共查询到17条相似文献，搜索用时 140 毫秒
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经典的Richards入渗控制方程属于偏微分方程,具有强烈的非线性,难以求得解析解。以入渗时间为最小作用量,基于Richards方程建立关于入渗路径的时间泛函,将考虑重力项的非饱和土垂直入渗问题转化为泛函极值问题,并构造等价的Euler-Lagrange方程进行求解。计算结果表明,扩散系数D（?）与概化湿润锋距离具有函数关系,当扩散系数D（?）形式已知时,可求得最优路径下湿润锋处含水率、较远处湿润锋最小含水率、土壤含水率最大熵分布3个问题,并基于最优路径检验了本研究条件下,Boltzmann变换和线性变换求解Richards方程的精度。求解过程未引进新变量化简Richards方程,不改变原方程结构,因此其解具有普遍性,可作为非饱和土力学计算的一个补充。 相似文献
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以多孔介质理论为基础,研究了稳态条件下非饱和土中温度?水分?盐分多场耦合问题。考虑非饱和土的孔隙被液态水、溶解的盐分、水蒸气和干燥气体等填充,在质量和能量守恒的基础上获得了非饱和土中水分、气体、盐分的质量守恒方程以及能量守恒方程。考虑一维稳态问题,选取温度、孔隙气压、孔隙水压和盐溶液浓度以及它们的导数作为状态变量,得到了问题的状态方程组。在给定的边界条件下,采用打靶法求解了该强耦合的非线性变系数微分方程组,通过与已有的试验结果相比较,验证了模型的有效性。基于数值算例,参数分析了含水率、温度边界、孔隙率等条件对非饱和土中温度场、水分场和盐分场分布的影响规律。 相似文献
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含裂隙土体在降雨条件下的渗流规律相对比较复杂,为进一步讨论含裂隙土体渗流机制,在一维解析解的基础上,建立二维饱和-非饱和含裂隙土渗流解析模型,并通过Fourier积分变化推导出二维渗流控制方程的显式解析解。此解析解考虑了多裂隙情况下的孔隙水压力分布和流量边界条件。二维解析解能够准确地获得渗流和变形耦合非饱和土中水的入渗影响规律,并进一步讨论了降雨条件下,不同裂隙模式(裂隙深度、裂隙发育位置及裂隙密集程度)对坡体渗流的影响规律,探讨了含裂隙区域的孔隙水压力分布规律。 相似文献
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库仑土压力的变分法研究 总被引：1，自引：1，他引：1
以滑动体静力平衡的两个力平衡方程为基础,引入拉氏乘子,将土压力问题以变分学观点来描述,转化为确定含有两个函数自变量的泛函极值问题。依据泛函取极值时必须满足的欧拉方程,得出了主动土压力和被动土压力在取极值时,墙后土体的破坏是沿平面滑动。然后,将土压力的泛函极值问题进一步转化为带有约束的函数极值问题。这种函数极值可利用M atlab6.1优化工具箱提供的fm incon函数进行求解。当土体的粘聚力等于0时,土压力计算结果与库仑土压力理论解完全一致;而当土体的粘聚力不等于0时,归纳给出了相应的土压力计算公式。 相似文献
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《岩土力学》2020,(3)
设计一种可以测量土体体积含水率的降雨入渗试验模型,通过试验得到土体初始含水率分布状态以及降雨入渗条件下土体含水率变化规律。在此基础之上,结合非饱和土抗剪强度理论与极限平衡理论,得到降雨入渗条件下土质边坡浅层稳定性计算方法。对杭新景高速公路七里连接线工程沿线土质边坡稳定性进行分析,具体结论如下:可采用含水率分布参数A、修正系数λ、μ表征的反比例函数表示自然状态下土体的初始含水率分布规律。含水率分布参数对边坡稳定性影响表现为随着A值的增大,边坡初始稳定性逐渐下降,边坡受降雨影响的敏感程度也随之下降。降雨强度相同时,初始表面含水率越大引起边坡失稳所需的降雨时间越短;降雨时间相同时,初始表面含水率越大引起边坡失稳所需的降雨强度越小。在相同地下水位条件下,边坡降雨强度与导致边坡失稳所需的降雨时间成反比。 相似文献
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从基坑柔性支护结构后的滑动土楔体的整体静力平衡方程出发,推导了考虑作用点位置的主动土压力泛函极值等周模型。在此基础上引入拉格朗日乘子,将主动土压力问题转化为确定含有两个函数自变量的泛函极值问题。对于一般黏性土,依据泛函取极值时必须满足的欧拉方程,得到了对数螺旋线的滑裂面函数和沿滑裂面分布的法向应力函数。结合边界条件和横截条件,主动土压力泛函极值问题进一步转化为以两个拉格朗日常数为未知量的函数优化问题。同时,讨论了滑裂面为平面和圆弧面两种特殊情况。通过算例表明,对于一般土体,在作用点位置系数下限处,主动土压力最小,滑裂面为平面;随着作用点位置的上移,主动土压力呈非线性增长,相应滑裂面为对数螺旋面。对于砂性土,位置系数上限值随内摩擦角的增大而增大,其相应的土压力值也随之增加。对于软黏土,滑裂面为圆弧面,随着作用点位置的上移,主动土压力呈非线性下降,滑裂面背离基坑方向移动。 相似文献
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温度梯度、含水率梯度和压力梯度对非饱和土体中的水热迁移有重要影响。用非饱和黄土填筑室内模型,通入0.10MPa高温水蒸气,研究蒸汽压梯度、温度梯度和含水率梯度耦合作用下的水热迁移规律。结果表明:在水蒸气迁移范围之内,土体的升温速率、增湿速率和增湿程度较大,以蒸汽传热和压力梯度驱动的水蒸气增湿为主。而在水蒸气未到位置,以温度梯度引起的热传导和含水率梯度与温度梯度耦合驱动的水热迁移为主;水蒸气迁移时,受土颗粒阻碍和蒸汽压消散的影响,土体升温速率、增湿速率和温度传导速率均随径向距离的增大而减小,且增湿速率小于升温速率;水蒸气增湿土体的最大含水率接近最优含水率,增湿效果较好,可有效提高一定范围内土体的压实性能;基于模型试验边界条件,确定含湿毛细多孔介质中二维热湿迁移方程的一组代数显式特解,并以20 cm测点为例,将温度和含水率实测值和计算值进行对比分析。研究结果可为非饱和黄土水-汽-热耦合传输规律和水蒸气增湿新技术研究提供理论支持。 相似文献
