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A new fracture test method—the bottom-notched splitting (BNS) test—is proposed in this study to determine the double-K fracture parameters of concrete. In the BNS test, the concrete cube with a preset crack on the bottom surface is subjected to a line compressive load on the top surface. Numerical analyses are first carried out to simulate the stress distributions along the ligament and crack opening profiles of the BNS specimens. Then, the fitting expressions of the stress intensity factor and the crack center opening displacement are derived based on the linear elastic fracture mechanics. A series of BNS tests and three-point bending (TPB) tests with different ratios of the preset crack length to the specimen height are conducted to determine the double-K fracture parameters of the concrete. The results indicate that the preset cracks in the BNS tests could initiate and propagate throughout the whole cross-sections of the concrete cubes. By substituting the obtained initial fracture loads, maximum loads, and critical crack center opening displacements in the BNS tests into the fitting expressions, the double-K fracture parameters could be determined. By comparing with the TPB tests, the BNS tests proved to be an effective method to determine the double-K fracture parameters of concrete. The BNS tests are convenient to operate and can reduce the damage risk of the preset cracks. Meanwhile, they also would be appropriate for assessing the fracture properties of existing concrete structures in service because the cubes can be easily obtained from the samples core-drilled from existing concrete structures. [ABSTRACT FROM AUTHOR]

This study investigated the time-dependent crack propagation of the rock–concrete interface under sustained loading. First, sustained loading tests were performed on the composite rock–concrete beams under three-point bending with respect to three interface roughness degrees, i.e., natural, 4×4 , and 7×7 interfaces, and three sustained load levels, i.e., 80% of the maximum load, the initial cracking load, and 97% of the maximum load. Then, by employing the Norton-Bailey model and the time-dependent fictitious crack model, the constitutive relationships of bilateral materials and the rock–concrete interface were established and the mechanical responses of the rock–concrete interface under sustained loading were simulated. In addition, a crack propagation criterion proposed in this study was applied in the numerical procedure to simulate the time-dependent crack propagation process under sustained loading. The criterion implied that the interface crack propagated when the difference between the average elastic strain energy densities near the crack tip caused by the external load and cohesive stress exceeded that at the initial fracture status under quasi-static loading. The results indicated that the crack propagation under sustained loading could be interpreted from the view of energy balance between the driving energy from the external load and the resistance energy from the cohesive stress. The time-dependent crack propagation under sustained loading experienced three stages, i.e., decelerated propagation, uniform propagation, and accelerated propagation. A linear relationship between the logarithms of the crack mouth opening rate in the uniform propagation period and the failure time was established to predict the failure time of the rock–concrete interface under sustained loading. [ABSTRACT FROM AUTHOR]

To investigate the fracture property of the rock–concrete interface after sustained loading, creep tests were conducted on composite rock–concrete beams with two mechanical grooving interfaces, 4×4 and 7×7 interfaces, under two sustained load levels, 50% and 75% of the maximum load. After 90-day sustained loading, the creep specimens were unloaded and reloaded to failure in the subsequent three-point bending tests. The viscoelastic characteristic of the rock–concrete interface was numerically simulated by employing the Bailey–Norton creep law to describe the constitutive relationships of bilateral materials. Based on the numerical results, the elastic and creep strain energies within the whole specimen and the core region near the crack tip were calculated during the loading process. The results indicated that during the creep tests, the local elastic strain energy decreased due to the stress relaxation near the crack tip, and the local creep strain energy increased due to the accumulated creep strain. It was found that, at crack initiation status, the average elastic strain energy density in the core region after sustained loading was identical to that under static loading, which indicates that the elastic energy in the core region dominated the fracture behavior. Then, an energy-based fracture criterion was proposed to judge the crack initiation of the rock–concrete interface considering viscoelastic characteristics. It was found that the average elastic strain energy density of the rock–concrete interface was not affected by the viscoelasticity, which can be regarded as a material parameter. [ABSTRACT FROM AUTHOR]

