考虑裂缝-胶囊相遇概率的自修复水泥基材料胶囊掺量研究

Reasonable amounts and geometric features (size, shape) of capsules embedded in matrix are the key factors which are determining the effect of crack self-repairing via capsules technology of cementitious materials. Using modelling investigation and numerical simulation with some experiments on the basis of previous researches, this project will explore the determination basis and the analytical models of amount and geometric features of capsules required in the self-repairing theory of crack via capsules technology of cementitious materials. From the appearances and distribution features of macro- and micro- crack induced in the cracked cementitious material under practical service environments, simplified crack patterns will be presented. Then based on the fact that the fracture of capsules embedded are forced by cracks, the hitting probability model (hitting model of crack - capsule) and the analytical model of amount of capsules required will be developed. Meanwhile, the computational method of the analytical amount models will also be given. Further, the influence rules of geometric features and distribution characteristics of capsules embedded on self-repairing efficiency will be revealed and quantitatively expressed, and then the optimal geometric features of the capsule embedded in the matrix are determined. Meanwhile, the amount model of capsules proposed and the geometric features obtained are verified by experiments. From the actual existing crack pattern of cementitious composite material, the modeling methods and analytical models presented for capsules in the project are universal applicability. This project will provide the theoretical guidance for the determinition of capsules embedded and enrich the design theory of self-repairing cementitious materials via capsules technology.

胶囊的合理掺量及其几何特征（尺寸、形貌）是决定水泥基复合材料胶囊法裂缝自修复效果的关键因素之一。本项目在已有研究的基础上，运用模型研究和数值模拟的方法并辅以试验手段，探究胶囊法裂缝自修复理论中胶囊掺量及其几何特征的确定依据和解析模型。基于实际服役环境下水泥基复合材料基体开裂所形成的宏观与微观裂缝形貌和分布特征，模型化地提出简化的裂缝格局；继而利用几何概率和随机几何学理论构建裂缝迫使胶囊发生破裂的相遇概率模型（裂缝-胶囊概遇模型）以及所需胶囊掺量的解析模型，提出所需胶囊掺量的计算方法；进而揭示胶囊的几何特征和分布特征对自修复效率的影响规律及其量化关系，并确定胶囊的最优几何特征。同时试验验证所建胶囊掺量模型与所得几何特征的结果。本项目研究从水泥基复合材料实际已有裂缝格局出发，所用模型化方法和所建解析模型具有普适性，可为确定胶囊的掺量提供理论指导，并将充实胶囊法裂缝自修复水泥基材料的设计理论。

胶囊法自修复理论及技术是解决水泥基材料服役过程中开裂问题、提高服役性能的重要途径。而胶囊的合理掺量及其几何特征（尺寸、形貌）的选择是决定水泥基复合材料胶囊法裂缝自修复效果的关键因素之一。.基于不同物理化学因素导致的水泥基材料基体开裂所形成的裂缝形貌和分布特征，提炼出了反映基材实体裂缝形态布局的简化裂纹模型，即宏观取向型裂缝格局和微观离散型裂缝格局。胶囊随机分布于基体的假设下，分别在宏观和微观尺度下建立了裂缝迫使胶囊发生破裂的相遇概率模型——裂缝-胶囊概遇模型，计算出了不同裂缝格局下裂缝与胶囊相遇的概率，该概率能刻画胶囊掺量、胶囊尺寸、裂缝尺寸和形貌等因素。.基于自修复复合材料裂缝被修复的实际状况和风险设计理念，提出了胶囊法自修复水泥基材料裂缝的目标修复水平概念，并利用此概念建立了相应的数学模型来确定所需胶囊的理论掺量。同时，研究了不同胶囊形貌（球形和长形）和大小对相遇概率和胶囊掺量的影响，分析了裂缝尺寸、宽度以及裂缝生长等因素对自修复效率的影响。针对在三维基体中掺入球形胶囊和圆柱体形胶囊，以及基体内随机出现的离散型裂缝，研究结果表明在胶囊同等掺量情况下单纯地使用具有一定长径比的圆柱体胶囊所得到自修复效果未必一定高于使用球形胶囊的结果。.利用积分几何学理论和几何概率理论，采用严格的数学推导过程，以球形和棒状胶囊为例，建立了无限大裂缝面贯穿基体情况下胶囊几何特征（形貌、尺寸）对自修复效率影响的通用解析表达式。结果表明，为了提高修复剂的释放效率，胶囊的形貌和尺寸参数需要兼顾考虑。此结论不同于已有文献所申明的“对比随机分布的棒状和球形胶囊，修复剂释放效率提升率仅与胶囊的长径比有关，与胶囊的尺寸无关”。.胶囊理论掺量计算方法与自修复效率关于胶囊几何特征（形貌、尺寸）的解析模型将充实胶囊法自修复水泥基材料的优化设计理论。