, 2003). Fig. 27 shows the relationship between the perimeter and the resistance to fragility (LA: Los Angeles test value) and abrasion (STT: studded tyre test value) of granites from central Sweden. As can be seen from the figure, in general, the samples with the highest perimeter values showed the best resistance to fragility and abrasion. The best correlation is between the perimeter and the LA values (R = 0.84) whereas the STT values show a weaker correlation (R = 0.72) with the perimeter values. This indicates that the size, shape and dispersion of the minerals have an influence on the rock’s resistance to fragmentation. In the LA drum, the rocks are crushed by brittle deformation which has a greater effect on the rocks than the STT. Fig. 26 Relationship between the number of equal to or smaller than 0.18 mm grains and a) LA value, and b) AN value of rocks (Räisänen, 2004) Fig. 27 Relationship between the LA and STT values and the perimeter of granites: correlation coefficients are 0.84 and 0.72, respectively (Åkesson et al, 2001) Fig. 28 Relationship between the LA and STT values and the specific surface of granites: correlation coefficients are 0.61 and 0.77, respectively (Åkesson et al, 2001) 23 The complexity of grain spatial arrangement improves the mechanical properties of rock aggregates. Lundqvist and Göranssion (2001) found that puzzle-like, sutured and interlocking boundaries as a result of plastic deformation and dynamic recrystallisation strengthen the Precambrian rocks from Sweden accordingly. Almost all rocks with an equilibrated, low energy, granoblastic-polygonal texture with well developed triple points and straight grain boundaries show low ability to resist abrasion and in particular to brittle fragmentation. The specific surface is used by Åkesson et al (2001) to describe the area of the mineral boundaries: 2 3 Sv = 2PL mm / mm , where PL is the number of mineral boundaries per 1 mm of line transect. The relation between the specific surface and the mechanical properties is given in Fig. 28. It is evident that the largest specific surface value shows the best resistance to fragility and abrasion and the correlation between the STT value and the specific surface (R = 0.77) is better than that between the LA value and the specific surface (R = 0.61). Therefore, the abrasion is more dependent on the specific surface. A foliation index (FIX), the ratio between the sums of the number of grain boundaries parallel and perpendicular to the mineral from all measured lines transects, is calculated by Åkesson et al (2003) to quantify the foliation of grain spatial arrangements. A strong relation is found between the LT-index and FIX, as shown in Fig. 29, which demonstrates the control of foliation on the crushed aggregate shape and the ability of FIX to predict the aggregate shape. Åkesson et al (2004) quantified the grain spatial arrangement using the adjacent grain analysis (AGA) and built a relation between microstructure and bowing properties of calcite marble claddings. It is showed that the samples with a granoblastic texture showing the greatest degree of bowing all had six adjacent grains and the samples with a greater complexity of the microstructure (seriate interlobate texture) showing the lowest degree of bowing had up to 13 adjacent grains. Fig. 29 Relationship between the foliation index (FIX) and the length-thickness (LT-3) index (Åkesson et al, 2003) As described in Section 2.3.1, the porosity decreases the rock strength. In rock aggregates, the porosity of most rocks is low and the influence on mechanical properties is not significant. However, pores may act as flaws where cracks can initiate and it requires no energy for a crack propagate through a pore. In this case, the influence of porosity on mechanical properties of rock aggregate is the same as that of the microcracks. Besides, the porosity change of rock aggregates in services leads to a change in the moisture properties of the rock, 24 which in turn are important for durability of rock material exposed to moisture in different environments (Lindqvist et al, 2003). Fig. 30 Linear correlation between the microcracks number and flakiness of