Modelling two-dimensional heat and moisture transfer in unsaturated soils,including gravity effects

A theoretical model is presented to predict simultaneous transient coupled heat and moisture transfer in partly saturated soils. The formulation is in terms of volumetric moisture content, is two dimensional, includes gravitational flow and takes into account latent heat of vaporization effects. The numerical solution of the problem is accomplished by means of a finite element solution algorithm. Predictions from the numerical model are used to investigate the importance of gravitational flow, for the case of a soil stratum subjected to evaporation losses at the surface. The results achieved show good qualitative agreement with expected behaviour.     

Three-dimensional heat,moisture and air transfer in unsaturated soils

A new three-dimensional numerical model of coupled heat, moisture and air transfer in unsaturated soil is presented. In particular, the model accommodates moisture transfer in the form of liquid and vapour flow and heat transfer arising from conduction, convection and latent heat of vaporization. The bulk flow of dry air and the movement of air in a dissolved state are also included. The theoretical basis of the model, the finite element solution of the spatial terms and finite difference solution of the temporal terms are briefly presented. Attention is focused on the verification of the new numerical solution. This is achieved via comparisons with independent solutions of heat, moisture and air transfer in an unsaturated soil. The physical problem considered includes the highly non-linear hydraulic properties of sand. Thermal conductivity is also included as a function of soil moisture content. Excellent correlation of results is shown thus providing confidence in the new model. The new model is also applied to a number of test cases which illustrate the need for the development of a model which can fully include three-dimensional behaviour. In particular, three applications are presented each increasing in complexity. The first application illustrates three-dimensional heat transfer. This particular application is verified against existing commercial finite element software. Subsequent applications serve to illustrate how the coupled processes of heat moisture and air transfer combine to yield three-dimensional problems even within a simple geometric domain. Visualization of three-dimensional results is also addressed. © 1998 by John Wiley & Sons, Ltd.     

非饱和介质中热能传输及水分迁移的数值积分解

在给出非饱和介质热能-水分传输的耦合质量控制方程和基于Fourier热传导定律的热能平衡方程的基础上,对热能传输及水分迁移的基本特征和机理进行了分析。其中,考虑了温度势、吸力势和重力势的耦合作用影响。给出有热源时控制方程的简化形式,并对半无限体自由表面作用平面热源条件下介质内非稳态温度场、体积含水率分布场进行数值积分求解。利用这些解答给出常热源强度和变热源强度两种情况下,温度场随时间的变化特征以及水分迁移的演化过程,并分析了重力项对计算结果的影响。     

Solution of the unsaturated soil moisture equation using repeated transforms

An alternative method of solution for the linearized ‘theta‐based’ form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ξ. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis‐equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi‐analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd.     

正冻土水热迁移的移动泵模型

通过引入脉冲函数将流量边界条件转化为源（汇）项,冻结锋面处的假想泵从未冻土中抽吸水分并储存在冻结锋面附近的狭窄区域.将水分扩散方程在整体求解域上等效分解为两个方程,避免了处理移动冻融边界的难题.在一个分解方程中引入汇项以表达未冻区水分的流出,在另一个分解方程中引入相同大小的源项以表达冻土中水分的聚集.将移动泵模型相关场方程和变量输入COMSOL Multiphysics模拟软件的数学模块中,对一个封闭系统非饱和土冻结过程中水分和温度的变化过程进行了数值模拟,将模拟结果与前人试验和模拟结果进行了对比.     

