The classically lattice model assumes the local elements behave elastic brittle, neglecting the ductility of the mortar matrix. This leads to the simulated load⁃displacement response more brittle than the realistic. To solve the aforementioned issue, a piece⁃wise approach was introduced to describe the elastic⁃plastic constitutive relation of lattice element. The fracture process and the load⁃displacement response were obtained through the sequentially⁃linear solution approach. The model was calibrated using the uniaxial tension and compression tests. It is found that the model can precisely simulate the fracture process and load⁃displacement response. Moreover, the model was used to model the size effect in uniaxial tension and the influence of the specimen’s slenderness and boundary confinement on the fracture behavior under compression. It offers a new theoretical method and approach for studying the fracture of concrete.

It was widely acknowledged that dissolved organic matter (DOM) in natural water has ubiquitous competitiveness against organic micropollutants (OMPs) during adsorption onto activated carbon. However, some (model) low molecular weight organics have been reported to adsorb onto activated carbon, but were not competitive against co-adsorbates. The objective of this study is to identify which adsorbable DOM fractions in natural water contribute to the DOM competitiveness, and what is the impact of the OMP adsorbability and initial OMP concentration on this competitiveness. We, therefore, disassociated the adsorption of DOM fractions and OMPs (carbamazepine, caffeine and sulfamethoxazole) using a two-stage adsorption procedure, removing various adsorbable DOM fractions with powdered activated carbon pretreatment and then unraveling the competitiveness against OMPs of the remaining DOM. Our results demonstrated that DOM competition was not ubiquitous for all adsorbable fractions in natural water, and ∼ 25% of the adsorbable DOM was not competitive. The poorly adsorbable DOM was shown to be a non-competitive co-adsorbate, and its complexation even elevated the adsorption capacity of one of the OMPs (carbamazepine). The amount of DOM competitors increased for weaker adsorbable OMPs, and at higher initial OMP concentrations. The variability in DOM competition, differentiated by DOM adsorbability, has advanced the understanding of DOM competition, from ubiquitous competition to variable roles (varying competitiveness/complementary adsorption) of differently adsorbable DOM fractions during OMP adsorption.