granitoid rocks (Miskovsky et al, 2003) Fig. 31 Linear correlation between the microcracks number and abrasion value II of granitoid rocks (Miskovsky et al, 2003) The propagation of cracks will cause the fatigue or even disarticulation of the rock aggregates. Therefore, the cracks have an important influence on the mechanical properties of rock aggregates. However, few studies have investigated the relationship between the cracks and the mechanical properties of rock aggregates in rock aggregate tests. Miskovsky et al (2003) investigated the influence of microcracks of the granitoid rocks on the quality of coarse aggregates. It is statistically established that the main factor that influences abrasion value II is the propagation of microcracks, as shown in Fig. 30. The strength of the rock to the abrasion decreases with increasing frequency of microcracks (Abrasion II = 7.16 + 0.045*X, R = 0.4375, p = 0.0791). The results of the correlation analysis, shown in Fig. 31, indicate that the flakiness is positively influenced by the increasing frequency of microcracks (Flakiness = 1.40 – 0.0006*X, R = -0.475, p = 0.054). 25 3. Characterization of rock textures The characterization of the rock texture has been examined using optical microscopy and scanning electron microscopy with backscattered detector (SEM/BSE). The textural parameters that have been measured are grain size distribution, perimeter of mineral phases and micro cracks. 3.1 Rock material The objective for the first part of the project was to find three granites with similar mineralogy and grain size but with different mechanical properties. The selection of rock types were done in discussion with Mattias Göransson, SGU, who also performed the sample collection for two of the specimens. Two of the rocks are younger Stockholm granites sampled in the Stockholm (LEP) and Västerås (Vändle) area. The third sampled rock type is a Bohus granite (Ävja). The mineral composition of the samples is quartz > plagioclase > K- feldspar > biotite. Both plagioclase and K-feldspar show a slight sericite alteration and in the point count analysis (Table 4) have the minerals been classified according to the degree of alteration. This is done because the degree of alteration influences the mechanical properties (Åkesson 2004). In the two Stockholm granites the fresh plagioclase is mainly myrmekite. Table 4 Mineral composition of the investigated samples Sample Qtz Pl Pl< 50 Pl > 50 Kfsp Kfsp ser Bt Ass. (fresh) % ser % ser alt. Ävja 37.7 0.3 12.5 10.1 32.7 2.3 2.9 0.8 LEP 33.5 2.9 8.5 18.3 30.9 0.9 4.5 Vändle 28.5 - 23.3 10.3 2.5 29.5 5.3 0.1 The mineral mode is based on point counting using a polarizing microscope. Qtz = quartz, Pl = plagioclase, < 50 % ser = less than 50 % of the plagioclase grain show sericite alteration, > 50 % ser = more than 50 % of plagioclase grain show sericite alteration, Kfsp = K-feldspar, Kfsp ser = K-feldspar with sericite alteration, Bt = Biotite, Ass = Assessory minerals. 3.2 Sample preparation Drill cores with diameter of 40 mm were drilled from each sample. These cores were used for the mechanical tests and thin sections. Two thin sections were prepared from each sample. Before the preparation the samples were vacuum impregnated with epoxy resin containing fluorescent dye. This was done in order to detect micro cracks. 3.3 Grain size distribution Traverses were randomly drawn on microscopic images. The maximum ferret diameter was then measured on each mineral cutting a traverse. From these measurements could the grain size distribution be determined for the investigated samples (Fig. 32). 26 grain size distribution 100 90 80 70 60 50 40 Vändle (0,45) 30 Lep (0,48 accumulated % accumulated 20 ävja (0,75) 10 0 1 2 >2 1,5 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 grain size (mm) Fig. 32. Grain size distribution of the investigated samples. (Median values within parentheses). 