A nonlinear analysis of two-dimensional heat and moisture transfer in partly saturated soil

The subject of this paper is the nonlinear analysis of heat and moisture transfer in partly saturated soil. In particular, an extension of the previous work of the author to two-dimensional applications is presented. Problems of greater complexity and engineering significance can hence be solved. The theoretical basis of the problem is first outlined before the two-dimensional formulation of the numerical solution is given. The finite element method is employed to give the spatial distributions of the variables, with a finite difference scheme being used to predict the temporal variations. The method allows the nonlinear nature of the soil parameters to be modelled, predictions being given of the coupled transient simultaneous transfer of heat and volumetric moisture content. The two-dimensional nature of the work is illustrated for the case of surface evaporative soil moisture losses from sloping ground. Subsoil conditions of a uniform deposit of loam are considered with values of representative material parameters assumed after a literature search. The coupled nature of heat and mass transfer is illustrated by means of an analysis of the moisture migration patterns that occur. Two-dimensional moisture flow, out of and into the soil, is shown to take place.     

非饱和路基土水分运移的室内试验研究

模拟路基填土的实际情况,研究设计了不同表面辐射温度和降雨强度的非饱和土水分运移的室内试验方法。通过测定土样在相应边界条件下土体不同深度位置的含水率随时间的变化,揭示了温度、压实度、降雨强度3个因素对非饱和土水分运移影响的规律,据此探讨了路基填土的水分运移规律,认为提高压实度能显著减少水分运移变化。     

Coupled solution of heat and moisture flow in unsaturated clay barriers in a repository geometry

An analytical solution in the Laplace transform domain is obtained for the transient heat and moisture transport in an unsaturated clay buffer with a geometry simulating repository conditions. A numerical inversion scheme based on Crump's method is used to obtain the time‐domain solution. The coupled effect of thermally driven moisture transport is especially investigated because of its importance to alter the flow field in low‐permeability buffers. The practical background is based on the case of an engineering bentonite barrier placed in a drift excavated in rock in the context of underground disposal of high‐level radioactive waste. Parametric study has been performed to assess the effects of dimensionless geometry and material parameters on flow field. Despite the simplified assumptions required in order to obtain analytical expressions, the results incorporate the main mechanisms involved in the coupled thermo‐hydraulic (T–H) problem, and they may be eventually used for validation purposes. Copyright © 2006 John Wiley & Sons, Ltd.     

Efficient approach in modeling the shear strength of unsaturated soil using soil water retention curve

Acta Geotechnica - Currently, there are debates on the relationship between the effective stress and shear strength of unsaturated soils. Thus, it is imperative to present an efficient method that...     

A model for moisture and heat flow in fractured unsaturated porous media

The present study investigates propagation of a cohesive crack in non‐isothermal unsaturated porous medium under mode I conditions. Basic points of skeleton deformation, moisture, and heat transfer for unsaturated porous medium are presented. Boundary conditions on the crack surface that consist of mechanical interaction of the crack and the porous medium, water, and heat flows through the crack are taken into consideration. For spatial discretization, the extended finite element method is used. This method uses enriched shape functions in addition to ordinary shape functions for approximation of displacement, pressure, and temperature fields. The Heaviside step function and the distance function are exploited as enrichment functions for representing the crack surfaces displacement and the discontinuous vertical gradients of the pressure and temperature fields along the crack, respectively. For temporal discretization, backward finite difference scheme is applied. Problems solved from the literature show the validity of the model as well as the dependency of structural response on the material properties and loading. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled heat and mass transfer in unsaturated soil—a potential-based solution

An analysis of coupled heat and moisture movement in unsaturated soil in terms of the fundamental potentials for flow is examined. The approach adopted is based on the assumption that the total potential for liquid flow consists of two components, the elevation and the capillary potential. The fundamental potentials employed in the work are, therefore, temperature and capillary potential. The full theoretical formulation of the problem is presented, together with full details of the solution algorithm employed. Spatial discretization is achieved via the use of the finite element method, with the time-varying behaviour described by a finite difference technique. Soil parameter variations as functions of both temperature and moisture content are included in a one-dimensional approach. The work is applied to a practical engineering problem, namely heat and mass transfer in the upper layers of a soil stratum. This problem is of importance to the utilities, since many services are buried in this zone. Material parameters obtained from an associated programme of experimental work are employed. Moisture content and temperature profiles indicating the extent and rate of penetration of drying and heating fronts are produced.     

