Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.

Two-dimensional plane strain consolidation of unsaturated soils considering the depth-dependent stress

In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.

Stability analysis of unsaturated soil slope during rainfall infiltration using coupled liquid-gas-solid three-phase model

Generally, most soil slope failures are induced by rainfall infiltration, a process that involves interactions between the liquid phase, gas phase,and solid skeleton in an unsaturated soil slope. In this study, a loosely coupled liquid-gas-solid three-phase model, linking two numerical codes,TOUGH2/EOS3, which is used for water-air two-phase flow analysis, and FLAC^(3D), which is used for mechanical analysis, was established. The model was validated through a documented water drainage experiment over a sandy column and a comparison of the results with measured data and simulated results from other researchers. The proposed model was used to investigate the features of water-air two-phase flow and stress fields in an unsaturated soil slope during rainfall infiltration. The slope stability analysis was then performed based on the simulated water-air two-phase seepage and stress fields on a given slip surface. The results show that the safety factor for the given slip surface decreases first, then increases, and later decreases until the rainfall stops. Subsequently, a sudden rise occurs. After that, the safety factor decreases continually and reaches its lowest value, and then increases slowly to a steady value. The lowest value does not occur when the rainfall stops, indicating a delayed effect of the safety factor. The variations of the safety factor for the given slip surface are therefore caused by a combination of pore-air pressure, matric suction, normal stress, and net normal stress.

Surficial Stability Analysis of Unsaturated Loess Slopes Subjected to Rainfall Infiltration Effects

According to theory of unsaturated soil strength and Green-Ampt model, an analysis method based on limit equilibrium theory is introduced to consider rainfall infiltration effects in loess slope stability analysis. The relationships between wetting band depth and surficial stability of slopes are analyzed. It is found that the infiltration adds to the weight of the soil and at the same time reduces the shear strength provided by matric suction of the soil. The wetting band depth plays a key role in the stability of slopes. The minimum rainfall intensity and the minimum rainfall duration needed to infiltrate to the wetting front depth are calculated based on the Green-Ampt model. The method in this paper will contribute to the predication of slope stability considering rainfall characteristics.

An Analytical Solution for One-Dimensional Water Infiltration and Redistribution in Unsaturated Soil

Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.

Stability analysis of an unsaturated soil slope considering rainfall infiltration based on the Green-Ampt model

Based on the principle of saturated infiltration and the Green-Ampt model,an unsaturated infiltration model for a soil slope surface was established for either constant moisture content,or depth-varying moisture content and the slope.Infiltration parameters in the partially saturated slope were revealed under sustained rainfall.Through analysis of the variation of initial moisture content in the slope,the ponding time,infiltration depth,and infiltration rate were deduced for an unsaturated soil slope subject to rainfall infiltration.There is no ponded water on the surface of the slope under sustained low-intensity rainfall.The results show that the infiltration parameters of an unsaturated slope are influenced by the initial moisture content and the wetting front saturation,the soil cohesion and rainfall intensity under sustained rainfall.More short-term slope failures can occur with the decrease of cohesion of the soil of the slope.The ponding time and infiltration depth differ considering constant or different initial moisture content respectively in the soil slope.Then,best-fit curves of the infiltration rate,ponding time,and infiltration depth to the wetting front saturation were obtained with constant or different initial moisture contents.And the slope failure time is roughly uniform when subject to a rainfall intensity I>5 mm/h.

Effect of particle size and grain composition on two-dimensional infiltration process of weathered crust elution-deposited rare earth ores

The two-dimensional infiltration experiment was carried out by means of digital image technology.The evolution process of the wetting body was described.The wetted front distance and the time show a very significant power function relationship.The horizontal wetted distance is larger than the vertical wetted distance in the initial stage.Then,the vertical distance of the wetted body gradually approaches to the horizontal distance.The infiltration distance decreases as the content of fine particles increases.The wetted front migration rate curve shows a three-stage change law,and it increases with the increase of coarse particle content.The directional velocity ratio is defined.The initial value of horizontal infiltration rate is larger than that of vertical one,and then the vertical infiltration rate is gradually close to the horizontal value.The empirical relationship between the characteristic particle size and the stable infiltration rate is established,which provides a theoretical basis for the prediction of the stable infiltration rate in in-situ leaching.

The Unsaturated Hydraulic Parameters for Aeolian Sand

The water characteristic curve for aeolian sand in two processes of wetting and drying was obtained by the negative water column technique.The values of fitting parameters were calculated according to Van Genuchten formula and the parameters that characterized the prosperities of aeolian sand such as the unsaturated infiltration coefficient and specific water capacity were obtained.The results showed that the water characteristic curve for aeolian sand in wetting process had greater hysteresis quality than ...