This study investigated the fracture properties and FPZ evolution of concrete/rock bi-material interface after low-level fatigue loading. Firstly, the fatigue loading tests were performed under the frequency of 1.0 Hz with respect to two upper limits less than the initial cracking load, i.e. 60 % and 70 % of the peak loads. After 80,000 loading cycles, the quasi-static loading tests were performed to measure the fracture behavior of concrete/rock bi-material interface. Thereafter, the DIC tests were conducted to observe the crack extension process and analyze the FPZ evolution. According to the comparisons of fracture behaviors between the fatigue specimen and control specimen, the effects of the low-level fatigue loading on the fracture properties and FPZ evolution of concrete/rock bi-material interface were discussed. The results indicate that the unloading paths follow the loading paths coincidentally for each loading cycle, and this means that the mechanical response of the concrete/rock bi-material interface under low-level fatigue loading is elastically dominated. After the low-level fatigue loading, the initial cracking load and initial fracture toughness exhibit obvious increasing tendency, whereas the unstable fracture toughness decreases obviously, which is induced by the significant decrease of the critical crack length. In addition, the fully-developed FPZ length and the corresponding crack length of fatigue specimen are less than that of control specimen, indicating that the brittleness of concrete/rock bi-material interface becomes larger after low-level fatigue loading. [ABSTRACT FROM AUTHOR]

This study proposes an effective method to determine the stress intensity factors (SIFs) of the interface crack considering the viscoelasticities of the bilateral materials and verifies the feasibility of the initial fracture toughness-based fracture criterion for the concrete-rock interface under sustained loading. Firstly, low-level sustained loading tests were conducted on the composite concrete-rock specimens with respect to two interface roughness degrees and two sustained load levels less than the initial cracking load. Then, an implicit creep equation was employed to characterise the viscoelasticities of bilateral materials and then calculate the mechanical responses of the concrete-rock interface in the low-level sustained loading test. The SIFs of the interface crack under sustained loading were determined by using the elastic strain energy density ahead of the crack tip. By averaging the SIFs over the radius of the core region of the crack tip, the representative SIFs under sustained loading were obtained. The test results indicated that the SIFs showed decreasing tendencies under sustained loading, and the initial fracture toughness can be considered as a material property of the concrete-rock interface. The initial fracture toughness-based fracture criterion was verified to be feasible to determine the initial cracking status of the concrete-rock interface under sustained loading. In addition, due to the reductions of the SIFs under sustained loading, additional loads were required to compensate the losses of the SIFs, leading to the enhancement of the initial cracking loads after experiencing the sustained loading. [ABSTRACT FROM AUTHOR]

• Concrete rings with various thickness tested for restrained shrinkage cracking. • Both top/bottom drying and outer circumference surface drying investigated. • Effects of ring geometry, thickness & drying conditions on cracking revealed. • Increasing ring thickness increases restraint to a circular concrete ring. • Rings exhibit different fracture behaviour under different drying conditions. The restrained shrinkage elliptical ring test has been established as an efficient method for assessing the cracking potential of concrete at early ages because an elliptical ring can provide a higher degree of restraint compared with a circular one. In this study, a series of circular and elliptical concrete rings restrained by steel rings with various thicknesses were tested under top & bottom surfaces drying or outer circumferential surface drying. By comparing concrete cracking age under different geometrical and drying conditions, the effects of ring geometry, restraining steel ring thickness and drying condition on the cracking process in concrete rings were revealed. Furthermore, numerical analyses were conducted to investigate the fracture mechanism for circular and elliptical rings by applying a fictitious temperature field to simulate the shrinkage effect of concrete. It is found that the increase of steel ring thickness can enhance the degree of restraint, therefore shorten the cracking age for both circular and elliptical rings. However, the improvement is more significant for circular rings. The fracture processes under the two drying conditions, i.e. top & bottom surfaces drying and outer circumferential surface drying are completely different: for drying from outer circumferential surface, the crack initiates at the outer surface and propagates towards the inner surface; for drying from top & bottom surfaces, the crack initiates partially along the height direction at the inner circumference of a concrete ring, and propagates along the radial direction, step by step, until the crack propagates throughout the whole ring wall. In both cases, the self-restraint caused by the non-uniform shrinkage of concrete and the external restraint from the inner steel ring contribute the driving effects for crack propagation. In general, compared with circular rings, the elliptical rings demonstrate the advantage of providing a higher degree of restraint. The elliptical ring test method can, therefore, supplement the traditional circular ring test method for assessing cracking tendency of concrete with higher cracking resistance. [ABSTRACT FROM AUTHOR]