3.4. Characterization of micro cracks Two images taken with optical microscopy were used for the microcrack analyses, one using fluorescent light and one using polarised light. The area for each image is 3.977×3.997 mm per side and the resolution is 2304 × 2320 pixels. The thin section was fixed on a motorised stage programmed so the images were photographed edge to edge creating a 12- image mosaic. For each rock, four thin sections are taken each parallel and perpendicular to the drill-core axis except that for Ävja, three thin sections are taken parallel to the drill-core axis and for Vändle, three thin sections are taken perpendicular to the drill-core axis. Thus, for Ävja and Vändle, an area of 112 mm2 (4×4×3+4×4×4 = 112 mm2) is analysed for each rock. For LEP, an area of 128 mm2 (4×4×4+4×4×4 = 128 mm2) is analysed. The fluorescent and polarised images were considered together to make an evaluation of where the micro cracks are formed. Fig. 33, 34 and 35 shows examples of the observed microcracks in Ävja, LEP and Vändle, respectively. 27 a) b) c) Fig. 33 Observations of microcracks in Ävja3: a) fluorescent image, b) polarised image, and c) combination of fluorescent and polarised images (area of each image is 3.977×3.997 mm) 28 a) b) c) Fig. 34 Observations of microcracks in LEP0: a) fluorescent image, b) polarised image, and c) combination of fluorescent and polarised images (area of each image is 3.977×3.997 mm) 29 a) b) c) Fig. 35 Observations of microcracks in Vändle0: a) fluorescent image, b) polarised image, and c) combination of fluorescent and polarised images (area of each image is 3.977×3.997 mm) 30 Those images were analysed using the Carl Zeiss Vision KS 400 image-analysing system and the image-analysing procedure described by Åkesson et al (2004). According to Kranz (1983), the microcracks in rocks can be divided into three types: 1) intra-granular cracks, which are confined to the interior of a single grain, 2) trans-granular cracks, which cross more than one grain, and 3) grain boundary cracks, which are associated and perhaps coincident with the grain boundary. In order to identify each crack type, the combined images were printed with a size of 272×269 mm, and by using transparent paper, each crack type was traced and coloured (red = trans-granular cracks, green = grain boundary cracks, and black = intra-granular cracks), as shown in Fig. 36 for an example of microcracks (Fig. 33) in Ävja. The line-drawings were scanned into the computer, and by using RGB-threshold technique, the number and length of the different crack types could be measured separately. In order to measure the length, the width of the cracks was reduced to 1 pixel, which corresponds to 5.33 μm. In order to do this operation, the length of the crack will correspond to the number of pixels. Fig. 36 Line-drawings of microcracks: red = trans-granular cracks, green = grain boundary cracks, black = intra-granular cracks Fig. 37 and 38 show the distributions of cracks observed in samples parallel and perpendicular, respectively, to drill-core axis for the rocks Ävja, LEP and Vändle. It is evident that most of intra-granular cracks are shorter than 400 um, most of trans-granular cracks are longer than 400 um, and the grain boundary cracks have a wide size distribution. Table 5 summarizes the crack length measurements of the rocks Ävja, LEP and Vändle. 31 50 a) Ävja0 (1.05) 45 LEP0 (0.49) 40 ) Vändle0 (0.45) % ( 35 30 25 20 15 Crack numbers 10 5 0 0-100 100-200 200-400 400-800 >800 Crack length (μm) 60 b) Ävja0 (0.31) LEP0 (0.11) 50 ) Vändle0 (9.18) % ( 40 30 20 Crack numbers 10 0 0-100 100-200 200-400 400-800 >800 Crack length (μm) 45 c) Ävja0 (0.96) 40 LEP0 (1.58) ) 35 Vändle0 (1.30) % ( 30 25 20 15 Crack numbers 10 5 0 0-100 100-200 200-400 400-800 >800 Crack length (μm) Fig. 37 Size distributions of cracks observed in Ävja0, LEP0 and Vändle0: a) intra- granular cracks, b) trans-granular cracks and c) grain boundary cracks (The number in parentheses is the crack length in mm/mm2) 32 60 a) Ävja90 LEP90 50 Vändle90 ) % ( 40 30 20 Crack numbers 10 0 0-100 100-200 200-400 400-800 >800 Crack length (μm) 60 Ävja90 b) LEP90 50 ) Vändle90 % ( 40 30 20 Crack numbers 10 0 0-100 100-200 200-400 400-800 >800 Crack length (μm) 40 c) Ävja90 35 LEP90 Vändle90 ) 30 % ( 25 20 numbers 15 k 10 Crac 5 0 0-100 100-200 200-400 400-800 >800 Crack length (μm) Fig. 38 Size distributions of cracks observed in Ävja90, LEP90 and Vändle90: a) intra- granular