均质非饱和土一维稳态流水头垂直分布的解析解

渗流场水头分布计算是进行渗流量和渗流水力坡降计算的基础，准确、有效地求取渗流场水头分布是渗流计算的关键环节。对均质非饱和土体一维稳态流的流动方程进行分析，考虑到渗透系数是与基质吸力相关的函数，通过数学变换，给出了稳定渗流场的解析通式，并基于渗透性函数中的Gardner模型，给出了非饱和土一维稳态流水头垂直分布的解析解。该解析通式表明，均质非饱和土一维稳态流水头垂直分布主要受地表水头、深度和流动率3个因素控制。分别计算了一维稳态蒸发条件下粉土和黏土两种典型土类水头沿垂直方向的分布。计算结果表明：稳态蒸发条件下粉土层和黏土层内的水头分布表现出相似的变化规律，即自地表至地下水位处随着土层深度的增加，水头分布呈现出加速递减的趋势；在相同的蒸发条件下，对于相同深度处的黏土和粉土而言，黏土层内水头更高些；对同一种土类而言，在较大的蒸发状态下同一深度处土层内水头更高。反之，则较低。

Analytical solution of unidimensional steady flow hydraulic head vertical distribution in homogeneous unsaturated soil

The hydraulic head distribution of seepage field is the basis of seepage discharge and seepage hydraulic gradient calculation. Calculating the hydraulic head distribution of seepage field accurately and effectively is the key link in the calculation of seepage. According to the flow equation of unidimensional steady flow in homogeneous unsaturated soil and the functional relationship between hydraulic conductivity and matric suction, an analytical general formulation of seepage field is obtained with mathematical transformation. In addition, based on the Gardner model, the analytical solution of unidimensional steady flow hydraulic head vertical distribution in unsaturated soil is derived. The general formulation indicates that the unidimensional steady flow hydraulic head vertical distribution is mainly controlled by such three factors as surface water head, depth and rate of flow. Under the condition of unidimensional steady evaporation, the hydraulic head distributions of two typical soils in vertical direction, namely silt and clay, are calculated respectively. The result shows that under the steady evaporation condition, the laws of hydraulic head distribution of silt and clay in vertical direction are similar. With the increase of depth, the characteristic of hydraulic head distribution shows an accelerating degressive tendency from surface to groundwater level. The hydraulic head in clay is higher than that in silt under the same evaporation condition. For the same soil, the faster the evaporation, the higher the hydraulic head. Conversely, the hydraulic head is lower.