Due to uniform shrinkage along the radial direction, drying from both top and bottom surfaces has been recommended to replace drying from outer circumference surface in the restrained circular ring test to assess cracking tendency of concrete. However, non-uniform shrinkage along the height direction under drying conditions is significant, and its effect on crack initiation and propagation in a concrete ring is not clearly understood. To investigate the fracture mechanism of the restrained ring test under drying from top and bottom surfaces, three series of circular and elliptical ring specimens with heights of 30 mm, 50 mm and 75 mm are tested to measure the cracking ages. A fracture mechanics based numerical method is proposed by introducing fictitious crack model to simulate the fracture process and predict the cracking age of a concrete ring under restraint. The effects of ring geometric profile, specimen height and moisture gradient on crack development are discussed. The results indicate that, under drying from both top and bottom surfaces, crack initiates partly along the height direction at the inner circumference of a concrete ring, and propagates along the radial direction, one by one, until the crack propagated throughout the whole cross-section. The moisture gradient along the height direction has significant effect on the crack driving force, which is dominated by the moisture gradient and steel ring restraint near the exposed surface, whose proportion increases with the increase in distance from the exposed surface. [ABSTRACT FROM AUTHOR]

This paper explored the viscoelasticity-induced fracture behavior of rock-concrete interface after sustaining the creep process. Creep tests were firstly conducted on the composite rock-concrete specimens under three-point bending loading at the load levels of 50% and 75% of the maximum load. After 90-day sustained loading, composite specimens were unloaded and then reloaded under quasi-static loading conditions, and the digital image correlation technique was employed to quantify the crack profiles at the rock-concrete interface. The results indicate that the pre-set crack at the rock-concrete interface would not initiate further during the creep tests if the sustained load was below the initial cracking load. After sustaining a creep process, the initial cracking load increased obviously but the elastic strain energy near the pre-crack tip remained unchanged. The creep deformations during the creep tests made the characteristic lengths of the rock-concrete interfaces decreased largely, leading to the obvious enhancement of the interfacial brittleness. As a result, the interfacial nonlinear fracture behavior from the initial cracking state to the unstable fracture state would become weaker. In addition, the fully formed fracture process zone length and the corresponding crack length increased with the increase of the sustained load level, indicating that the boundary effect of the rock-concrete interface would decreased. [ABSTRACT FROM AUTHOR]

It is necessary to optimize the design of the missile aerodynamic shape for better performance while meeting tactical specifications. However, current design methods for aerodynamic shape are based on manual design and physical model simulations, which are very time-consuming. Therefore, we propose an optimization framework based on conditional Wasserstein Gan-GP (CWGAN-GP), convolutional neural network (CNN), multi-task learning with multi-gate mixture-of-Experts-3D (MMoE-3D) and differential evolution (DE). This method consists of four stages. In the first step, CWGAN-GP can learn the relationship between existing missile shape designs and shape conditions, generating diverse missile shapes as required. In the second step, CNN is used for feature extraction of missile design drawing, and the missile shape generated by CWGAN-GP is transformed into missile shape parameters. In the third step, the MMoE-3D model is trained in the subsonic and supersonic ranges to efficiently generate aerodynamic data corresponding to the missile shape. In the fourth step, DE is used to select the optimal missile shape by adjusting the potential variables of CWGAN-GP. The efficiency of the proposed optimization framework is verified by optimizing the rate of change of the center of pressure and the lift-to-drag ratio, with the neural network-based optimization framework achieving almost the same optimization results in a shorter time compared to conventional optimization with DATCOM. [ABSTRACT FROM AUTHOR]

