Two-Level Hierarchical PCG Methods for the Quadratic FEM Discretizations of 2D Concrete Aggregate Models

The concrete aggregate model is considered as a type of weakly discontinuous problem consisting of three phases:aggregates which randomly distributed in different shapes,cement paste and internal transition zone(ITZ).Because of different shapes of aggregate and thin ITZs,a huge number of elements are often used in the finite element(FEM)analysis.In order to ensure the accuracy of the numerical solutions near the interfaces,we need to use higher-order elements.The widely used FEM softwares such as ANSYS and ABAQUS all provide the option of quadratic elements.However,they have much higher computational complexity than the linear elements.The corresponding coefficient matrix of the system of equations is a highly ill-conditioned matrix due to the large difference between three phase materials,and the convergence rate of the commonly used solving methods will deteriorate.In this paper,two types of simple and efficient preconditioners are proposed for the system of equations of the concrete aggregate models on unstructured triangle meshes by using the resulting hierarchical structure and the properties of the diagonal block matrices.The main computational cost of these preconditioners is how to efficiently solve the system of equations by using linear elements,and thus we can provide some efficient and robust solvers by calling the existing geometric-based algebraic multigrid(GAMG)methods.Since the hierarchical basis functions are used,we need not present those algebraic criterions to judge the relationships between the unknown variables and the geometric node types,and the grid transfer operators are also trivial.This makes it easy to find the linear element matrix derived directly from the fine level matrix,and thus the overall efficiency is greatly improved.The numerical results have verified the efficiency of the resulting preconditioned conjugate gradient(PCG)methods which are applied to the solution of several typical aggregate models.

Physical Model of Drying Shrinkage of Recycled Aggregate Concrete

We prepared concretes（RC0, RC30, and RC100） with three different mixes. The poresize distribution parameters of RAC were examined by high-precision mercury intrusion method（MIM） and nuclear magnetic resonance（NMR） imaging. A capillary-bundle physical model with random-distribution pores（improved model, IM） was established according to the parameters, and dry-shrinkage strain values were calculated and verified. Results show that in all pore types, capillary pores, and gel pores have the greatest impacts on concrete shrinkage, especially for pores 2.5-50 and 50-100 nm in size. The median radii are 34.2, 31, and 34 nm for RC0, RC30, and RC100, respectively. Moreover, the internal micropore size distribution of RC0 differs from that of RC30 and RC100, and the pore descriptions of MIM and NMR are consistent both in theory and in practice. Compared with the traditional capillary-bundle model, the calculated results of IM have higher accuracy as demonstrated by experimental verifi cation.

Experimental study on behavior of mortar-aggregate interface after elevated temperatures

A push-out test program was designed and conducted to study the meso-scale behavior of mortaraggregate interface for concrete after elevated temperatures ranging from 20℃ to 600℃ with the concept of modeled concrete （MC） and modeled recycled aggregate concrete （MRAC）. The MCs and MRACs were designed with different strength grade of mortar and were exposed to different elevated temperatures. Following that the specimens were cooled to room temperature and push-out tests were conducted. Failure process and mechanical behaviors were analyzed based on failure modes, residual load-displacement curves, residual peak loads and peak displacements. It is found that failure modes significantly depended on specimen type, the elevated temperature and the strength grade of mortar. For MC, major cracks started to propagate along the initial cracks caused by elevated temperatures at about 80% of residual peak load. For MRAC, the cracks appeared at a lower level of load with the increasing elevated temperatures. The cracks connected with each other, formed a failure face and the specimens were split into several parts suddenly when reaching the residual peak load. Residual load-displacement curves of different specimens had similarities in shape. Besides, effect of temperatures and strength grade of mortar on residual peak load and peak displacement were analyzed. For MC and MRAC with higher strength of new hardened mortar, the residual peak load kept constant when the temperature is lower than 400℃ and dropped by 43.5% on average at 600℃. For MRAC with lower strength of new hardened mortar, the residual peak load began to reduce when the temperatures exceeded 200℃ and reduced by 27.4% and 60.8% respectively at 400℃ and 600℃. The properties of recycled aggregate concrete （RAC） may be more sensitive to elevated temperatures than those of natural aggregate concrete （NAC） due to the fact that the interracial properties of RAC are lower than those of NAC, and are deteriorated at lower temperatures.