Coupled hydro-mechanical analysis of slope under rainfall using modified elasto-plastic model for unsaturated soils

Two modifications for the basic Barcelona model(BBM) are present. One is the replacement of the net stress by the average skeleton stress in unsaturated soil modeling, and the other is the adoption of an expression for the load-collapse(LC) yield surface that can match flexibly the normal compression lines at different suctions. The predictions of the modified BBM for the controlled-suction triaxial test on the unsaturated compacted clay are presented and compared with the experimental results. A good agreement between the predicted and experimental results demonstrates the reasonability of the modified BBM. On this basis, the coupled processes of groundwater flow and soil deformation in a homogeneous soil slope under a long heavy rainfall are simulated with the proposed elasto-plastic model. The numerical results reveal that the failure of a slope under rainfall infiltration is due to both the reduction of soil suction and the significant rise in groundwater table. The evolution of the displacements is greatly related to the change of suction. The maximum collapse deformation happens near the surface of slope where infiltrated rainwater can quickly reach. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.

Numerical Simulation of Moisture Movement in Unsaturated Expansive Soil Slope Suffering Permeation

This study develops a way of analyzing moisture movement in unsaturated expansive soil slope. The basic equations and the integrated finite difference method for moisture movement in unsaturated soils are briefly described, and the calculation code MFUS2 has been developed. The moisture movements in unsaturated expansive soil slopes suffering precipitation were simulated numerically. The simulation results show that expansion or contraction must be taken into account in an analysis model. A simplified equivalent model for calculating rainwater infiltration into expansive soil slopes has been developed. The simplified equivalent model divides the soil slope into two layers according to the extent of weathering of the soil mass at depth. Layer Ⅰ is intensively weathered and moisture can be fully evaporated or rapidly absorbed. The moisture movement parameters take into account the greater soil permeability caused by fissures. Layer Ⅱ is unweathered and the soil is basically undisturbed. The moisture movement parameters of homogeneous soils are applicable. The moisture movements in unsaturated ex- pansive soil slopes suffering precipitation were simulated numerically using the simplified equivalent model. The simulation results show that the moisture movement in the expansive soil slope under rainfall permeation mainly takes place in the extensively weathered layer Ⅰ which closely simulates the real situation.

降雨条件下植被根系对非饱和土浅层滑坡的加固作用

为了研究降雨条件下植被根系对非饱和土边坡浅层滑移的稳定性,基于可计算任意时刻任意土层深度处孔隙水压力分布与变化特征的降雨入渗解析模型,通过理论解析方法研究降雨入渗作用、植被根系抗拉强度、根面积指数以及根系生长方向等因素对边坡浅层滑移稳定性的影响。结果表明,植被根系的抗拉强度越大或根面积指数越大,则边坡的稳定性越强。随着边坡坡角的增大,植被根系对边坡稳定性的加固效应越加明显。此外,植被根系的生长方向也会对加固效果产生明显影响。在实际工程中,应在合理控制植被根系生长方向的基础上,选择根系发达且发育较长同时具有较大根面积指数的植被,以达到更好的护坡效果。

稳态渗流下非饱和土涵洞竖向土压力的迭代解与简化

为描述稳态渗流下不同类别非饱和土涵洞的竖向土压力变化,应用圆弧小主应力轨迹法和Mohr应力圆获得考虑土拱效应的滑移面土压力系数,继而基于非饱和土的有效应力强度公式与吸应力理论,由水平薄层单元的竖向力平衡分别建立稳态渗流下上埋式/沟埋式非饱和土涵洞竖向土压力的迭代解,给出应用步骤并开展对比验证与方法拓展,最后结合吸应力沿深度分布规律提出涵洞竖向土压力的简化实用公式。研究结果表明:涵洞竖向土压力迭代解能合理反映土体类别、水分蒸发、降雨入渗和土拱效应的综合影响,并得到文献现场实测和理论公式数据的正确性验证以及对非饱和土涵洞的适用性;涵洞竖向土压力实用公式可显式表达且精度良好,方便估算不同稳态渗流下涵洞主要荷载;砂土涵洞可忽略非饱和特性影响而按饱和土计算竖向土压力,粉土和黏土涵洞可简化吸应力沿深度为线性分布;上埋式涵洞土拱负效应使得竖向土压力增大,而沟埋式涵洞土拱正效应使得竖向土压力减小。

