一維穩(wěn)態(tài)流非飽和土滲透系數(shù)垂直分布模型及其線性簡化

程大偉 陳茜 安鵬 郭鴻 鄭睿

摘要：滲透系數(shù)是控制地下水流動的重要參數(shù)，對滲透系數(shù)的空間分布規(guī)律進行研究具有重要的意義。基于Gardner模型獲取了一維穩(wěn)態(tài)流非飽和土滲透系數(shù)沿垂直分布模型，該模型用指數(shù)函數(shù)描述，受飽和滲透系數(shù)和無量綱的深度與流動率等因素的控制；該模型表明一維穩(wěn)態(tài)流條件下均質(zhì)典型土類的滲透系數(shù)其沿垂直方向變化趨勢主要受比流量與飽和滲流系數(shù)的負數(shù)值二者之間的相對大小影響。分別采用泰勒級數(shù)方法和以地下水位處及地表處的滲透系數(shù)作為控制條件方法對一維穩(wěn)態(tài)流非飽和土滲透系數(shù)沿垂直分布模型進行線性近似簡化。采用泰勒級數(shù)方法獲取的簡化模型其計算誤差隨無量綱的深度增大而增大。簡化后的模型具有形式簡單、參數(shù)少等特點。通過算例對比簡化模型與原模型的差異，計算結(jié)果表明：采用以地下水位處及地表處的滲透系數(shù)作為控制條件的方法進行線性近似簡化的模型計算誤差比采用泰勒級數(shù)方法獲得的線性近似簡化模型的計算誤差小。

關鍵詞：一維穩(wěn)態(tài)流；滲透系數(shù)；垂直分布；簡化模型

中圖分類號：TU435

文獻標志碼：A 文章編號：1674-4764（2016）02-0029-06

Abstract：The permeability coefficient is important to investigate permeability coefficient spatial distribution of groundwater flow. Based on Gardner model， the permeability coefficient vertical distribution model is established， expressed as exponential， which is controlled by saturation permeability coefficient， dimensionless depth and dimensionless flow rate. The model shows that the permeability coefficient vertical distribution for homogeneous typical soils is influenced by the difference between flow rate and aturation permeability coefficient. And then， simplifies the model is simplified as linear model based on Taylors series and permeability coefficient of groundwater level and the earths surface as control conditions. The error of linear model with the method of Taylors series increases when dimensionless depth increases. The calculation results of the simplified model and the original model are compared . The result shows that the linear model with the method of permeability coefficient of groundwater level and the earths surface as control conditions is more accurate than the linear model with the method of Taylors series.

Keywords：unidimensional steady flow； permeability coefficient； vertical distribution； simplified model

非飽和土的滲透系數(shù)是控制土層中水分和污染物遷移的重要參數(shù)之一[1]。試驗獲取滲透系數(shù)的方法分為穩(wěn)態(tài)方法和非穩(wěn)態(tài)方法的瞬時截面法[2]。滲透試驗的測試結(jié)果表明，滲透系數(shù)對飽和度的依賴性較大[3]，在低飽和度時，滲透系數(shù)的測試非常困難。……