• Analytical expressions of the interfacial stress intensity factor and the critical crack length were derived. • With the increase of the interfacial roughness, the full fracture process length decreased. • The ratio of the fracture energy to the tensile strength for interface approximately remained constant. • With the increase of the interfacial roughness, the interfacial brittleness became larger. To investigate fracture properties and find analytical solutions of fracture parameters at rock-concrete interface, three-point bending tests were performed on the composite rock-concrete specimens with different degrees of interface roughness. Numerical simulations were conducted to analyse the crack propagation and the fracture process zone evolution at rock-concrete interface. For convenient applications in practice, a series of analytical solutions were derived or curve-fitted to calculate the fracture parameters of rock-concrete interface. The results indicate that the roughness degree has significant effects on the fracture properties of rock-concrete interface. With the increase of the roughness degree, the fracture energy, the critical crack length and the double- K fracture parameters exhibit obvious increasing tendencies. Meanwhile, the ratio of the unstable fracture toughness of rock-concrete interface to concrete is much less than that of the initial fracture toughness, indicating the much weaker cohesive effect of rock-concrete interface compared with concrete. In addition, with the increase of the roughness degree, the length of the fully formed FPZ and the corresponding ratio of the crack propagation length to the ligament length decrease. The characteristic length of rock-concrete interface is proved to decrease with the increase of the roughness degree, indicating larger brittle behaviour with the increase of the roughness degree. Finally, a series of analytical expressions were curve-fitted or derived to calculate the fracture parameters of rock-concrete interface under three-point bending loading, including the mode-I stress intensity factor, the critical crack length and the characteristic length of rock-concrete interface. [ABSTRACT FROM AUTHOR]

• Under different exposure conditions, the initial fracture toughness of concrete increases but the unstable fracture toughness of concrete decreases with the increase of exposure duration. • The stress-free crack opening displacement decreases largely under exposure conditions, indicating the brittleness of the concrete becomes stronger. • The sulphate ion contents under dry-wet cycling are obviously higher than those under the other exposure conditions, demonstrating that dry-wet cycling has the most serious sulphate attack. The fracture properties of concrete subjected to sulphate attack are investigated. First, concrete beams were subjected to different exposure conditions, i.e., full immersion, partial immersion and dry-wet cycling, for 90, 180 and 270 days, and a subsequent three-point bending test was conducted. A softening constitutive relationship of concrete was then derived and a simplified bilinear model was proposed for different exposure conditions. Finally, a chemical titration test was conducted to obtain the profiles of sulphate ion contents along the depth of concrete. The results indicate that, when concrete is subjected to different exposure conditions, the initial fracture toughness increases but the unstable fracture toughness decreases with the exposure duration. The stress-free crack opening displacement in the simplified bilinear model decreases significantly, indicating that concrete attacked by sulphate becomes more brittle. In addition, the sulphate ion content decreases rapidly along the depth and the sulphate ion content in concrete under dry-wet cycling is obviously higher than those under the other exposure conditions, demonstrating that dry-wet cycling results in the most serious sulphate attack on concrete. [ABSTRACT FROM AUTHOR]

Distribution centers are quite important for logistics. In order to save costs, reduce energy consumption and deal with increasingly uncertain demand, it is necessary for distribution centers to select the location strategically. In this paper, a two-stage model based on an improved clustering algorithm and the center-of-gravity method is proposed to deal with the multi-facility location problem arising from a real-world case. First, a distance function used in clustering is redefined to include both the spatial indicator and the socio-economic indicator. Then, an improved clustering algorithm is used to determine the optimal number of distribution centers needed and the coverage of each center. Third, the center-of-gravity method is used to determine the final location of each center. Finally, the improved method is compared with the traditional clustering method by testing data from 12 cities in Inner Mongolia Autonomous Region in China. The comparison result proves the proposed method's effectiveness. [ABSTRACT FROM AUTHOR]

