Akbardoost, J., Ayatollahi, M. R., Aliha, M. R. M., Pavier, M. J., & Smith, D. J. (2014). Size-dependent fracture behavior of Guiting limestone under mixed mode loading. International Journal of Rock Mechanics and Mining Sciences, 71, 369-380.
ASTM International Standard E399-06 (2006) Standard Test Method for Linear-Elastic Method Plane-Strain Fracture Toughness KIC of Metallic Materials. Copyright ASTM International, West Conshohocken, U.S., 1-32.
Bažant, Z.P., & Oh, B.H. (1983). Crack band theory for fracture of concrete. Materials and Structures, 16(93), 155–177.
Bažant, Z.P., Kim, J.K., & Pfeiffer, P.A. (1986). Determination of fracture properties from size effect tests. Journal of Structural Engineering, ASCE, 112(2), 289-307.
Carpinteri, A. (1989). Cusp catastrophe interpretation of fracture instability. Journal of the Mechanics and Physics of Solids, 37(5), 567-582.
CEB-Comite Euro-International du Beton-CEB-FIP Model Code (1990). Bulletin D’Information, EPF Lausanne.
Choubey, R.K., & Kumar, S. (2018). Simplified equations for determining double-k fracture parameters of concrete for 3-point bending test. Fatigue & Fracture of Engineering Materials & Structures, 4, 1615-1626.
Choubey, R.K., Kumar, S., & Rao, M.C. (2016). Modeling of fracture parameters for crack propagation in recycled aggregate concrete. Construction and Building materials, 106, 168-178.
Choubey, R.K., Kumar, S., & Rao, M.C. (2017). Numerical evaluation of simplified extreme peak load method for determining the double–K fracture parameters of concrete. International Journal of Engineering & Technology, 9(3), 2097-2110.
Elices, M., Rocco, C., & Roselló, C. (2009). Cohesive crack modeling of a simple concrete: Experimental and numerical results. Engineering Fracture Mechanics, 76, 1398-1410.
Fakhri M., Yousefian, F., Amoosoltani, E, Aliha, M. R. M. & Berto, F. (2021). Combined Effects of Recycled Crumb Rubber and Silica Fume on Mechanical Properties and Mode-I Fracture Toughness of Self-Compacting Concrete (SCC)” Fatigue & Fracture of Engineering Materials & Structures
Fakhri, M., Amoosoltani, E., & Aliha, M. R. M. (2017). Crack behavior analysis of roller compacted concrete mixtures containing reclaimed asphalt pavement and crumb rubber. Engineering Fracture Mechanics, 180, 43-59.
Guan, J.F., Li, C.M., Wang, J. (2019). Determination of fracture parameter and prediction of structural fracture using various concrete specimen types. Theoretical and Applied Fracture Mechanics. 100, 114–127.
Hillerborg, A., Modeer, M., & Petersson, P.E. (1976). Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement & Concrete Research, 6, 773–782.
Hou, Y.K., Duana, S.J., & An, R. M. (2019). Solving the cohesive zone model analytic function for concrete based on wedge-splitting test on a compact tension specimen. Theoretical and Applied Fracture Mechanics, 102, 162-170.
Hu, S., & Lu, J. (2012a). Experimental research and analysis on Double-K fracture parameters of concrete. Advanced Science Letters, 12(1), 192-195.
Hu, S., Mi, Z., & Lu, J. (2012b). Effect of crack-depth ratio on double-K fracture parameters of reinforced concrete. Applied Mechanics & Materials, 226, 937-941.
Hu, S., Zhang, X., & Xu, S. (2015). Effects of loading rates on concrete double-K fracture parameters. Engineering Fracture Mechanics, 149, 58-73.
Jenq, Y.S., & Shah, S.P. (1985). Two parameter fracture model for concrete. Journal of Engineering Mechanics, ASCE, 111(10), 1227-1241.
Karihaloo, B.L., & Nallathambi, P. (1991). Notched beam test: Mode I fracture toughness, Fracture Mechanics Test methods for concrete. Report of RILEM Technical Committee 89-FMT (Edited by S.P. Shah and A. Carpinteri), Chamman & Hall, London, 1-86.
Kumar, S., & Barai, S.V. (2008a). Influence of specimen geometry on determination of double-K fracture parameters of concrete: A comparative study. International Journal of Fracture, 149, 47-66.
Kumar, S., & Barai, S.V. (2008b). Cohesive crack model for the study of nonlinear fracture behaviour of concrete. Journal of The Institution of Engineers (India), CV, 89, 7-15.
Kumar, S., & Barai, S.V. (2009a). Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function. Engineering Fracture Mechanics, 76, 935-948.
Kumar, S., & Barai, S.V. (2009b). Effect of softening function on the cohesive crack fracture parameters of concrete CT specimen. Sadhana Academy Proceedings in Engineering Sciences, 36(6), 987-1015.
Kumar, S., & Barai, S.V. (2010a). Determining the Double-K fracture parameters for three-point bending notched concrete beams using weight function. Fatigue and Fracture of Engineering Materials and Structures, 33(10), 645-660.
Kumar, S., & Barai, S.V. (2010b). Size-effect prediction from the double-K fracture model for notched concrete beam. International Journal of Damage Mechanics, 19, 473-497.
Kumar, S., & Pandey, S.R. (2012). Determination of double-K fracture parameters of concrete using split-tension cube test. Computers and Concrete, An International Journal, 9(1), 1-19.
Kumar, S., Pandey, S.R., & Srivastava, A.K.L. (2014). Determination of double-K fracture parameters of concrete using peak load method. Engineering Fracture Mechanics, 131, 471-484.
