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Coalescence among fractures would have influence on the stability of rock masses. Deep understanding of mechanical behavior of fractured rock masses is an important mean to identify failure mechanism of geological disaster. In this study, crack propagation processing was studied through loading pre-fractured specimens of concrete block, termed as rock-like material, in uniaxial compression tests. New non-parallel double-crack geometry was introduced to observe crack coalescence. The flaw combinations are different from the normally used flaw configurations. In addition, ultrasonic detection tests were performed on the test blocks. The stress and strain data of these tests and characteristic parameters of sound wave were recorded. The stress-strain curves of each test block under the uniaxial compression test were drawn, relations among deformation characteristics and crack angle of the crack specimens, and their overall strength were analyzed. It is found that strength of the specimen decreases as crack inclination increases under two crack inclinations. The highest uniaxial compressive strength is found in the specimen with the cracks at the same angle in different directions. Based on description of the crack initiation location, crack surface and the ultimate failure patterns, failure modes of eight subtype for test blocks are divided into three categories. It is expected that the study results could be beneficial for engineering application of jointed rock masses.

In this paper, we consider a fuzzy portfolio selection problem with systematic risk and non-systematic risk simultaneously. These two kinds of risks are measured by beta coefficient and random error variance obtained by Sharp Single Index Model. The total risk as the objective of portfolio decision is obtained by weighting the two kinds of risk. Among them, the weight of systematic risk is regarded as the degree of investors' attention to system risk in economic sense. In addition, the fuzzy return and the degree of diversification are measured by triangular fuzzy number and entropy, respectively. And they are also considered the goal of investment decisions. Hence, a tri-objective portfolio is proposed in this paper. For the fuzzy objectives in the model, a goal programming method based on fuzzy dominance is proposed, which can help investors better capture the ideal point of fuzzy returns according to their risk preference. Finally, combined with the systematic impact of COVID-19 on the financial market, we make an empirical analysis based on our proposed model. The results show that the total risk will be on the high side when value is too large or too small. That means paying too much or little attention to the systematic risk will lead investors to bear more risk. In addition, when investors ignore the systematic risk; that is, the value is low, and investors will concentrate their funds in the same industry.

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