• Shrinkage cracking propagates from inner surface of specimen by pre-setting initial crack. • Pre-setting crack propagates unstably once it initiates. • By pre-setting initial crack, crack occurrence is completely driven by the restrained shrinkage. • With the increase of pre-set crack length, the ages of cracking decreased. Self-restraint caused by differential shrinkage along the radius of a concrete ring has great driving effect on the restrained cracking in the traditional ring test. In order to estimate cracking potential of concrete under restrained shrinkage, i.e. steel ring restraint effect, an improved circular/elliptical ring test was proposed by pre-setting a 6 mm long real crack at the inner circumference of the concrete specimen. Meanwhile, a numerical study based on fracture theory was conducted to investigate the cracking mechanism of the improved ring test. By introducing the fictitious crack model, the crack initiation age and propagation process in the ring specimen were simulated using the initial fracture toughness-based cracking criterion. The driving forces of the shrinkage cracking, provided by self-restraint and steel ring restraint, were analyzed and the influence of the pre-set crack length on the cracking age was discussed. The results indicated that, different from the traditional ring test, the shrinkage crack firstly initiated from the pre-set crack and then unstably propagated toward the outer circumference of the concrete in the improved method. In the crack propagation process, the self-restraint provided cracking insistence rather than driving force on the shrinkage cracking due to the bending effect along the radial direction caused by non-uniform moisture distribution in concrete. Therefore, the driving force of the shrinkage cracking was totally provided by the steel ring restraint and would overcome the cracking resistances from concrete material and non-uniform shrinkage. Furthermore, the advantage of the elliptical geometry in increasing the restraining level was still available for the improved ring test with a pre-set crack, which could make the shrinkage cracking occur in advance and enhance the steel ring restraint. [ABSTRACT FROM AUTHOR]

Highlights • Non-uniform shrinkage of concrete provides approximate 40% restraint. • Crack initiates at outer surface and propagates towards inner surface of a ring. • Under uniform shrinkage assumption, external restraint is overestimated. • With increasing of concrete strength, the proportion of self-restraint increases. Abstract The non-uniform shrinkage caused by moisture gradient in concrete provides self-restraint, which has a significant effect on the assessment of cracking potential of concrete through the restrained shrinkage ring test. Furthermore, moisture gradient in concrete would be also affected by concrete strength because concretes designed for different strength grades usually have different water to cement ratio. In this paper, three series of circular and elliptical concrete rings with a 37.5 mm thick wall and three distinguished concrete strength grades of C30, C50 and C80 were tested to investigate the effect of the moisture gradient on crack initiation and propagation in restrained concrete rings. An integrative model based on the nonlinear diffusion theory is introduced to calculate the moisture distributions in concrete rings, and the fictitious temperature fields are derived for the simulation of the shrinkage effect in concrete. Meanwhile, a fracture mechanics-based numerical method is proposed to analyze the crack initiation and propagation in a concrete ring in the restrained ring test. The effects of ring geometry, concrete strength and uniform/non-uniform shrinkage assumption on the cracking initiation and propagation process are elaborated. The results indicate that the non-uniform shrinkage in concrete provides driving energy for concrete cracking, which is approximately 40% of the total driving energy. Accordingly, it significantly affects the crack initiation position and propagation direction, occurring at the outer surface and propagating toward the inner surface of the concrete ring. With the increase of concrete strength, the cracking potential of restrained concrete ring increases and the proportion of the self-restraint caused by the non-uniform shrinkage in the total restraint decreases because of the reduced moisture distribution. [ABSTRACT FROM AUTHOR]

Numerical simulation in Computational Fluid Dynamics mainly relies on discretizing the governing equations in time or space to obtain numerical solutions, which is expensive and time-consuming. Deep learning significantly reduces the computational cost due to its great nonlinear curve fitting capability, however, the data-driven models is agnostic to latent relationships between input and output. In this paper, a novel deep learning named Navier–Stokes Generative Adversarial Network integrated with physical information is proposed. The Navier–Stokes Equation is added to the loss function of the generator in the form of residuals, which means physics loss in this paper. Then, the proposed model is trained in the framework of generative adversarial network. Experimental results show that proposed model significantly outperform similar models, mean absolute error are decreased by 62.29, 78.42 and 78.61% on pressure and velocity components. What’s more, effectiveness of introducing physics loss is also verified. [ABSTRACT FROM AUTHOR]