cracks, b) trans-granular cracks and c) grain boundary cracks (The number in parentheses is the crack length in mm/mm2) 33 Table 5 Summary of the crack length measurements in the rocks Ävja, LEP and Vändle Rock Grain boundary crack Intra-granular crack Trans-granular crack type pixel mm mm/mm2 pixel mm mm/mm2 pixel mm mm/mm2 Ävja01 6640 11,42 0,72 9932 17,08 1,07 2467 4,24 0,27 Ävja03 9317 16,03 1,01 11210 19,28 1,21 5455 9,38 0,59 Ävja04 10528 18,11 1,14 7948 13,67 0,86 710 1,22 0,08 Sum 26485 45,5542 2,87 29090 50,0348 3,15 8632 14,85 0,93 Average 8828 15,2 0,96 9697 16,7 1,05 2877 4,9 0,31 Total crack length /mm2: 2,32 Ävja901 8360 14,38 0,90 9807 16,87 1,06 6458 11,11 0,70 Ävja902 11742 20,20 1,27 9016 15,51 0,98 1137 1,96 0,12 Ävja903 11849 20,38 1,28 9165 15,76 0,99 1006 1,73 0,11 Ävja904 7240 12,45 0,78 7440 12,80 0,80 4361 7,50 0,47 Sum 39191 67,41 4,24 35428 60,94 3,83 12962 22,29 1,40 3240,5 Average 9797,75 16,85 1,06 8857 15,23 0,96 5,57 0,35 Total crack length /mm2: 2,37 (Ävja: 2.35) LEP01 13452 23,14 1,46 4588 7,89 0,50 LEP02 12673 21,80 1,37 4819 8,29 0,52 1116 1,92 0,12 LEP03 16690 28,71 1,81 4110 7,07 0,44 949 1,63 0,10 LEP04 15557 26,76 1,68 4605 7,92 0,50 1053 1,81 0,11 Sum 58372 100,40 6,31 18122 31,17 1,96 3118 5,36 0,34 Average 14593 25,1 1,58 4530,5 7,8 0,49 1039 1,8 0,11 Total crack length /mm2: 2,18 LEP901 13692 23,55 1,48 3728 6,41 0,40 1688 2,90 0,18 LEP902 10960 18,85 1,19 5896 10,14 0,64 1269 2,18 0,14 LEP903 21108 36,31 2,28 2969 5,11 0,32 814 1,40 0,09 LEP904 21299 36,63 2,30 3628 6,24 0,39 1282 2,21 0,14 Sum 67059 115,34 7,25 16221 27,90 1,75 5053 8,69 0,55 Average 16764,75 28,84 1,81 4055,25 6,98 0,44 1263,25 2,17 0,14 Total crack length /mm2: 2,39 (LEP: 2.29) Vändle01 14816 25,48 1,60 6051 10,41 0,65 736 1,27 0,08 Vändle02 12106 20,82 1,31 4542 7,81 0,49 2781 4,78 0,30 Vändle03 10797 18,57 1,17 2530 4,35 0,27 1949 3,35 0,21 Vändle04 10379 17,85 1,12 3367 5,79 0,36 1282 2,21 0,14 Sum 48098 82,73 5,20 16490 28,36 1,78 6748 11,61 0,73 4122,5 Average 12024,5 20,68 1,30 7,09 0,45 1687 2,90 0,18 Total crack length /mm2: 1,93 Vändle901 13943 23,98 1,51 1531 2,63 0,17 1807 3,11 0,20 Vändle902 15542 26,73 1,68 2405 4,14 0,26 1770 3,04 0,19 Vändle903 16797 28,89 1,82 3069 5,28 0,33 0 0,00 Sum 46282 79,61 5,01 7005 12,05 0,76 3577 6,15 0,39 Average 15427 26,5 1,67 2335 4,0 0,25 1789 3,1 0,19 Total crack length /mm2: 2,11 (Vändle: 2.02) 34 a) b) Fig. 39 SEM/BSE image of Ävja: a) parallel and b) perpendicular to the drill-core axis a) b) Fig. 40 SEM/BSE image of LEP: a) parallel and b) perpendicular to the drill-core axis a) b) Fig. 41 SEM/BSE image of Vändle: a) parallel and b) perpendicular to the drill-core axis 35 3.5. Characterization of perimeters The perimeter of mineral grains and grain aggregates of the same phase was measured from SEM/BSE images using image analysis. Two samples were cut parallel and perpendicular to the drill core axis of the rocks Ävja, LEP and Vändle and one polished thin sections were made from each sample. Images, as shown in Fig. 39, 40 and 41 for the rocks Ävja, LEP and Vändle, respectively, were obtained using a low vacuum SEM (Jeol 5310LV) with 50 times instrumental magnification, which is the lowest magnification the instrument could perform with the backscattered detector. The area for each image is 1.75×1.75 mm per side and the resolution is 1024×1024 pixels. Two thin sections were analysed for each rock and 15 images were taken from each thin section. The BSE images were analysed using Carl Zeiss Vision KS 400 image analysing system according to the procedure described by Åkesson et al (2003). Table 6 summarizes the measurements of perimeters for the rocks Ävja, LEP and Vändle. According to Lindqvist et al (2003) and Åkesson et al (2003), the perimeter is the circumference of an object, and by using this perimeter it is possible to describe the shape of a mineral phase. For mineral phases with similar area, the perimeter will increase with increasing complexity of the grain boundaries, such as interfingering, cuspate or sutured. The grain size is also included. Because all analyzed image have the same area, if the number of objects increase (decreasing grain size), the