岩土介质非稳态热固结耦合问题的热源函数法

HEAT SOURCE FUNCTION METHOD FOR COUPLING ANALYSES OF THERMAL CONSOLIDATION IN SATURATED SOIL

考虑耦合效应的饱和土体热固结问题控制方程,利用Fourier变换、Laplace变换给出其在变换域上的解,将初始温度场分布视为虚拟的热源或者将热源等价为特定的初始温度分布,利用热源函数法给出瞬时线热源非稳态温度场、应力场和位移场的解析求解方法,通过在时间域和空间域上进行积分,给出有初始温度场分布以及有分布内热源存在且热源强度随时间变化条件下的热固结问题计算方法。对一无限大物体内存在有平面矩形域热源情况下周围介质的温度、孔隙水压力以及位移等的变化特征进行分析。研究表明,热源函数法可有效地求解一系列复杂情况下的热固结问题。

Based on the governing equations of thermal coupling consolidation for saturated homogeneous isotropic porous materials, the solutions in transform space are given by repeated Fourier transformations and Laplace transformation. Considering initial temperature field as a fictitious heat source or equalizing heat source as specified initial temperature field, an analytical method for calculating the unsteady temperature field, stress field and displacement field of saturated soils due to instantaneous line heat source is deduced by using the so-called heat source function method. The influence of full coupling effects between the field quantities are considered. By integration in temporal and spatial domain, a calculation method of two-dimensional thermal consolidation problem with initial temperature field and variable strength of heat source with time is established. For convenience of analyses, the concepts of thermal consolidation time factor and coefficient of thermal consolidation are defined. The evolutions of temperature, pore water pressure and displacement with time factor around rectangular heat source are analyzed by the proposed method. The thermal consolidation characteristics and its mechanism are studied. It is showed that this method can be used to solve some complicated thermal consolidation problems effectively, and has an important theoretical and practical meaning.