高温下混凝土水力、热及变形耦合数学模型

针对受高温载荷的混凝土提出了一个水力-热-变形耦合的数学模型，模型中采用了3种不同的连续介质：水蒸汽与干燥空气的混合气体相，液态水以及固态混凝土骨架。在连续介质的Navier-Stokes方程基础上，推导了各相介质的质量守恒方程、动量守恒方程以及混合物整体的能量守恒方程。为了简化问题，引入了若干假设，给出了基于文献资料数据拟合的某些变量的用基本未知量表达的经验公式，建立了基于物理定律的各类运动学变量与其热力学共轭力的本构关系，并给出了系统偏微分方程。

Mathematical modelling of thermo-hydro-mechanical behaviour for concrete under elevated temperature

A hydro-thermo-mechanical model is presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation are derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables are given with existing data from references. Specifications of the constitutive relations are made for the kinetic variables and their conjugate forces. Consequently a set of governing partial differential equations are obtained.