total perimeter will increase assuming similar shape of the mineral phases. The SEM can not identify boundaries between minerals of the same phase and adjacent grains will be measured as one object. For this reason, the spatial dispersion of the mineral is also taken into consideration when the perimeter is measured. The perimeter has a fractal dimension and the measured perimeter will increase with increasing resolution in the measurement. Therefore, the SEM must be similarly set up for all analysed samples. Table 6 Summary of the perimeter measurements in the rocks Ävja, LEP and Vändle Type Ävja0 Ävja90 LEP0 LEP90 Vändle0 Vändle90 Perimeter 66,399 51,808 74,805 68,067 75,064 78,130 (mm) Average 59,103 71,436 76,597 Perimeter 14,615 11,404 16,466 14,983 16,523 17,197 (mm/mm2) Average 13,009 15,724 16,860 4. Mechanical tests of rock properties In this study, both the fundamental mechanical tests and the rock aggregate tests are conducted to investigate the mechanical properties of the rock aggregate. 4.1. Fundamental mechanical tests – UCS and BTS The fundamental mechanical tests conducted in this study are uniaxial compressive test and Brazilian tensile test. The uniaxial compressive test is carried out in the RTR-150HS9 high stiffness rapid rock triaxial test system. Cylindrical specimens, with a diameter of about 36 50 mm and a length to diameter ratio of approximate 2.5, were tested to obtain the uniaxial compressive strength, elastic modulus, elastic modulus and Poisson’s ratio. For each rock type, two tests are conducted. Fig. 43 records the stress-strain curves obtained in the uniaxial compressive test of the rocks Ävja1, LEP1 and Vändle1 and Table 7 summarises the obtained mechanical properties of the rocks Ävja, LEP and Vändle. The uniaxial compressive strength is calculated from the peak load, the elastic modulus is determined from the slope of the straight-line portion (40~60% of the peak load) of the stress-strain curve and Poisson’s ratio is the negative ratio between the slopes of the axial stress-strain curve and the radial stress-strain curve. 250 Avja1 LEP1 200 Vandle1 150 100 Axial stress (MPa) 50 0 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 Axial strain (%) Fig. 42 Stress-strain curves obtained in the uniaxial compressive tests of the rocks Ävja, LEP and Vändle Table 7 Results obtained in the uniaxial compressive tests of the rocks Ävja, LEP and Vändle Rock type Ävja1 Ävja2 LEP1 LEP2 Vändle1 Vändle2 E (GPa) 63.18 62.43 72.35 71.09 69.97 70.56 Average E 62.80 71.72 70.26 (GPa) ν 0.36 0.32 0.34 0.31 0.28 0.21 Average ν 0.34 0.33 0.24 σ c (MPa) 193.1 196.5 219.8 208.6 240.8 173.7 Average 194.8 214.2 207.3 σ c (MPa) D (mm) 49.8 49.7 49.7 49.7 49.8 49.8 H (mm) 125.8 125.8 125.9 125.9 125.9 125.9 Brazilian tensile tests were carried out in a load frame where the crossbar is mechanically driven by screws and has a maximum load capacity of 100 kN in compression. The frame was equipped with a pair of curved bearing blocks with pins for guiding the vertical deformation. The top platen includes a spherical seating in order to have a fully centred loading position. The two samples for each type of rock were inserted into the loading device one by one, with 37 correct orientation, and then loaded up to failure during the deformation control. Table 8 summarizes the obtained tensile strengths of the rocks Ävja, LEP and Vändle. Table 8 Results obtained in the Brazilian tensile tests of the rocks Ävja, LEP and Vändle Rock type Ävja1 Ävja2 LEP1 LEP2 Vändle1 Vändle2 Peak stress 9.9 9.0 14.8 15 13.5 16.0 (MPa) Average 9.5 14.9 14.8 (MPa) 4.2. Rock aggregate test – DSC The rock aggregate test conducted for the rocks Ävja, LEP and Vändle is the Dutch static compressive (DSC) test. According to Ballmann et al (1997), the DSC test is carried out on a size fraction d/D mm (where D = 2d ). The size of the test specimen is determined as the mass of this size fraction of the aggregate required to fill a one-half litre measure. The test is performed by crushing the aggregate in a compression testing machine using a cylindrical steel mould. The load is increased from zero to 200 kN over 60 seconds, and then maintained at 200 kN