降雨条件下堆积体饱和-非饱和渗流场分析与稳定性演化

降雨是工程区域堆积体边坡失稳的重要诱因,如何评价降雨条件下饱和-非饱和渗流对堆积体边坡稳定性的影响,其挑战在于准确获取堆积体的非饱和渗流参数。以梅家台滑坡典型治理工程为研究对象,采用饱和-非饱和有限元分析,并基于监测资料对渗流场动态反演,准确获得了非饱和水力参数和边界水位,进而采用极限平衡法对滑坡稳定性演化分析。结果表明:坡体后缘补给水位在692.0~694.5 m内动态变化,在后缘补给和降雨入渗作用下坡体内地下水位变幅为3.0~12.0 m;排水措施实施后地下水位下降9.0 m,且变幅降为1.0~5.5 m,同时在暴雨条件下,滑坡中部堆积薄弱带暂态饱和区范围减小84.5%,坡脚饱和区也被抑制到一号公路以下,发挥了很好的排水降压作用;滑坡存在沿中部薄弱带浅层滑动、沿下部前缘浅层滑动、沿老滑带从一号公路剪出3种失稳模式,降雨入渗时稳定性明显下降,稳定系数分别降低至0.82、0.99、0.98,小于稳定安全系数1.05,综合治理措施下,稳定系数分别增加0.28、0.13、0.19,目前稳定系数分别为1.10、1.12、1.17,各个失稳模式稳定系数均大于稳定安全系数,滑坡处于稳定状态。研究成果可为类似工程治理设计和渗流稳定分析提供参考。

强降雨作用下尾水边坡非饱和渗流特征及稳定性分析

为探究抽水蓄能电站尾水边坡在强降雨作用下的稳定性,基于饱和-非饱和渗流理论模拟了强降雨条件下尾水边坡渗流场的分布及变化情况,并结合渗流计算结果,利用强度折减法对降雨条件下边坡稳定性进行了分析。结果表明:当降雨强度超过土体的饱和渗透系数时,坡脚和坡表下部率先出现暂态饱和区域,随着降雨历时的增加,润湿锋不断向坡体内部移动;长期降雨期间,边坡稳定性系数的变化主要由两个因素决定,一是孔隙水压力增加导致的有效应力减小,二是表层土体饱和容重增加导致的下滑力增加;降雨过程中边坡的稳定性系数不断减小,在降雨3d后稳定性系数发生突变;降雨前期边坡潜在滑面为弧形,随着降雨历时的增加滑面深度变浅,降雨后期边坡潜在滑面表现为沿润湿峰分布的直线形滑面,且随降雨持续作用,滑面随润湿锋向坡体内部移动。

不同降雨类型循环下二元边坡渗流场及稳定性分析

为研究不同降雨条件对二元边坡的影响,以福建某公路边坡为例,基于饱和-非饱和渗流理论,利用Geo-Studio软件,模拟不同类型降雨对二元边坡渗流场和稳定性的影响,探讨不同降雨类型循环条件下二元边坡的渗流场和安全系数的变化规律。结果表明,降雨引起的孔隙水压力变化在边坡表层土体和内部岩层之间存在显著差异,土-岩接触面存在潜在滑动面;总降雨量相同时,表层土体孔隙水压力变化曲线呈现不同变化规律,前期型呈上凸型,中期型、均匀型都呈直线型,后期型呈下凹型;下部岩层坡顶、坡面处孔隙水压力变化曲线在降雨周期前期不变,在后期突然增大升至饱和状态,坡脚处岩层的孔隙水压力变化趋势与表层土体一致;安全系数变化与降雨时间分布一致,并具有明显的滞后性;降雨最不利时,潜在滑动面由边坡内部上移到土-岩接触面处及内部岩层接触面处。

强降雨作用下引入分形理论的浅层边坡入渗及稳定性分析

为探究降雨过程中土体实际入渗能力动态变化对边坡降雨入渗规律及其稳定性的影响,从土体级配特征的角度出发,首先基于分形理论推导了不同级配特征土体的饱和渗透系数分析模型;进一步考虑入渗区椭圆形过渡带的影响,根据不同降雨历时下过渡带与入渗区的厚度比例关系对入渗区等效渗透系数进行实时修正,提出了不同级配特征土体的改进GA入渗模型;最后,基于改进GA入渗模型建立了考虑土体抗剪强度随级配特征及降雨时间变化的浅层边坡稳定性分析修正模型。与已有结果对比表明建立的模型能够准确地表征降雨过程中土体入渗状态及剪切强度变化特征。参数分析表明:土体孔隙分布特征与饱和渗透系数具有明显的正相关关系,其直接影响坡体水分剖面分布及坡面径流出现时间;湿润峰推移速率随坡体初始含水率的增大而加快,致使相同降雨历时下入渗区过渡带占比减小,进而实时影响入渗区等效渗透系数;坡体过渡带稳定性受土体级配特征及初始含水率的影响较为显著,坡体容易在过渡带发生失稳破坏。故在强降雨作用下边坡的失稳分析中,需额外注意入渗区过渡带的稳定性。

