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www.nature.com/scientificreports OPEN Study on mechanical behavior and damage process of concrete with initial damage under eccentric load Ge Lina 1,2*, Yi Fu1, Zhou Junxia1 & Du Changbo2 In order to analyze the infuence of eccentric load on mechanical properties and damage process of concrete with initial damage, the eccentric load compression tests of concrete under diferent confning pressures were carried out with the help of PFC particle fow program. The results show that: the eccentric load does not change the relationship between peak stress, crack initiation stress and confning pressure of concrete under uniform load, but decrease the value of them. The peak stress increasing coefcient under uniform load is higher than that under eccentric load, and the peak stress increasing coefcient increases in a linear function with the confning pressure, and the increasing rate is approximately the same. Under uniaxial compression of eccentric load, a type I shear crack approximately parallel to the loading direction is formed, while under biaxial compression, a bending type shear crack with the lower tip of the initial crack as the infection point is formed. The number of microcracks in concrete under uniform load and eccentric load can be divided into three stages: the calm period at the initial loading stage, the pre-peak expansion period from crack initiation point to peak point, and the rapid increase period after the peak. In practical engineering, most concrete structures have experienced a certain load history, such as the water level change of dams, the load change of bridges, the dynamic load action of buildings such as earthquakes or explosions. Te existence of load history will produce micro-cracks of diferent sizes in concrete, that is, the ini- tial damage. Te existence of initial damage will afect the deterioration process of concrete damage and reduce the service life of concrete1,2. Te concrete in the tunnel or the coal and rock mass in the sinking and driving engineering are ofen subjected to eccentric load due to the undulation of the mountain or the excavation of the project (Fig. 1). Te internal stress state, damage deterioration process and deformation feld evolution law of concrete, rock and other solid materials under eccentric load are diferent from those under uniform load3,4. Terefore, the research on the mechanical behavior and damage law of concrete with initial damage under eccentric load is of great signifcance for mastering its macroscopic mechanical properties and guiding feld engineering practice. Meanwhile, it is also helpful to establish a constitutive model that can accurately describe the complex mechanical properties of such media under actual engineering conditions. On the mechanical properties and damage mechanism of concrete, scholars all over the world have carried out extensive research and achieved fruitful results. Yu et al.5 carried out full area and local area multiaxial compres- sion tests on ordinary concrete, compared the failure modes of concrete under diferent loading conditions, and proposed the failure criteria of ordinary concrete under local load based on the true triaxial compression test data. Zingg et al.6 studied the infuence of cement matrix porosity on the triaxial properties of concrete under high confning pressure, and considered that the contribution of cement matrix porosity to concrete strength decreased under high confning pressure, which enriched the research results of triaxial compression of mass ordinary concrete. Wang et al.7 studied the infuence of water saturation and loading rate on the performance of dam concrete under biaxial compression, and considered that the ultimate strength of dry and saturated concrete increased with the increase of strain rate, while the damage pattern and ultimate strength were closely related to the magnitude of lateral pressure exerted on the specimen. Te dynamic failure criterion was pro- posed to characterize both the efects of strain rate and water content on the ultimate strength of dam concrete under biaxial compressive stress states. Tian et al.8 studied the damage characteristics of concrete under uniaxial 1College of Architecture and Transportation, Liaoning Technical University, No. 88 Yulong Road, Xihe District, Fuxin 123000, Liaoning, People’s Republic of China. 