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为了研究压实黄土中的水分垂直入渗规律和非饱和渗透系数函数,在实验室内利用一维土柱垂直入渗模型试验装置,对两组压实黄土土柱试样分别进行了常水头入渗和降雨入渗试验。得到主要结论如下:（1）常水头入渗试验中,累积入渗量和湿润锋前进距离都随入渗时间呈幂函数形式增长,累积入渗量和湿润锋前进距离之间存在线性关系。入渗率在入渗初期最大,之后随入渗时间而快速降低,并在土柱试样底部出水以后达到稳定,且与湿润锋前进距离呈反比关系。（2）降雨入渗试验中,得到两组试样入渗过程中土-水特征曲线数据,分别用van Genuchten模型和Fredlund-Xing模型对两组试样进行了特征曲线拟合。并利用瞬时剖面法处理了入渗过程中水分和水势传感器的监测数据,得到两组试样的非饱和渗透系数,并拟合得到非饱和渗透系数与体积含水率之间的指数函数关系式。同时,采用van Genuchten和Fredlund等渗透系数模型分别对两组试样的非饱和渗透系数进行预测,通过对比模型预测结果和瞬时剖面法实测值,发现van Genuchten渗透系数模型预测结果更接近实测值。 相似文献
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Li Jiwei Wang Huabin Wei Changfu Lin Fali Liu Zizhen Zhu Zancheng 《Acta Geotechnica》2022,17(5):1803-1814
A generalized analytical solution for one-dimensional nonlinear horizontal infiltration in unsaturated soil is presented. The solution is an improved functional extremum method based on the principle of stationary action. Any prior assumption about the form of moisture diffusion functions is not implemented in the method. By considering a function of time, the water content type governing equation in the horizontal infiltration process is transformed into a function extremum problem. After solving the Euler–Lagrange equation, combined with boundary conditions, a linear relationship between the moisture diffusion function and the ratio of spatial location to the wetting-front distance is proposed. Furthermore, by using the square relationship between the wetting front and time, the spatial and temporal distribution characteristics of the water content profile are finally expressed. In contrast to most other work, the physical meanings of the parameters in this study are clear and can be derived explicitly. By utilizing the simultaneous Brooks–Corey moisture diffusion function, the development and distribution law of the water content profile was explicitly presented. The results of the solution matched well with the existing theoretical results of the four different soil samples. Owing to the high nonlinearity of the van Genuchten moisture diffusion function, the distribution of the water content profile was implicitly found based on the study method. The results obtained using this method were also consistent with the MATLAB routine, pdepe, numerical solutions for different types of soil properties.
相似文献12.