A comparison of field-monitored and numerically predicted moisture movement in unsaturated soil

This paper presents the results of the application of a numerical model of flow of water in unsaturated soil to simulate real field behaviour. Numerical predictions are compared with field-monitored results as part of an assessment of the approach adopted. The numerical approach is based on a finite element solution of Richards' theoretical formulation, adopting a finite difference recurrence relationship to model the transient nature of the problem. The field results have been collected by British Gas in Kimmeridge clay at a site in Swindon. The simulation addressed the autumn wetting of the soil during 1983. Comparisons of volumetric moisture content readings from the field and numerical predictions give good correlation. It is concluded that the numerical model has adequately represented field behaviour over the depth of interest. Taken in conjunction with previous results, it is claimed that the model should now be capable of use in a predictive mode.     

Operational mesoscale atmospheric dispersion prediction using a parallel computing cluster

An operational atmospheric dispersion prediction system is implemented on a cluster supercomputer for Online Emergency Response at the Kalpakkam nuclear site. This numerical system constitutes a parallel version of a nested grid meso-scale meteorological model MM5 coupled to a random walk particle dispersion model FLEXPART. The system provides 48-hour forecast of the local weather and radioactive plume dispersion due to hypothetical airborne releases in a range of 100 km around the site. The parallel code was implemented on different cluster configurations like distributed and shared memory systems. A 16-node dual Xeon distributed memory gigabit ethernet cluster has been found sufficient for operational applications. The runtime of a triple nested domain MM5 is about 4 h for a 24 h forecast. The system had been operated continuously for a few months and results were ported on the IMSc home page. Initial and periodic boundary condition data for MM5 are provided by NCMRWF, New Delhi. An alternative source is found to be NCEP, USA. These two sources provide the input data to the operational models at different spatial and temporal resolutions using different assimilation methods. A comparative study on the results of forecast is presented using these two data sources for present operational use. Improvement is noticed in rainfall forecasts that used NCEP data, probably because of its high spatial and temporal resolution     

Modelling soil erosion from a watershed using cubic splines

Erosion in a watershed exhibits spatial and temporal variability, and its determination is fundamental to determining sediment yield which is a key to proper watershed management. In this study, we propose a relationship between the curve number (SCS 1956) and Sediment Yield Index (SYI) using cubic splines. The method is illustrated with a case study of one watershed of Narmada Basin located in Mandla district of Madhya Pradesh, India. Cubic splines are found to perform satisfactorily with Nash efficiency of 63.64%, absolute prediction error of 2.64%, integral square error of 1.22%, coefficient of correlation of 93.78% and degree of agreement of 0.99%. The relation between observed and computed SYI values is correlated with a coefficient of determination (R ²) of 0.87. Such a relationship can be used to determine SYI from the available CN value, which may be quite useful in field applications.     

Modelling the mechanical behaviour of unsaturated soils using a genetic algorithm-based neural network

Modelling the mechanical behaviour of unsaturated soils has been the subject of many research works in the past few decades. A number of constitutive models have been developed to describe the complex behaviour of unsaturated soils. Despite the significant advances in the constitutive theories for unsaturated soils, none of the existing models can completely describe the various aspects of the real behaviour of unsaturated soils. In this paper, a new unified approach is presented, based on the integration of a neural network and a genetic algorithm, for the modelling of unsaturated soils. In the proposed approach, a genetic algorithm was used to optimise the weights of the neural network. A three-layer sequential architecture was chosen for the neural network. The network had eight input neurons, five neurons in the hidden layer and three neurons in the output layer. The eight input neurons represented the initial gravimetric water content, initial dry density, degree of saturation, net mean stress with respect to pore-air pressure, axial strain, deviatoric stress, soil suction and volumetric strain, and the three neurons in the output layer represented the deviatoric stress, suction and volumetric strain at the end of each increment. The network was trained and tested using a database that included results from a comprehensive set of triaxial tests on unsaturated soils from the literature. The predictions of the proposed model were compared with the experimental results. The comparison of the results indicates that the proposed approach was accurate and robust in representing the mechanical behaviour of unsaturated soils.     

