基于水头和饱和度分布的双变量土坝渗流研究
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摘要
渗流现象是多孔介质中普遍客观存在的运动规律,其对水工建筑物稳定性、地下水资源利用、污染控制、石油天然气开采等工程问题均具有重要的影响,随着国内外在上述领域中工程需求的增加,渗流研究日益成为热点问题。
本文在饱和、非饱和渗流理论基础上,结合非饱和渗透系数研究成果,对达西速度的表达式进行变形,建立了饱和一非饱和渗流数值模型。该模型中以测压管水头和饱和度为变量对渗流场进行描述。将渗流域分为饱和区与非饱和区,为避免研究复杂的多相流问题,可以认为非饱和区是与大气相通的,则测压管水头中的压力与大气压相等,使测压管水头等于位置水头,从而渗流控制方程在两个区域中分别退化为关于测压管水头的拉普拉斯方程和关于饱和度的对流方程。空间用伽辽金有限元方法,时间采用隐式差分方法对方程进行离散。分别对饱和区的拉普拉斯方程采用预处理共轭梯度法(PCG)、非饱和区的对流方程采用Gauss—Seidel方法进行耦合迭代求解,得到渗流场的测压管水头分布和饱和度分布,并引入VOF的概念,由饱和度的分布自动扑捉渗流自由面。
为测定非恒定水位边界条件下的土坝渗流自由面和坝体内测压管水头的变化,在实验室内进行了模型土坝的非恒定渗流实验。通过对实验结果进行分析,初步认识了不透水地基上均质土坝在非恒定边界条件下的非稳定渗流的物理力学特性。推导了双介质土柱表层水入渗的下渗锋面解析表达式、稳定状态时测压管水头分布与饱和度分布的解析表达式,并给出了有周期性边界条件的有限潜水层内渗流自由面的解析表达式。用本文提出的饱和—非饱和渗流模型分别对几个解析解问题以及渗流实验进行了数值模拟,通过所得结果与解析解和实验的对比,证明了模型的合理性、可靠性和准确性。
将饱和—非饱和渗流模型用于几个工程实例,其二维模拟结果同渗流电模拟实验结果进行了对比,证明本文的渗流模型完全能够准确计算坝内的渗流浸润线以及逸出面位置;三维数值模拟的结果在相近剖面处与二维结果作了比较,考虑三维网格剖分及剖面截取位置的差异,三维结果与二维结果吻合的较好,证明本文的饱和—非饱和渗流模型在三维计算中是可靠的且具有较高的实用价值。在串行程序的基础上,应用OpenMP编程接口进行了并行化改造,对渗流场实现了并行求解。通过相同位置剖面与二维结果的比较很好的证明了计算结果的可靠性和准确性;通过对不同规模问题的加速比的测定,证明了应用OpenMP改造的串行程序能够很好的实现渗流场并行求解,达到减小计算耗时、便于工程应用的目的。
Seepage flow is a motion law that exists in porous media impersonally.It has important effects for the stability of water conservancy building,the using of groundwater resource,the pollution controlling,the exploitation of rock oil and natural gas.And the needs of projects for those fields are increasing home and abroad.So the research of seepage flow becomes focuse.
In this article,a saturated and unsaturated seepage model has been established which includes double variables:piezometric tube waterhead and saturation.The model theory bases on the saturated theory and unsaturated theory.The form of Darcy velocity is changed according to the production of unsaturated hydraulic conductivity in the model.The seepage field was divided into two regions:saturation and unsaturation.The saturation equals 1 in saturated region.The piezometric tube waterhead equals position head by neglecting the effect of capillarity in unsaturated region.So the nonlinear parabolic equation of seepage flow will degenerate to Laplace equation about piezometric tube waterhead in saturated region and convective equation about saturation in unsaturated region respectively.The equations are discretized with the Galerkin FEM in space and the implicit difference method in time.And the equations are solved coupling iteratively whith PCG method for Laplace equation and Gauss—Seidel method for convective equation.So the distribution of piezometric tube waterhead and saturation can be obtained.And the seepace free surface will be captured automatically according to the distribution of saturation with the concept of VOF.
An experiment of unsteady seepage flow through dam is done in laboratory.In the experiment,the changes of seepage surface and pressure head in dam are mensurated.By analyzing the result of experiment,the characteristic of physicsdynam is gotten for unsteady seepage flow with movement boundary on staunch groundwork.Three analytical solutions are given including the wet front analysis solution of double medium soil column,the analytical expression of piezometric tube water head and saturation for steady state and the analysis solution of seepage in unconfined aquifer with a periodic boundary condition.The problems of analysis and experiment are modeling by the seepage model that presented in this paper.The dependability and accuracy of model are proved by comparing with the analytical solutions and experiments results.
The model is used to count several engineering example.Comparing the 2D numerical results with electrical simulations,it is proved that the seepage model can count the seepage surface and the location of search results in dam well and truly.Comparing 3D results with 2D results at close section,the results are tally well except the difference of meshes and the interceptive position of section.So the model is credible and has upper practicality value.In the projects,the spending of account is increasing because of the bigger account field.In this article,the seepage field is parallelly solved rapidly by changing serial program to parallel program with OpenMP API.It was proved that the parallel result is reliability and accuracy by comparing the results of 3D and 2D at close position.It is proved that the parallel program can account the seepage field well and rapidly by comparing the speedup of different scale.And the paralle program will do well in works.