降雨入渗下非饱和土边坡浅层破坏机制分析

通过孔隙表面分维描述土的孔隙结构,应用分形模型确定非饱和土的水力特性。选取基质吸力变化分布作为评价指标,通过二维渗流计算获取降雨-蒸发循环作用下非饱和土边坡的扰动程度和大气影响深度。进一步分析土的孔隙表面分维、进气值和饱和渗透系数及降雨强度与非饱和土边坡的浅层破坏形式的相关性。研究结果表明:降雨-蒸发循环作用引起的边坡土层的基质吸力变化比体积含水率的变化显著;土的孔隙表面分维、进气值和饱和渗透系数均与大气影响深度呈正相关,降雨强度影响较小;基质吸力可以作为边坡扰动程度和大气影响深度的评价指标;非饱和土边坡浅层破坏形式受土的孔隙表面分维、进气值和饱和渗透系数控制,与降雨强度相关性低。本研究可为非饱和土边坡浅层破坏及相关工程地质问题研究提供参考。

下蜀土降雨入渗光纤感测及渗透系数估算研究

下蜀土中裂隙较为发育,在降雨时入渗能力强,因此容易诱发浅层滑坡等灾害。为了研究下蜀土的降雨入渗特征,本文采用主动加热光纤光栅(AH-FBG)法开展了地基土水分分布及其动态变化的原位监测研究。基于监测数据,掌握了冬季和夏季土体体积含水率的时空分布特征,并计算得到降雨事件的降雨入渗量及入渗补给系数。在此基础上,通过稳态法计算获取了原位下蜀土的非饱和渗透系数,并与间接法估算值进行比较。结果表明:将AH-FBG法应用于下蜀土含水率的原位监测具有可行性,其中5 cm深度的均方根误差较大,为0.0252 m^(3)·m^(-3),主要受到浅层土体和空气的热量交换作用以及土体裂隙的影响,其余深度均不超过0.01 m^(3)·m^(-3)。原位监测系统对降雨入渗和蒸发作用引起的含水率变化均具有良好的响应。无论是冬季还是夏季,由稳态法计算得到的原位非饱和渗透系数均大于间接法估算值,表明下蜀土中的裂隙为降雨入渗提供了优先渗流通道。

基于混沌理论的非饱和土含水率预测

针对无资料区土体含水率数据难以获取的问题,提出了一种基于卫星反演-相空间重构-非饱和入渗计算的组合方案,以研究区110 d土体表层含水率为基础,预测未来100 d无资料时段土体表层及内部含水率分布规律。计算结果表明:研究区含水率时间序列具备混沌特征,可由一维时间序列拓扑为一个嵌入维数m=5,迟滞τ=10的相空间,由该相空间预测的土体表层含水率在验证期最小相对误差为0.7%,最大相对误差为2.4%,在预测期最小相对误差为2.2%,最大相对误差为8.3%,均满足工程需求,因此将其用于后续非饱和入渗计算的边界条件是真实有效的。该方案具有动力学特性和物理力学意义,可为无资料地区土体含水率估计借鉴。

考虑降雨入渗的高边坡开挖支护稳定性分析

【目的】为研究降雨入渗对多级开挖支护后高边坡的稳定性,针对四川达州市某高边坡工程,基于ABAQUS软件并结合现场工程地质和水文地质条件,建立高边坡开挖降雨渗流模型。【方法】考虑不同降雨条件的影响,引入多层非饱和土计算方法,结合现场监测情况,对降雨工况进行研究,进而研究非饱和土边坡的稳定性。【结果】研究结果表明,孔隙水压、边坡位移与降雨强度和降雨持续时间呈正相关,长时间高强度降雨易使多级开挖的高边坡产生较大滑移。【结论】建议采取边开挖边支护的施工措施。研究成果可为高边坡多级开挖支护的稳定性研究提供一定的参考。