for a further 30 seconds. The test specimen is then sieved on a test sieve with aperture size d/2 mm, and the result of the test, the DSC value, is the amount of the test specimen that passes the test sieve, expressed as a percentage by the mass of the test specimen (Ballmann et al, 1997): mass _ of _ fragment _ passin g _ the _ test _ sieve DSC = ×100% mass _ of _ the _ test _ sepcimen The test is carried out on two test specimens, and the average of the DSC values for two test specimen is reported as the crushing strength. The rock materials of Ävja, LEP and Vändle are firstly crushed with a laboratory crusher to achieve the desired fraction. Then the Dutch static compressive tests are conducted according the procedures described above. Finally, the crushing strengths are calculated as shown in Table 9. Table 9 Crushing strengths of the rocks Ävja, LEP and Vändle obtained in the Dutch static compressive test Rock type Ävja1 Ävja2 LEP1 LEP2 Vändle1 Vändle2 Weight of the 641,1 654,3 649,5 640 619,15 646,9 test specimen Sum 1295,4 1289,5 1266,05 Average 647,7 644,75 633,025 Weight of over- 355,6 344,0 431,1 411,1 405,0 432,0 size Sum 699,6 842,5 837 Average 349,8 421,25 418,5 DSC value (%) 46,0 34,7 33,8 38 START Heterogeneous material model Stress disturbances FEM stress analyzer Mohr-coulomb Tensile Compute tensile damage strength criterion damage variable Update property YES Compute stiffness damage, parameters with Damage? residual strength, etc damaged values NO Damage type NO End of Compressive Compute compressive analysis? damage damage variable YES END 2D Fig. 43 Flowchart of the calculation module in the R-T code 5. Numerical simulation of rock aggregate breakage properties In this section, the breakage properties of rock aggregates under different loading conditions will be modelled using the rock and tool interaction code (R-T2D). The R-T2D code is developed on the basis of the rock failure process analysis (RFPA) model (Tang, 1997) and the finite element analysis (FEA) method. Fig. 43 summarizes the executive routine of the calculation module in the R-T2D code (Liu, 2004). Firstly the numerical model is built according to the heterogeneous material model (Liu et al, 2004a) with the homogeneous index m, and the elemental seed parameters for the main physical-mechanical properties of rock, such as elastic modulus E0, compressive strength σ0, etc. Then in order to perform the finite element failure analysis, other parameters, such as Poisson’s ratio, friction angle, ratio between compressive strength and tensile strength, etc are specified for the numerical model, and the initial boundary conditions are applied to it. Following this procedure, the elements are brought to the equilibrium state under the initial boundary conditions. After that, a stress 39 disturbance is applied to the numerical model, which may be caused by force loading, displacement loading or stress redistribution. A finite element stress analyser is used to calculate the stress and strain distributions in the finite element network because of the stress disturbance. The calculated stresses are substituted into the Mohr-Coulomb strength criterion to check whether or not elemental damage occurs. If the strength criterion is not satisfied, the external loading is increased further. Otherwise, the element is damaged and becomes weak according to the rules specified by the mesoscopic elemental mechanical model for elastic damage (Liu et al, 2004b), which results in a new perturbation. The R-T2D code has been successfully modelled the rock fragmentation in rock cutting (Liu et al, 2002a), rock drilling (Liu et al, 2002b), rock crushing (Liu et al, 2005a) and rock blasting (Liu et al, 2005b). 