本文在饱和、非饱和渗流理论基础上,结合非饱和渗透系数研究成果,对达西速度的表达式进行变形,建立了饱和一非饱和渗流数值模型。该模型中以测压管水头和饱和度为变量对渗流场进行描述。将渗流域分为饱和区与非饱和区,为避免研究复杂的多相流问题,可以认为非饱和区是与大气相通的,则测压管水头中的压力与大气压相等,使测压管水头等于位置水头,从而渗流控制方程在两个区域中分别退化为关于测压管水头的拉普拉斯方程和关于饱和度的对流方程。空间用伽辽金有限元方法,时间采用隐式差分方法对方程进行离散。分别对饱和区的拉普拉斯方程采用预处理共轭梯度法(PCG)、非饱和区的对流方程采用Gauss—Seidel方法进行耦合迭代求解,得到渗流场的测压管水头分布和饱和度分布,并引入VOF的概念,由饱和度的分布自动扑捉渗流自由面。
为测定非恒定水位边界条件下的土坝渗流自由面和坝体内测压管水头的变化,在实验室内进行了模型土坝的非恒定渗流实验。通过对实验结果进行分析,初步认识了不透水地基上均质土坝在非恒定边界条件下的非稳定渗流的物理力学特性。推导了双介质土柱表层水入渗的下渗锋面解析表达式、稳定状态时测压管水头分布与饱和度分布的解析表达式,并给出了有周期性边界条件的有限潜水层内渗流自由面的解析表达式。用本文提出的饱和—非饱和渗流模型分别对几个解析解问题以及渗流实验进行了数值模拟,通过所得结果与解析解和实验的对比,证明了模型的合理性、可靠性和准确性。
将饱和—非饱和渗流模型用于几个工程实例,其二维模拟结果同渗流电模拟实验结果进行了对比,证明本文的渗流模型完全能够准确计算坝内的渗流浸润线以及逸出面位置;三维数值模拟的结果在相近剖面处与二维结果作了比较,考虑三维网格剖分及剖面截取位置的差异,三维结果与二维结果吻合的较好,证明本文的饱和—非饱和渗流模型在三维计算中是可靠的且具有较高的实用价值。在串行程序的基础上,应用OpenMP编程接口进行了并行化改造,对渗流场实现了并行求解。通过相同位置剖面与二维结果的比较很好的证明了计算结果的可靠性和准确性;通过对不同规模问题的加速比的测定,证明了应用OpenMP改造的串行程序能够很好的实现渗流场并行求解,达到减小计算耗时、便于工程应用的目的。
Seepage flow is a motion law that exists in porous media impersonally.It has important effects for the stability of water conservancy building,the using of groundwater resource,the pollution controlling,the exploitation of rock oil and natural gas.And the needs of projects for those fields are increasing home and abroad.So the research of seepage flow becomes focuse.
In this article,a saturated and unsaturated seepage model has been established which includes double variables:piezometric tube waterhead and saturation.The model theory bases on the saturated theory and unsaturated theory.The form of Darcy velocity is changed according to the production of unsaturated hydraulic conductivity in the model.The seepage field was divided into two regions:saturation and unsaturation.The saturation equals 1 in saturated region.The piezometric tube waterhead equals position head by neglecting the effect of capillarity in unsaturated region.So the nonlinear parabolic equation of seepage flow will degenerate to Laplace equation about piezometric tube waterhead in saturated region and convective equation about saturation in unsaturated region respectively.The equations are discretized with the Galerkin FEM in space and the implicit difference method in time.And the equations are solved coupling iteratively whith PCG method for Laplace equation and Gauss—Seidel method for convective equation.So the distribution of piezometric tube waterhead and saturation can be obtained.And the seepace free surface will be captured automatically according to the distribution of saturation with the concept of VOF.
An experiment of unsteady seepage flow through dam is done in laboratory.In the experiment,the changes of seepage surface and pressure head in dam are mensurated.By analyzing the result of experiment,the characteristic of physicsdynam is gotten for unsteady seepage flow with movement boundary on staunch groundwork.Three analytical solutions are given including the wet front analysis solution of double medium soil column,the analytical expression of piezometric tube water head and saturation for steady state and the analysis solution of seepage in unconfined aquifer with a periodic boundary condition.The problems of analysis and experiment are modeling by the seepage model that presented in this paper.The dependability and accuracy of model are proved by comparing with the analytical solutions and experiments results.
The model is used to count several engineering example.Comparing the 2D numerical results with electrical simulations,it is proved that the seepage model can count the seepage surface and the location of search results in dam well and truly.Comparing 3D results with 2D results at close section,the results are tally well except the difference of meshes and the interceptive position of section.So the model is credible and has upper practicality value.In the projects,the spending of account is increasing because of the bigger account field.In this article,the seepage field is parallelly solved rapidly by changing serial program to parallel program with OpenMP API.It was proved that the parallel result is reliability and accuracy by comparing the results of 3D and 2D at close position.It is proved that the parallel program can account the seepage field well and rapidly by comparing the speedup of different scale.And the paralle program will do well in works.
引文
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