# Determination of Fracture Properties of Concrete Using Size and Boundary Effect Models  
[PERSON]  
1 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China;  
[EMAIL_ADDRESS]  
[PERSON]  
2 China Three Gorges Projects Development Co., Ltd., Chengdu 610017, China;  
[EMAIL_ADDRESS]  
[PERSON]  
2 China Three Gorges Projects Development Co., Ltd., Chengdu 610017, China;  
[EMAIL_ADDRESS]  
[PERSON]  
2 China Three Gorges Projects Development Co., Ltd., Chengdu 610017, China;  
[EMAIL_ADDRESS]  
[PERSON]  
2 China Three Gorges Projects Development Co., Ltd., Chengdu 610017, China;  
[EMAIL_ADDRESS]  
[PERSON]  
1 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China;  
[EMAIL_ADDRESS]  
appear during the construction and operation periods. In fact, cracking is a very common, classical, but also complicated problem in concrete structures in real-life service conditions [4], which has been studied comprehensively from different perspectives by many researchers [5; 6; 7; 8; 9]. In terms of cracking risk analysis, the true fracture toughness \(K_{c}\) and tensile strength \(f_{t}\) of the concrete are the key material parameters that should be provided. The improper fracture properties may lead to a result with great deviation from the reality. Many test results showed that the fracture toughness \(K_{c}\) of concrete has obvious size effect, and tensile strength \(f_{t}\) usually depends on the specimen size and test method. To overcome the problem of size effect in fracture properties, it is often necessary to pour different sizes of concrete specimens to obtain the stable material parameter values. Thus, the test process is often complicated, especially for dam concrete, and the stable material parameters can only be measured from huge specimens [1; 10]. In addition, the experimentally measured tensile strength of concrete varies for different test methods (uni-axial tension test, splitting test, flexure test, etc.) [11; 12] due to the different fracture mechanisms. These size- or test method-dependent fracture parameters increase the difficulty of structure design and cracking risk analysis. Hence, it is crucial to find out a simple and relatively more accurate way to measure or predict the real fracture parameters of dam concrete. Size effect laws (SEL) [13; 14; 15; 16; 17] and boundary effect models (BEM) [18; 19] are two main asymptotic approaches to capture the size effect of concrete fracture. With these two kinds of models, the failure stress of structure with any specimen size or any crack size can be estimated, if the model parameters are fully known. On the contrary, if the test results of geometrically similar specimens with constant crack-length-to-height ratios or specimens with different crack to width ratios are available, size and boundary effect models can predict the material tensile strength \(f_{t}\) and fracture toughness \(K_{c}\). The applicability of the different size and boundary effect models on the determination of fracture toughness and tensile strength have been carefully examined with many test results in the literature [20; 21; 22; 23]. It is widely accepted that the size effect laws can provide the fracture toughness directly based on the geometrically similar fracture tests; however, in order to estimate the tensile strength, a material characteristic length \(l_{ch}\) must be assumed in advance [20]. The different versions of boundary effect models proposed by [PERSON] et al. [19; 21; 23; 24; 25] can directly determine the tensile strength and fracture toughness. These models can be classified as the local and non-local models, according to the stress value adopted in the models to predict the failure due to the strength of material. The local models only use the point stress information at the crack tip, while an average stress information along a certain length emanated from the crack tip is needed for the non-local boundary effect models.