11Corrosion-induced concrete cracking is a significant durability problem for reinforced 12 concrete structures. Considerable research has been carried out in the last few decades to 13 understand and model the expansion mechanism of the corrosion products around the 14 reinforcing bar and simulate the cracking behaviour of the concrete cover. In this paper, a 15 new corrosion model based on non-uniform corrosion expansion is formulated and validated 16 against experimental data. A meso-scale fracture model, consisting of aggregates, cement 17 paste/mortar and ITZ, is established for the cases of both middle and side reinforcing bars. 18Under the developed corrosion and concrete fracture model, the cracking phenomena of the 19 concrete cover are accurately simulated. It has been found that the non-uniform corrosion 20 model can be used to express the realistic corrosion rust progression around the reinforcing 21 bar, with the best accuracy. It has also been found that some microcracks occur before they 22 are connected to form the dominating discrete crack which usually appears on the concrete 23 surface. Moreover, the effects of the corrosion variables, as well as other key material and 24 geometric parameters, on surface cracking of concrete are investigated. 25 Keywords: non-uniform corrosion, cohesive crack model, meso-scale, reinforced concrete 26 structures, finite element method. 27 * Corresponding author. Tel: +44 141 548 3273. Email: shangtong.yang@strath.ac.uk. 28 reduction. Li et al. [8] developed an analytical model to calculate the crack width of concrete 48 cover by assuming the cracks smeared in concrete and considering concrete as a quasi-brittle 49 material. Among these existing studies, most are focused on uniform or general corrosion of 50 the reinforcement. 51 52Chlorides, as well as moisture and oxygen, diffuse into concrete and reach a threshold value 53 at the surface of steel bar, before the passive layer on steel surface is destroyed and corrosion 54 is initiated [9]. However, it is rare to have a uniform corrosion around the reinforcing bar, due 55 to different amount of chlorides, moisture and oxygen that are available on different sides of 56 the reinforcement; for example, the side of a reinforcing bar facing concrete cover should 57 have more sources to advance corrosion and hence more corrosion products accumulated on 58 this side. Recently, many researchers have started to model the cracking of concrete cover 59 induced by non-uniform corrosion of reinforcement. González et al. [10] perhaps first 60 compared the depth of pitting corrosion penetration on steel bar with the depth of general 61 corrosion and found that the maximum penetration of pitting corrosion on the steel bar is 62 equivalent to about three to sixteen times of the penetration of general corrosion. Jang and Oh 63 [11] extended the experimental results in [10] and designed a factor for the ratio of the 64 maximum thickness of non-uniform corrosion layer to the thickness of uniform corrosion 65 layer to express the n...

Rock mass behavior is determined not only by the properties of the rock matrix but also mostly by the pre-existing cracks in the rock mass. Before the overall failure of rock, the crack initiation and propagation around the tip of pre-existing cracks (i.e., pre-crack) will occur and contribute to rock failure. In this paper, the deep granite from a gold mine is taken and made to specimens with the pre-crack of 0.3 mm thickness. Uniaxial compression tests are carried out on the pre-cracked specimens. The acoustic emission (AE) sensors and digital image correlation (DIC) system are employed to record the failure characteristics of the specimens. The extended finite element method (XFEM) with the non-local stress field calculation is used to simulate the crack initiation and propagation of pre-cracks. The crack patterns, opening and shearing displacements of the cracked surface, and the crack length development are obtained from numerical simulations. Finally, the effects of friction of crack surface on the crack pattern and crack propagation are investigated and discussed. It has been found that, for pre-cracked specimens, crack initiation and propagation will occur when the stress is much smaller than the rock compressive strength. And in the range of pre-crack angle 30-60°, the larger the pre-crack angle is, the larger the compressive strength is. The crack patterns from numerical simulations have a good agreement with those from experimented DIC results. Moreover, the order of crack propagation speed is consistent with the order of the compressive strength. The crack pattern and crack propagation are affected by the friction coefficient of the cracked surface.

Corrosion-induced concrete cracking is a significant problem affecting the durability of reinforced concrete structures. Considerable research has been carried out in addressing this problem but few have considered the cracking process of concrete as a mixed-mode fracture and the concrete as a multi-phase material. This paper develops a meso-scale mixed-mode fracture model for the cracking of concrete structures under non-uniform corrosion of reinforcement. Concrete is treated as a three-phase heterogeneous material, consisting of aggregates, mortar and interfaces. An example is worked out to demonstrate the application of the derived model and is then partially verified against previously published experimental results. In agreement with experimental results, the new model reproduces the observation that microcracks tend to form first at the interfaces before they connect to generate a discrete crack. Toughening mechanisms, e.g., microcrack shielding, crack deflection, aggregate bridging and crack overlap, have been captured in the model. Further, effects of aggregate randomness on the crack width development of concrete structures, differences between uniform and non-uniform corrosion and a comprehensive parametric study have been investigated and presented.