Micromechanical modeling of drying shrinkage of cement based on pore size distribution and on capillary forces

由于相对湿度的变化，混凝土的干燥、收缩和膨胀对混凝土构件的耐久性、弹性和结构设计非常重要。即使在较低的相对湿度下，液态水也已经存在于微孔中，并作为C-S-H相的层间水存在。在几种不同成分的硬化水泥浆体中，经常观察到低湿条件下固体结构的水蒸气吸附和体积变化的明显滞后。通过比较普通硅酸盐水泥和钙铝水泥不同处理和制备的硬化水泥浆体的性能，我们能够确认低湿度下的滞后与微孔的存在有关。基于微孔和层间水的吸水性，建立了一个可以解释水蒸气吸附滞后及其与膨胀收缩滞后关系的理论模型。该模型能够再现与微孔数量相关的吸附等温线的重要拓扑特征，以及低水蒸气压下不同类型的水蒸气和氮气吸附等温线。实验吸附图的建模和解释以及硬化水泥浆体在整个湿度范围内的膨胀和收缩，需要同时考虑微孔和中孔，并通过计算机模拟改进对不同水泥浆体裂隙孔壁化学细节的建模。在项目继续中，将根据实测孔径分布纳入相应的滞回效应，完成部分开发的吸附、膨胀、收缩和滞回计算模型的理论基础。在不同的养护条件下，还可以用不同水灰比的高炉矿渣水泥生产出不同类型的水泥膏体。它们的吸水和吸氮性能以及相关的膨胀/收缩将作为相对湿度的函数进行测量。采用高压压汞法和SAXS测定相应的孔隙尺寸分布。在改进的水泥模型的实际层状结构上直接进行了水蒸气吸附的计算机模拟。特别要分析二价离子如钙离子对水泥浆中毛细力的影响。在这里，冷凝物与微孔壁之间的力（壁应变）以及封闭孔壁的粘附能将被确定。模拟结果为水泥浆体中水蒸气吸附和由此产生的体积变化的模型提供了额外的一致性测试。

Drying, shrinkage, and swelling of concrete due to variations of the relative humidity are very important for durability, resilience, and the structural design of concrete members. Even at a low relative humidity, liquid water is already present in micropores and as interlayer water within the C-S-H phases. In several types of hardened cement pastes with different compositions, pronounced hysteresis of water vapor sorption and volume change of the solid structure at low humidity is frequently observed. By comparing the behavior of differently treated and prepared hardened cement pastes from Ordinary Portland- and Calcium Alumina Cement, we were able to confirm a hysteresis at low humidity which is linked to the presence of micropores. We developed a theoretical model that can explain water-vapor sorption hysteresis and its connection to hysteresis of swelling and shrinkage based on water sorption in micropores and interlayer water. The model is capable of reproducing important topological features of sorption isotherms in relation to the amount of micropores as well as the different types of isotherms of water vapor and nitrogen sorption for low water vapor pressures. Modelling and interpretation of experimental sorption diagrams as well as the swelling and shrinkage of hardened cement paste in the whole humidity range needs to take into account both micro- and mesopores as well as an improved modeling of chemical details of slit-pore walls in different cement pastes by computer simulations. In the project continuation, the theoretical foundations of a partially developed model for calculating sorption, swelling, shrinkage, and hysteresis are to be completed by inclusion of the corresponding hysteresis effects based on measured pore size distributions. Additional types of cement pastes from Blast-furnace slag cement with several water to cement ratios will be produced at different curing conditions. Their water- and nitrogen sorption properties and the associated swelling/shrinkage will be measured as a function of relative humidity. The corresponding pore size distribution will be determined by high-pressure mercury intrusion porosimetry and SAXS. Direct computer simulations of water vapor sorption on realistic layer structures of improved cement models are planned. In particular, the effect of divalent ions such as calcium ions on the capillary forces in cement pastes are to be analyzed. Here, the forces (wall strain) between the condensate and the micropore walls as well as the adhesion energy for the walls of closed pores are to be determined. The simulation results provide additional consistency tests for the models of water vapor sorption and the resulting volume changes in cement paste.