5.1. Microstructural modelling of rock aggregate breakage properties In the previous modelling of rock fragmentations using the R-T2D code, the numerical model is built according to the heterogeneous material model on the basis of Weibull distribution. Here the heterogeneous material model is based on the microstructure of rock aggregates. Thus, if we name the previous modelling as statistical modelling, the numerical modelling here can be called as microstructural modelling. Table 10 Physical-mechanical properties of the major constituent phases in Ävja, LEP and Vändle Properties Elastic modulus Compressive strength Poisson ratio Mineral type (GPa)*1 (MPa)*2 K-Feldspar (K) 69,7 1600 0,301 Mica (M)*3 88,1 3000 0,248 Quartz (Q) 95,6 5200 0,079 Plagioclase (P) 80,4 1600 0,300 Crack*4 8,52 1,43 0.300 *1 From Bass (1995) *2 From Ichikawa et al (2001) *3: Mica includes Muscovite, Biotite and Chlorite *4: It is assumed that cracks are filled with weak materials 5.1.1. Microstructure observation, image analaysis and microstructural modelling The microstructural modelling needs the detail microstructure of rock aggregates. In Section 3, thin sections are prepared to observe the microstructure of the three types of rock aggregates (Ävja, LEP and Vändle) using microscope. The left images in Fig. 44, 45 and 46 show the observed microstructures of the rocks Ävja, LEP and Vändle, respectively. The top images are taken using the polarising microscope to record the mineral information. The middle images are fluorescent images to distinguish the cracks. The bottom images are combined polarising and fluorescent images to show the crack types (grain boundary cracks, trans-granular cracks, and intra-granular cracks). Identifying the mineral grains and cracks in those microstructures is difficult. Image analysis provides a powerful tool to simplify the microstructure, identify the mineral composition, and obtain the morphological information. In this study, an image analysis program, Particle2D (Wang, 1998), is used to process the microstructure images, segment the constituent phases, and polygon the mineral and crack 40 O O Bright Bright Fig. 44 Image analyses on the representative volume element (RVE) of Ävja and numerical models for RVE of Ävja 41 Fig. 45 Image analyses on the representative volume element (RVE) of LEP and numerical models for RVE of LEP 42 Fig. 46 Image analyses on the representative volume element (RVE) of Vändle and numerical models for RVE of Vändle 43 shapes. Once the morphological information of the constituent phases has been gained, it is possible to conduct physical and mechanical computations, for instance, through the finite element method after specifying the physical-mechanical properties of the major constituent phases. Table 10 records the main physical-mechanical properties of the major constituent phases (K-Feldspar, Plagioclase, Quartz, Mica and Crack) in Ävja, LEP and Vändle taken from the literatures (Bass, 1995; Ichikawa et al, 2001). It should be noted that mica includes Muscovite, Biotite and Chlorite, and it is assumed that cracks are filled with weak materials in this study. On the basis of morphological information and physical-mechanical properties of the constituent phases in the microstructures of Ävja, LEP and Vändle, the corresponding numerical models can be built, as shown in the right images in Fig. 44, 45 and 46, respectively. Therefore, in microstructural modelling, the microscopic observation, image analysis and numerical modelling are integrated on-line to simulate the breakage properties of rock aggregates: image acquisition, image processing, meshing, computation of stress, strains and displacements, crack initiation, propagation, coalescence and interaction. Firstly, the representative volume element (RVE) of the rock aggregate is observed using microscope. Then the microstructure of RVE is recorded in the memory of the computer and image analysis is used to simplify the microstructure, segment the constituent phases and polygon mineral and crack shapes. After the image analysis, the position, morphology and type of the constituent phases are recorded in a data file. After that, a dynamic data exchange module is developed in the R-T2D code to receive the data files from the image analysis and the numerical model is built. Finally, the R-T2D code is used to simulate the breakage properties of the built numerical model under the various loading conditions. a) UCS c) UCS b) RVE Fig. 47 Numerical models for the microstructural modelling The area, where the microscopic observation is conducted, is usually very small. The numerical simulation needs specimens that