A bidirectional B-spline QR method (BB-sQRM) for the study on the crack control of the reinforced concrete (RC) beam embedded with shape memory alloy (SMA) wires is presented. In the proposed method, the discretization is performed with a set of spline nodes in two directions of the plane model, and structural displacement fields are constructed by the linear combination of the products of cubic B-spline interpolation functions. To derive the elastoplastic stiffness equation of the RC beam, an explicit form is utilized to express the elastoplastic constitutive law of concrete materials. The proposed model is compared with the ANSYS model in several numerical examples. The results not only show that the solutions given by the BB-sQRM are very close to those given by the finite element method (FEM) but also prove the high efficiency and low computational cost of the BB-sQRM. Meanwhile, the five parameters, such as depth-span ratio, thickness of concrete cover, reinforcement ratio, prestrain, and eccentricity of SMA wires, are investigated to learn their effects on the crack control. The results show that depth-span ratio of RC beams and prestrain and eccentricity of SMA wires have a significant influence on the control performance of beam cracks.

A new meso-mechanical testing scheme based on SEM was developed to carry out the experiment of microfracturing process of rocks. The microfracturing process of the pre-crack marble sample on surrounding rock in the immerged Long-big tunnel in Jinping Cascade II Hydropower Station under uniaxial compression was recorded by using the testing scheme. According to the stereology theory, the propagation and coalescent of cracks at meso-scale were quantitatively investigated with digital technology. Therefore, the basic geometric information of rock microcracks such as area, angle, length, width, perimeter, was obtained from binary images after segmentation. The failure mechanism of specimen under uniaxial compression with the quantitative information was studied from macro and microscopic point of view. The results show that the image of microfracturing process of the specimen can be observed and recorded digitally. During the damage of the specimen, the distribution of microcracks in the specimen is still subjected to exponential distribution with some microcracks concentrated in certain regions. Finally, the change law of the fractal dimension of the local element in marble sample under different external load conditions is obtained by means of the statistical calculation of the fractal dimension.

No abstract