Modelling soil moisture under different land covers in a sub-humid environment of Western Ghats,India

The objective of this study is to apply and test a simple parametric water balance model for prediction of soil moisture regime in the presence of vegetation. The intention was to evaluate the differences in model parameterization and performance when applied to small watersheds under three different types of land covers (Acacia, degraded forest and natural forest). The watersheds selected for this purpose are located in the sub-humid climate within the Western Ghats, Karnataka, India. Model calibration and validation were performed using a dataset comprising depth-averaged soil moisture content measurements made at weekly time steps from October 2004 to December 2008. In addition to this, a sensitivity analysis was carried out with respect to the water-holding capacity of the soils with the aim of explaining the suitability and adaptation of exotic vegetation types under the prevailing climatic conditions. Results indicated reasonably good performance of the model in simulating the pattern and magnitude of weekly average soil moisture content in 150 cm deep soil layer under all three land covers. This study demonstrates that a simple, robust and parametrically parsimonious model is capable of simulating the temporal dynamics of soil moisture content under distinctly different land covers. Also, results of sensitivity analysis revealed that exotic plant species such as Acacia have adapted themselves effectively to the local climate.     

压实膨胀土非饱和抗剪强度的湿度与密度效应

为获得压实膨胀土在湿度与密度变化范围内的抗剪强度全貌,采用非饱和直剪试验测定38种湿度与密度组合状态下荆门弱膨胀土的抗剪强度,获得了湿度从风干到饱和、密度在孔隙比0.539~1.089范围内的抗剪强度的分布规律。结果表明,(1)剪切过程中试样大多呈应变软化,仅在低密度与高湿度组合下产生应变强化。高密度与低湿度组合下易出现"应力跌落"。相同密度下,随湿度增大,土体塑性变形能力增强。相同湿度下,随密度降低,土体塑性变形能力增强;(2)非饱和抗剪强度与总黏聚力均随湿度增加先增大后减小而呈现出显著的"山峰效应";(3)非饱和抗剪强度、总黏聚力、总内摩擦角均随密度减小而显著降低,呈现出显著的"密度效应"。     

A mathematical model for predicting coupled heat and water movement in unsaturated soil

An investigation was conducted to develop a comprehensive moisture model for predicting non-isothermal moisture conditions in soils. An extensive literature review indicated that a model based on the Philip and de Vries equations for non-isothermal moisture movement and heat conduction would give the best results. By using numerical methods, the implicit finite difference approximations to the moisture movement and heat-transfer equations were programmed for computer solution of water content and temperature in the soil with time. Validation studies indicate that the moisture model can be used to predict accurately moisture conditions in the soil. The model was validated by using hydraulic data from laboratory studies conducted on soil columns compacted with AASHO A-3 and AASHO A-4 soil. The application of the moisture model to the study of non-isothermal moisture movement in the field is demonstrated. The influence of parameters such as water table depth, precipitation, and soil hydraulic properties on soil moisture content are shown by use of the moisture model. The model is shown to be applicable to a wide range of boundary conditions and that it predicts the moisture-temperature regime with time in soils utilizing climatic input data.     

An integrated approach for validating unsaturated soil parameters in seepage analyses

Soil–water characteristic curves (SWCCs) and soil permeability functions (SPFs) for a silty sand were validated based on soil suction and soil water content measurements in calibration box and constant-head seepage tests. Transient seepage analyses using finite element method (FEM) were performed to examine the accuracy of the derived SWCCs and SPFs, with a special focus on the wetting front propagation. Results show that the proposed new integrated system consisting of experimental and analytical techniques works well, in the sense that the soil moisture responses at specific depths of soil mimic those measured in constant-head seepage tests.