Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope

A key issue in assessment of rainfall-induced slope failure is a reliable evaluation of pore water pressure distribution and its variations during rainstorm, which in turn requires accurate estimation of soil hydraulic parameters. In this study, the uncertainties of soil hydraulic parameters and their effects on slope stability prediction are evaluated, within the Bayesian framework, using the field measured temporal pore-water pressure data. The probabilistic back analysis and parameter uncertainty estimation is conducted using the Markov Chain Monte Carlo simulation. A case study of a natural terrain site is presented to illustrate the proposed method. The 95% total uncertainty bounds for the calibration period are relatively narrow, indicating an overall good performance of the infiltration model for the calibration period. The posterior uncertainty bounds of slope safety factors are much narrower than the prior ones, implying that the reduction of uncertainty in soil hydraulic parameters significantly reduces the uncertainty of slope stability.     

Hierarchical approach to hydrological model calibration

Hydrological models have been widely used for water resources management. Successful application of hydrological models depends on careful calibration and uncertainty analysis. Spatial unit of water balance calculations may differ widely in different models from grids to hydrological response units (HRU). The Soil and Water Assessment Tool (SWAT) software uses HRU as the spatial unit. SWAT simulates hydrological processes at sub-basin level by deriving HRUs by thresholding areas of soil type, land use, and slope combinations. This may ignore some important areas, which may have great impact on hydrological processes in the watershed. In this study, a hierarchical HRU approach was developed in order to increase model performance and reduce computational complexity simultaneously. For hierarchical optimization, HRUs are first divided into two-HRU types and are optimized with respect to some relevant influence parameters. Then, each HRU is further divided into two. Each child HRU inherits the optimum parameter values of the parent HRU as its initial value. This approach decreases the total calibration time while obtaining a better result. The performance of the hierarchical methodology is demonstrated on two basins, namely Sarisu-Eylikler and Namazgah Dam Lake Basins in Turkey. In Sarisu-Eylikler, we obtained good results by a combination of curve number (CN2), soil hydraulic conductivity, and slope for generating HRUs, while in Namazgah use of only CN2 gave better results.     

水文响应单元空间离散化及SWAT模型改进

水文响应单元(Hydrological Response Units,HRU)是SWAT模型模拟的基本单元,传统方法划分的水文响应单元在空间分布上不连续且难以确定其明确的空间位置,不能反映HRU间的相互作用和进行精确空间分析。利用GIS工具对土地利用和土壤类型数据进行概化处理,提出了HRU空间离散化的方法,实现了水文响应单元在空间上的准确定位。在此基础上,针对SWAT模型中同一子流域所有HRU采取相同延迟的弱点进行改进,并选择太湖地区西苕溪流域对改进的SWAT模型进行水文模拟验证。改进后,校正期港口站Nash效率系数E_NS(Nash-Sutcliffe Efficiency)从0.64提高到0.67,验证期E_NS系数从0.70提高到0.76。研究表明:修正后的SWAT模型更能反映流域的水文特征,可以达到非常好的效果,考虑到HRU距离因素的径流延迟更为准确地刻画径流过程。实现HRU空间离散化将为模型改进和更小尺度的空间分析提供数据基础。     

黄土丘陵区堆积体边坡对上方来水的侵蚀响应

为探明上方来水类型对工程堆积体高陡边坡下部冲刷侵蚀的定量影响,以神府高速公路沿线典型工程堆积体陡坡坡面(36°)为例,设计4种上方来水类型,通过野外放水冲刷试验分析了不同上方来水类型下堆积体坡面的径流侵蚀输沙过程.结果表明:①上方来水类型对堆积体坡面下部的产流影响较小,却干扰了坡面侵蚀产沙过程,造成土壤流失量增加;②径流深、单宽径流侵蚀力和水流功率均可以较好地预测堆积体边坡下部输沙模数的变化;③单宽径流侵蚀功率可以作为表征坡面尺度次径流事件中径流侵蚀力变化的指标.研究结果可为工程堆积体土壤侵蚀强度评价、侵蚀模型建立及新增水土流失防治提供参考.     