are relatively large in comparison with the scale of microscopic observation. Owing to this, the numerical model can be constructed according to the two-dimensional microstructures of a specimen from a sequence of physical or optical 44 cuts, or according to the RVE of a specimen on the basis of homogenisation theory in engineering geology. In the numerical simulations conducted in this study, homogenisation modelling is coupled with the R-T2D code to simulate the rock aggregate breakage properties under typical loading conditions. In homogenisation theory, it is usually assumed that a composite material is locally formed by the spatial repetition of very small microstructures, i.e. microscopic cells, when compared with the overall macroscopic dimensions of the structures of interests (Seo et al, 2002). Here, the RVE is the microscopic cell. Fig. 47 shows the numerical models for UCS and BTS built using the method mentioned above, which is introduced in more detail in a previous paper (Liu et al, 2004a). Similarly, the numerical models are also built to simulate the breakage properties of rock aggregates under the point- to-point, plane-to-plane, point-to-plane and multiple-point loading conditions. 5.1.2. Calibration of the microstructural modelling In this section, the UCS modelling is conducted to calibrate the method of microstructural modelling by comparing the numerical results with experimental results. Fig. 48, 49 and 50 record the modelled failure processes of Ävja, LEP and Vändle in UCS tests in terms of the distributions of elastic modulus, major principal stress and acoustic emissions, respectively. In Fig. 48, the grey degree represents the relative value of the elemental elastic modulus. The brighter the colour, the bigger the elemental elastic modulus is. In Fig. 49, the grey degree represents the relative value of the elemental major principal stress. The brighter the colour, the higher the elemental major principal stress is. In Fig. 50, the colour represents the failure mechanism. The red colour indicates the tensile failure occurring in the current loading step, the blue colour records the compressive failure in the current loading step, and the black colour represent the tensile and compressive failures in the previous loading steps. The diameter of the circle represents the size of the elastic energy release (ENR). The bigger the circle, the higher the elastic energy release is. Fig. 51 depicts the force-loading displacement curves for Ävja, LEP and Vändle obtained in the modelling of UCS tests. It can be seen that the failures firstly occur in the weak materials filling in the cracks and the tensile failures are the main mechanics. Those failures make the pre-existing cracks open. Continuous loading displacement cause some pre-existing cracks to close and some pre-existing cracks to propagate. It is found that most of the crack propagations occur in the minerals of K-Feldspar and Plagioclase, which form the transgranular cracks. When the quartz mineral is located in front of the crack propagation, the cracks usually propagate following the boundaries of quartz to form the grain boundary cracks except the propagating crack meets the pre-existing crack in the quartz mineral. As the loading displacement increases, the individual cracks coalesce with each other to form long cracks. The long cracks further propagate to gradually form the failure surfaces. It seems that tensile splitting failures are the main mechanisms to form final failure surfaces in Ävja and LEP. The fracture pattern in Vändle is different from those in Ävja and LEP although there are also tensile splitting failures in Vändle: Vändle has a more zigzag failure surfaces compared with those in Ävja and LEP. All of the failure processes observed in the numerical simulations are consistent with the failure processes of UCS described in literatures (Wawersik and Fairhurst, 1970; Lockner et al, 1991) On the basis of the peak loads Pmax (Fig. 51 A2, B2 and C2) and the linear parts (Fig. 51 A11-A2, B11-B2 and C11-C2) of the force-loading displacement curves, the uniaxial compressive strength σ c and elastic modulus E can be calculated: P σ = max c A 45