Kwon, S.H., Zhao, Z., & Shah, S.P. (2008). Effect of specimen size on fracture energy and softening curve of concrete: Part II. Inverse analysis and softening curve. Cement and Concrete Research, 38, 1061-1069.
Li, Y., Qing, L., Cheng, Y., Dong, M., & Ma, G. (2019). A general framework for determining fracture parameters of concrete based on fracture extreme theory. Theoretical and applied fracture mechanics, 103 (102259), 1-16.
Murakami, Y. (1987), “Stress Intensity Factors Hand Book (Committee on Fracture Mechanics, The Society of Materials Science, Japan)”, Vol-1, Pergamon Press, Oxford.
Nallathambi, P., & Karihaloo, B.L.(1986). Determination of specimen-size independent fracture toughness of plain concrete. Magazine of Concrete Research, 38(135), 67-76.
Pandey, S.R., Kumar. S., & Srivastava, A.K.L. (2016). Determination of double-K fracture parameters of concrete using split-tension cube: a revised procedure. International Journal of Concrete Structures & Materials, 10(2), 163-175.
Park, K., Paulino, G.H., & Roesler, J.R. (2008). Determination of kink point in bilinear softening model for concrete. Engineering Fracture Mechanics, 7, 3806-3818.
Petersson, P.E. (1981). Crack growth and development of fracture zone in plain concrete and similar materials. Report No. TVBM-100, Lund Institute of Technology.
Planas, J., & Elices, M. (1991). Non-linear fracture of cohesive material. International Journal of Fracture, 51, 139-157.
Pradhan, S., Kumar, S., & Barai, S.V. (2018). Impact of particle packing mix design method on fracture properties of material and recycled aggregate concrete. Fatigue & Fracture of Engineering Materials & Structures, 2018, 1-16.
Qing, L.B., & Li, Q.B. (2013). A theoretical method for determining initiation toughness based on experimental peak load. Engineering Fracture Mechanics, 99, 295-305.
Qing, L.B., Nie, Y.T., & Hu, Y.A. (2017). Simplified extreme method for determining double-K fracture parameters of concrete using experimental peak load. Fatigue & Fracture in Engineering Materials & structures, 40(20), 254-266.
Qinga, L., Donga, M., & Guanb, J. (2018). Determining initial fracture toughness of concrete for split-tension specimens based on the extreme theory. Engineering Fracture Mechanics, 189, 427-438.
Reinhardt, H.W., Cornelissen, H.A.W., & Hordijk, D.A. (1986). Tensile tests and failure analysis of concrete. Journal of Structural Engineering, ASCE, 112(11), 2462-2477.
Roesler, J., Paulino, G.H., Park, K., & Gaedicke, C. (2007). Concrete fracture prediction using bilinear softening. Cement and Concrete Composites, 29, 300-312.
Rooholamini, H., Hassani, A., & Aliha, M. R. M. (2018). Evaluating the effect of macro-synthetic fibre on the mechanical properties of roller-compacted concrete pavement using response surface methodology. Construction and Building Materials, 159, 517-529.
Rooholamini, H., Hassani, A., & Aliha, M. R. M. (2018). Fracture properties of hybrid fibre-reinforced roller-compacted concrete in mode I with consideration of possible kinked crack. Construction and Building Materials, 187, 248-256.
Ruiz, G., Ortega, José J., Yu, R.C., Xu, S., & Wu, Y. (2016). Effect of size and cohesive assumptions on the double-K fracture parameters of concrete. Engineering Fracture Mechanics, 166, 198-217.
Xu, S., & Reinhardt, H.W. (1998). Crack extension resistance and fracture properties of quasi-brittle materials like concrete based on the complete process of fracture. International Journal of Fracture, 92, 71-99.
Xu, S., & Reinhardt, H.W. (1999). Determination of double-K criterion for crack propagation in quasi-brittle materials, Part I: Experimental investigation of crack propagation. International Journal of Fracture, 98, 111–149.
Xu, S., & Reinhardt, H.W. (1999). Determination of double-K criterion for crack propagation in quasi-brittle materials, Part II: analytical evaluating and practical measuring methods for three-point bending notched beams. International Journal of Fracture, 98, 151–77.
Xu, S., & Reinhardt, H.W. (1999). Determination of double-K criterion for crack propagation in quasi-brittle materials, Part III: compact tension specimens and wedge splitting specimens. International Journal of Fracture, 98, 179-193.
Xu, S., & Reinhardt, H.W. (2000). A simplified method for determining double-K fracture meter parameters for three-point bending tests. International Journal of Fracture, 104, 181-209.
Xu, S., & Zhang, X. (2008). Determination of fracture parameters for crack propagation concrete using an energy approach. Engineering Fracture Mechanics, 75, 4292-4308.
Xu, S., & Zhu, Y. (2009). Experimental determination of fracture parameters for crack propagation in hardening cement paste and mortar. International Journal of Fracture, 157, 33-43.
Zhang, X., & Xu, S. (2011). A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis. Engineering Fracture Mechanics,78, 2115-2138.
Zhang, X., Xu, S., & Zheng, S. (2007). Experimental measurement of double-K fracture parameters of concrete with small-size aggregates. Frontiers in Architecture and Civil Engineering in China, 1(4), 448-457.
Zhao, Y., & Xu, S. (2002). The influence of span/depth ratio on the double-K fracture parameters of concrete. Journal of China Three Georges University (Natural Science), 24(1), 35-41.
Zhao, Z., Kwon, S.H., & Shah, S.P. (2008). Effect of specimen size on fracture energy and softening curve of concrete: Part I. Experiments and fracture energy. Cement and Concrete Research, 38, 1049-1060.