Continuing the experiments on the double-edge notched pecimens on which the mode Ⅱ fracture toughness KIIc of concrete was measured, a practical testing approach to determine mode Ⅱ fracture energy GIIF is studied using the same geometry.

混凝土断裂能的尺寸效应一直是研究的热点问题之一。借助于断裂功的概念，目前采用不同的试件形式来测试混凝土断裂能GF。其中，楔入劈拉试件因其在实际操作过程中的诸多优点而有希望成为测试混凝土断裂能GF的标准。本文采用楔入劈拉法研究了试件韧带高度对GF的尺寸效应影响。在测试过程中为得到稳定的荷载位移下降段而采用了柔度测试法。根据RILEM推荐的公式计算混凝土断裂能GF时，对荷载一位移曲线的尾部进行了合理的拟合处理，并考虑了试验夹具自重的影响。结果发现混凝土断裂能GF数值随试件韧带高度的增加有上升的趋势，具有明显的尺寸效应。进一步证实了尺寸效应是传统意义上的混凝土断裂能的属性特征。

The results of experimental investigations using laser speckle interferometry on small size three-point bending notched beams and using photoelastic coating and the strain gauges on very large size compact tension specimens of concrete are presented in detail. The investigations showed that there exists a stage of stable crack propagation before unstable fracture occurs. The results are in agreement with other researchers' investigations using moire interferometry, holographic interferometry, dye-impregnation method and microscope. Further detailed study shows that the three different states, i.e., crack initiation, stable crack propagation and unstable fracture can be distinguished in the fracture process in concrete structures. In order to predict the crack propagation during the fracture process in quasi-brittle materials a double-K criterion is proposed. The double-K criterion consists of two size-independent parameters. Both of them are expressed in terms of the stress intensity factors. One of them reflects the initial cracking toughness, denoted with Kinic, which can be directly evaluated by the initial cracking load, Pini, and the precast crack length, a0, using a formula of LEFM. The other one refers to the unstable fracture toughness, denoted with Kun c, which can be obtained inserting the maximum load, Pmax, and the effective crack length, ac, into the same formula of LEFM. The values of the two parameters, Kini Ic and Kun Ic, obtained from the small size three-point bending notched beams and the large size compact tension specimens show that Kini Ic and Kun Ic are size-independent. Evaluating with the KR-resistance curves obtained from the same test data, it is found that the proposed double-K criterion is equivalent to it in basic principle, but, the double-K criterion can be applied more easily than the KR-resistance curve. Finally, as a practical example, the application of the double-K criterion to the prediction of the crack propagation in a concrete dam is discussed.

Based on the complete fracture process in concrete, the crack extension resistance associated with the cohesive force on the fictitious crack is investigated in detail for standard three-point bending notched beams. Five concrete materials are speci

本文基于作者及其合作者近年新提出的两端切口Ⅱ型断裂试件几何和相应的应力强度因子公式的基础上，建议一种无切口Ⅱ型断裂试件。然后对不同切口长度的Ⅱ型断裂试件和不同高度和宽度的无切口Ⅱ型断裂试件的断裂破坏过程采用以微面模型（Micro-Plane Model）为基础的三维非线性有限元分析商用程序进行数值模拟，发现无切口试件在韧带上由剪切应力集中引起剪切裂缝后，在韧带区形成纯Ⅱ型断裂和剪切裂缝扩展过程。然后较为系统地研究了试件宽度和试件高度对断裂破坏过程和断裂破坏形态的影响。

This paper shows how the double-K fracture parameters Kini Ic and Kun Ic can be determined for concrete using CT-specimens and wedge splitting specimens. The experimental results collected from the fracture tests on the very large size CT-specimens and small size wedge splitting specimens carried out by many researchers are utilized to investigate the characters of the obtained double-K fracture parameters Kini Ic and Kun Ic. It was found that the double-K fracture parameters Kini Ic and Kun Ic determined from fracture tests on the large size CT-specimens are size-independent. And the values of Kini Ic and Kun Ic determined from small size wedge splitting specimens with same dimensions are independent of the relative preformed notch length a0=D. However, when the dimensions of small size wedge splitting specimens change from 150

In this paper, an attempt is made to determine the double-K fracture parameters Kini Ic and Kun Ic using three-point bending notched beams. First, based on the knowledge from extensive investigations which showed that the nonlinearity of P-CMOD curve is mainly associated with crack propagation, a linear asymptotic superposition assumption is proposed. Then, the critical effective crack length ac is analytically evaluated by inserting the secant compliance cs into the formula of LEFM. Furthermore, an analytical result of a fictitious crack with cohesive force in an infinite strip model was obtained. The double-K fracture parameters Kini Ic and Kun Ic as well the critical crack tip opening displacement CTODc were analytically determined. The experimental evidence showed that the double-K fracture parameters Kini Ic and Kun Ic are size-independent and can be considered as the fracture parameters to describe cracking initiation and unstable fracture in concrete structures. The testing method required to determine Kini Ic and Kun Ic is quite simple, without unloading and reloading procedures. So, for performing this test, a closed-loop testing system is not necessary.

The crack extension resistance and fracture properties are studied in detail for quasi-brittle materials like concrete with a softening traction-separation law by investigating the complete fracture process. The computed samples are the three-point bending notched beams of concrete with different sizes tested by other researchers. The softening traction-separation law which was proposed by Reinhardt et al. based on direct tension tests for normal concrete materials was chosen in the computations. Different distribution shapes of the cohesive force on the fictitious crack zone were considered for the corresponding loading states. The computations were mainly based on the analytic solutions for this problem using Gauss-Chebyshev quadrature to achieve the integration which is singular at the integral boundary. The crack extension resistance curves in terms of stress intensity (KRcurves) were determined by combining the crack initiation toughness Kini Ic that is the inherent toughness of the material needed to resist the crack initiation in the case that is in the lack of an extension of the main crack with the contribution due to the cohesive force along the fictitious crack zone during the complete processes of fracture. The situation of crack propagation can be judged by comparing KR-curves of crack extension resistance with the stress intensity factor curves which were calculated using the lengths of the extending crack and the corresponding loads at each loading states, e.g., when the crack extension resistance curve (KR-curve) is higher than the stress intensity factor curve, the crack propagation is stable; otherwise, it is unstable. In the computation, the obtained relationship between the crack tip opening displacement CTOD and the amount of crack extension for the complete fracture process is in agreement with the testing results of other researchers.

采用标准三点弯曲梁砼试件，利用试验中测得的最大荷载Pmax及对应的裂缝口张开位移CMODc计算了砼裂缝亚临界扩展量Dac。提出了由虚拟裂缝闭合力s（x）产生的应力强度因子cKI的实用解析方法，进而计算了砼双K断裂参数ini KIC及un KIC。采用这一方法，只需在试验中测得最大荷载Pmax及对应的裂缝口张开位移CMODc、砼弹性模量及抗拉强度即可确定双K断裂参数并且无需对cKI进行数值积分。大量的计算分析表明，这一实用解析方法不但可使计算过程进一步简化，而且具有很高的精度。

The edoubIe-e notched no: ched specimen made of normal s: rengrh tin, crete has been stlbsected to compressive loads, kis shown that a shear crack develops at the notch tip. Visual observation and evaluation of displacement measurements have proven that this specimen allows pure mode I testing, It was possible to determine fracture toughness KIIc, Recommendations for the testing are made.