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、收缩和膨胀对于混凝土构件的耐久性、弹性和结构设计非常重要。即使在低相对湿度下，液态水也已经存在于微孔中，并以层间水的形式存在于C-S-H相中。在几种不同组成的硬化水泥浆体中，在低湿度条件下，经常观察到明显的水蒸气吸收滞后和固体结构的体积变化。通过比较不同处理和制备的硬化水泥浆体与普通硅酸盐水泥和钙氧化铝水泥的行为，我们能够确认低湿度下的滞后现象，这与微孔的存在有关。基于微孔和层间水的吸水特性，我们建立了一个理论模型来解释水蒸气吸附滞后现象及其与膨胀和收缩滞后的关系。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，以及在低水蒸气压力下不同类型的水蒸气和氮气吸附等温线。对实验吸附图以及硬化水泥浆体在整个湿度范围内的膨胀和收缩的模拟和解释需要同时考虑微孔和介孔，并需要通过计算机模拟来改进对不同水泥浆体中缝隙孔壁的化学细节的模拟。在项目继续中，部分开发的用于计算吸附、膨胀、收缩和滞后的模型的理论基础将通过包含基于测量的孔径分布的相应滞后效应来完成。在不同的养护条件下，将由几种水灰比的高炉矿渣水泥制成其他类型的水泥浆体。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。相应的孔径分布将通过高压压汞孔隙仪和SAXS来确定。计划对改进的水泥模型的真实层结构上的水蒸气吸收进行直接计算机模拟。特别是分析了钙离子等二价离子对水泥浆体毛细管力的影响。这里，冷凝液和微孔壁之间的力(壁应变)以及闭合孔壁的粘附能被确定。模拟结果为水蒸气吸收模型和由此引起的水泥浆体体积变化提供了额外的一致性检验。

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.