A coupled elastic–plastic finite element analysis based on simplified consolidation theory for unsaturated soils is used to investigate the coupling processes of water infiltration and deformation. By introducing a reduced suction and an elastic–plastic constitutive equation for the soil skeleton, the simplified consolidation theory for unsaturated soils is incorporated into an in-house finite element code. Using the proposed numerical method, the generation of pore water pressure and development of deformation can be simulated under evaporation or rainfall infiltration conditions. Through a parametric study and comparison with the test results, the proposed method is found to describe well the characteristics during water evaporation/infiltration into unsaturated soils. Finally, an unsaturated soil slope with water infiltration is analyzed in detail to investigate the development of the displacement and generation of pore water pressure. 相似文献
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多孔介质中的流动问题,与孔隙介质的特性,含水量状态以及含水量的变化历史密切相关。基于毛细循环滞回理论模型,考虑含水量变化历史对土水特征关系的影响,在开发的U-DYSAC2有限元程序中进行了相应的数值实施。在试验给定的初边值条件下进行了非饱和渗流模拟分析,并将模拟结果与实测数据比较,表明在压力边界条件反复变化下,考虑滞回效应能获得更接近实测的结果,证实该模型在模拟各种循环变化条件下非饱和土渗流初边值问题的适用性与必要性。对入渗重分布反复变化条件下非饱和土柱流动的数值模拟表明,考虑滞回与不考虑滞回条件下,含水量、孔隙水压力和湿峰的迁移的预测在入渗后的重分布过程差异较大。考虑滞回效应时,土柱上部的脱湿速率、下部的吸湿速率比不考虑滞回时要低。从而证实了非饱和多孔介质中的土水状态依赖于含水量变化,而且强烈依赖于土体的水力路径变化。因此,循环边界条件变化下,毛细滞回效应在非饱和渗流模拟中的影响显著,必须加以考虑。 相似文献
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在使用有限元方法求解非饱和土渗流问题时,土-水特征曲线和渗透率函数的强烈非线性经常会造成计算中出现迭代不收敛、计算误差大等问题。基于变量变换的思想,结合时间步长自适应技术提出了一种求解非饱和渗流问题的新方法--欠松弛RFT变换方法（ATUR1）。ATUR1方法通过变量变换,大大降低了Richards方程中未知数在空间和时间上的非线性程度,从而改善这种非线性所带来的计算收敛困难和精度差等问题。欠松弛技术的引入减少了迭代过程中的振荡现象,进一步提高了非线性迭代计算的效率。时间步长自适应技术则有效地控制整个计算过程的误差。数值算例结果说明,ATUR1可以有效地提高计算效率和精度,是一种准确有效的计算方法。 相似文献
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以一水平向具有空间变异而垂直向为均质的二维非饱和流动区域中的均匀入渗问题为例,应用Monte Carlo随机模拟方法分析了土壤水分变量的随机统计特性及其一、二阶矩的时空分布规律。在随机分析过程中,将所研究的流动区域土壤水力特性的空间变异性以随空间位置变化的标定参数δ(x)表示,并将标定参数δ(x)视为一维随机空间函数的实现,应用随机生成模型来生成参数δ(x)的随机样本。通过随机模拟分析得到:垂直方向上负压水头方差与平均负压水头近似呈一线性关系;随入渗时间的延长,不同深度处表征负压水头空间变异结构的自相关函数趋于一稳定结构。 相似文献
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This paper proposed a numerical formulation for unsaturated flow problems with nonlinear boundaries of seepage face and soil–atmosphere interface via the concept of parabolic variational inequality (PVI) method. A unified unilateral boundary condition was first proposed to represent the conditions on the seepage face and soil–atmosphere interface boundaries within the partial differential equation (PDE) formulation. A PVI formulation mathematically equivalent to the PDE formulation was then proposed, which automatically transforms the flux part of the unified unilateral boundary condition into the natural boundary condition and eliminates the singularity at seepage points. By discretizing the PVI formulation, a finite element procedure together with an iterative algorithm was suggested. An existing experiment of unsaturated flow in a layered hillside and a laboratory test of unsaturated flow through sand flume performed in this study were used to validate the proposed method, with a good agreement between the measured and computed results and a satisfactory balance of mass being maintained during the simulations. The numerical results also indicated that the problem of mesh dependence associated with unsaturated flow simulations is well addressed with the proposed numerical method. Finally, the process of unsaturated flow in a soil slope with layers of horizontal drains subjected to rainfall/evaporation was further examined. The numerical results reveal that the deployment of drains in a soil slope can significantly lower the pore water pressure around the drains, with the bottom layer drains being most effective in controlling the seepage flow. 相似文献
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Analytical solutions to 1-D horizontal and vertical water infiltration in saturated/unsaturated soils are developed that can consider the variation of rainfall with time. In this model, water content and the permeability coefficient are assumed to be exponential functions of the pressure head, and diffusivity is constant. By means of Fourier integral transformation, the analytical solutions are expressed as infinite series. The steady-state solutions for horizontal and vertical infiltration in unsaturated soils are then derived. The solutions can consider both flux and pressure head boundaries. The solutions are easy to implement compared with numerical solutions, although the restricted assumptions may limit their applicability in some ways. The analytical solutions provide a reliable tool for checking the accuracy of various numerical methods under the condition of constant diffusivity. Finally, the analysis carried out in a case study indicates that the pressure head differences caused by the transient infiltration in both the horizontal and vertical directions can be estimated using the steady-state solutions, and the effect of gravity on water infiltration mainly depends on the boundary conditions. 相似文献