2School of Civil Engineering, Liaoning Technical University, No. 88 Yulong Road, Xihe District, Fuxin 123000, Liaoning, People’s Republic of China. *email: [email protected] Scientifc Reports | (2021) 11:16425 | https://doi.org/10.1038/s41598-021-95964-x 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1. Te phenomenon of eccentric loading in engineering. compression using X-ray computed tomography (CT), Te process of concrete crack initiation, propagation, penetration and failure under uniaxial compression was given by using CT imaging technology, and the damage fracture zoning theory for quantitative analysis of concrete damage evolution was proposed by using CT. With the continuous development of computer technology, numerical simulation method has been widely used in the study of mechanical damage characteristics of materials. Ansari et al.9 used particle fow code (PFC) sofware based on discrete element method to simulate the performance of pervious concrete specimens with diferent aggregate size and void ratio. By comparing with the test results, the reliability of using discrete element method to simulate the mechanical properties of pervious concrete was proved. Lian et al.10 used PFC to simulate the mechanical behavior of porous concrete under compression and tension. Te accuracy and efectiveness of the simulation were verifed by comparing with the experimental results and empirical formula. Huang et al.11 used the particle fow code (PFC) to simulate the strength failure behavior of three non- coplanar specimens under uniaxial loading, and four typical crack merging modes were determined, namely shear, tension shear mixing and tension. Trough the analysis of the force feld and displacement feld, the evolution mechanism of cracks around the holes of granite specimens was revealed. In the framework of PFC, Song et al.12 proposed a three-dimensional multi-level stress corrosion model (MSC) to reproduce the mechanical properties of brittle geo materials and concrete under multi-level cyclic compression loading. Te simulation results of MSC model are in good agreement with the experimental results. Te results show that the MSC model can reproduce the cyclic loading mechanical properties of concrete specimens under diferent maximum and minimum load levels. To sum up, scholars from all over the world have carried out extensive research on the mechanical proper- ties and damage process of concrete under uniform load, but the research on the damage process of concrete under eccentric load is rarely reported, and most of the existing research is based on complete concrete samples, while the research on the mechanical law of concrete with initial damage is rare. Based on this, the mechanical properties and damage laws of concrete with initial damage under uniform load and eccentric load are studied by means of particle discrete element method on the basis of parameter calibration. Te research results have important guiding signifcance for the engineering design of concrete and the formulation of monitoring early warning indicators. Simulation scheme of particle fow code In this paper, PFC2D is used to simulate the eccentric compression test of concrete. PFC simulation sofware is based on DEM discrete element method, and the basic mechanical properties of materials are described by the motion of each particle and the force and moment acting on each contact point. Concrete is usually composed of a group of particles bonded by parallel bonds. Te strength of concrete is achieved by parallel bonding between particles, and its essence is the cementation between particles. Te program can track and show the crack initia- tion and growth process, and can distinguish the tensile crack and shear crack, which is widely used in concrete and other solid materials13–15. Establishment of numerical model. Te numerical simulation model is consistent with the indoor test. Te sample size is 100 mm in height, 50 mm in width, 0.25–0.415 in particle radius, and the number of particles is 12,392. Te parallel bond contact model is used and the number of contacts is 23,682. In this paper, the initial fracture is established by deleting particles. Te length of the initial fracture is 15 mm, the width is 0.5 mm, and the angle between the initial fracture and the horizontal direction is 45 degrees. Te fnal numerical model is shown in Fig. 2. Loading mode. Te displacement loading method is adopted. Te upper and lower walls are loading walls, and the moving speed of the wall is set to 0.05 m/s. According to the existing literature research results16,17, Scientifc Reports | (2021) 11:16425 | https://doi.org/10.1038/s41598-021-95964-x 2 Vol:.(1234567890) www.nature.com/scientificreports/ Figure 2. Numerical model of concrete with initial damage. Figure 3. Schematic diagram of eccentric load loading. the set wall velocity can simulate the quasi-static loading in laboratory test, and the loading will stop when the post peak stress drops to 80% of the peak stress. When the uniformly distributed load is compressed, the load is applied by moving the upper and lower walls, and the confning pressure is controlled by moving the lef and right walls. Under eccentric loading, fve loading walls are built around the specimen. Under uniaxial compres- sion, the two sides and the upper right walls are deleted afer the specimen is pre-molding, and the uniaxial compression is realized through the remaining two walls. When biaxial compression is conducted, axial stress is applied through the lower wall and the upper lef wall afer pre-molding, while the other walls are subject to confning pressure. Te schematic diagram of eccentric load uniaxial compression and biaxial compression loading is shown in Fig. 3.

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