Simulation of earthquake‐induced slope deformation using SPH method

This paper presents the development, calibration, and validation of a smoothed particle hydrodynamics (SPH) model for the simulation of seismically induced slope deformation under undrained condition. A constitutive model that combines the isotropic strain softening viscoplasticity and the modified Kondner and Zelasko rule is developed and implemented into SPH formulations. The developed SPH model accounts for the effects of wave propagation in the sliding mass, cyclic nonlinear behavior of soil, and progressive reduction in shear strength during sliding, which are not explicitly considered in various Newmark‐type analyses widely used in the current research and practice in geotechnical earthquake engineering. Soil parameters needed for the developed model can be calibrated using typical laboratory shear strength tests, and experimental or empirical shear modulus reduction curve and damping curve. The strain‐rate effects on soil strength are considered. The developed SPH model is validated against a readily available and well‐documented model slope test on a shaking table. The model simulated slope failure mode, acceleration response spectra, and slope deformations are in excellent agreement with the experimental data. It is thus suggested that the developed SPH model may be utilized to reliably simulate earthquake‐induced slope deformations. This paper also indicates that if implemented with appropriate constitutive models, SPH method can be used to model large‐deformation problems with high fidelity. Copyright © 2013 John Wiley & Sons, Ltd.     

分布式降雨径流物理模型的建立和应用

根据流域降雨径流的主要过程,考虑流域气象及下垫面要素的空间异质性,建立了具有物理基础的分布式降雨径流模型。模型将流域离散为栅格计算单元,并按水流特性分栅格单元为坡面单元和河网单元。在坡面单元上主要计算降雨、下渗、坡面流、壤中流等水文过程,而河网单元则主要计算河道汇流过程。模型利用空间权重插值方法将雨量站点的降雨量插值到各个计算单元,采用运动波方程来计算坡面流,将壤中流概化为垂向流和侧向流,分别用Green-Ampt公式和运动波方程来模拟,河道汇流也采用运动波方程。模型结构简单、参数的物理意义明确,大多数参数可利用DEM、土壤类型图、植被类型图直接获取,少数敏感参数通过率定确定。模型在浙江省甬江上游黄土岭流域和皎口流域进行了应用和检验,其结果令人满意。     

基于土壤属性的VIC模型基流参数估计框架

"异参同效"现象是水文模型参数率定过程中的一个难题。为了减少需要率定的模型参数个数,从而降低模型参数的相互作用,构建了利用土壤属性直接估计VIC(Variable Infiltration Capacity)模型3个基流参数的框架,并在3个位于不同水文气候条件下的典型流域中作了实例研究。传统的VIC模型参数估计方法需要率定6个参数;而在新的参数估计框架下,需要率定的模型参数从6个减少为3个。蒙特卡罗模拟结果表明新的参数估计框架提高了参数的敏感性。同时,新的参数估计方法模拟的径流过程和之前通过率定得到的径流过程差别很小。GLUE(Generalised Likelihood Uncertainty Estimation)方法分析得到径流模拟的不确定性结果表明:新的参数估计框架计算径流的90%置信区间要明显小于传统方法,而且对于低流量的模拟效果更加明显,也就是说采用新的参数估计框架可以显著降低径流模拟的不确定性。这种基流参数估计方法可以被应用于其他相似的水文模型中。     

Back analysis of slope failure with Markov chain Monte Carlo simulation

Field observed performance of slopes can be used to back calculate input parameters of soil properties and evaluate uncertainty of a slope stability analysis model. In this paper, a new probabilistic method is proposed for back analysis of slope failure. The proposed back analysis method is formulated based on Bayes’ theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis–Hasting algorithm. The method is very flexible as any type of prior distribution can be used. The method is also computationally efficient when a response surface method is employed to approximate the slope stability model. An illustrative example of back analysis of a hypothetical slope failure is presented. Effects of jumping distribution functions and number of samples on the efficiency of Markov chains are studied. It is found that the covariance matrix of the jumping function can be set to be one half of the covariance of the prior distribution to achieve a reasonable acceptance rate and that 80,000 samples seem to be sufficient to obtain robust posterior statistics for the example. It is also found that the correlation of cohesion and friction angle of soil does not affect the posterior statistics and the remediation design of the slope significantly, while the type of the prior distribution seems to have much influence on the remediation design.     

基于水位流量关系的流量估算不确定性分析

针对现有水位流量关系线型物理机制不强及流量估算不确定性来源考虑不充分问题,以北江流域石角水文站为例,推导该测站水位流量关系,基于BaRatin模型评估流量测量误差及率定样本选取对估算流量不确定性的影响。发现河槽控制宽浅矩形断面水位流量关系为幂函数,其系数可用糙率、河宽、比降表达,指数为定值5/3;考虑流量测量误差后高水估算流量总不确定性减小32%;率定数据增加1倍、3倍,高水估算流量总不确定性减小12%、34%。结果表明:①水位流量关系模型建立方法可推广至多类型测站;②高水测量误差对率定精度影响较大,建议提高高水流量测量精度;③现有实测水位与流量数据存在信息冗余,主要存在于低水数据中,本方法可减少率定数据使用,降低整编成本。     

基于水位流量关系的流量估算不确定性分析

针对现有水位流量关系线型物理机制不强及流量估算不确定性来源考虑不充分问题,以北江流域石角水文站为例,推导该测站水位流量关系,基于BaRatin模型评估流量测量误差及率定样本选取对估算流量不确定性的影响。发现河槽控制宽浅矩形断面水位流量关系为幂函数,其系数可用糙率、河宽、比降表达,指数为定值5/3;考虑流量测量误差后高水估算流量总不确定性减小32%;率定数据增加1倍、3倍,高水估算流量总不确定性减小12%、34%。结果表明:① 水位流量关系模型建立方法可推广至多类型测站;② 高水测量误差对率定精度影响较大,建议提高高水流量测量精度;③ 现有实测水位与流量数据存在信息冗余,主要存在于低水数据中,本方法可减少率定数据使用,降低整编成本。     

Bayesian approach for calibrating transformation model from spatially varied CPT data to regular geotechnical parameter

Cone Penetration Test (CPT) is widely utilized to gain regular geotechnical parameters such as compression modulus, cohesion coefficient and internal friction angle by transformation model in the site investigation. However, it is challenging to obtain simultaneously the unknown coefficients and error of a transformation model, given the intrinsic uncertainty (i.e., spatial variability) of geomaterial and the epistemic uncertainty of geotechnical investigation. A Bayesian approach is therefore proposed calibrating the transformation model based on spatial random field theory. The approach consists of three key elements: (1) three-dimensional anisotropic spatial random field theory; (2) classifications of measurement and error, and the uncertainty propagation diagram of geotechnical investigation; and (3) the unknown coefficients and error calibration of the transformation model given Bayesian inverse modeling method. The massive penetration resistance data from CPT, which is denoted as a spatial random field variable to account for the spatial variability of soil, are classified as type A data. Meanwhile, a few laboratory test data such as the compression modulus are defined as type B data. Based on the above two types of data, the unknown coefficients and error of the transformation model are inversely calibrated with consideration of intrinsic uncertainty of geomaterial, epistemic uncertainties such as measurement errors, prior knowledge uncertainty of transformation model itself, and computing uncertainties of statistical parameters as well as Bayesian method. Baseline studying indicates the proposed approach is applicable to calibrate the transformation model between CPT data and regular geotechnical parameter within spatial random field theory. Next, the calibrated transformation model was compared with classical linear regression in cross-validation, and then it was implemented at three-dimensional site characterization of the background project.     

时域反射仪（TDR）测定土壤含水量标定曲线评价与方案推荐

时域反射仪（Time Domain Reflectometry）可用于室内和田间快速、 准确、 自动测定土壤含水量, 是目前应用最广泛的土壤含水量测定方法之一。适宜的土壤含水量标定曲线（即土壤表观介电常数和土壤含水量之间的关系）是TDR准确测定土壤含水量的关键。目前文献中存在大量的土壤含水量标定曲线, 但尚未有研究对这些标定曲线进行系统的验证和分析评价。因此, 它们的准确性和适用范围尚不明晰, 严重影响到与土壤含水量测定相关的研究。通过查阅大量国内外文献, 收集整理了一系列土壤含水量标定曲线的经验公式（19个）和半经验半物理模型（5个）, 并利用大量的文献实测数据对其进行综合评价。同时运用均方根差（RMSE）, 平均误差（AD）, 纳什效率系数（NSE）等三个指标对比分析和评价这些标定曲线的准确性和可靠性。研究结果表明： 经验公式中Topp、 Roth（1992）2、 Jacobosen、 Yoshikawa2、 Alharathi模型和半经验模型中Malicki1公式及其修订模型综合性能较好。研究成果可为利用TDR准确测定土壤含水量及土壤含水量标定曲线的选择提供参考和指导。     

坡地氮磷流失过程模拟

根据农田坡面氮、磷流失的主要过程,建立了基于次降雨事件的坡面氮、磷迁移模型。模型采用改进的Green-Ampt方程和运动波方程计算下渗与坡面流,土壤侵蚀采用修改的欧洲土壤侵蚀模型计算,用考虑了侵蚀影响与扩散作用的迁移模型计算坡面氮、磷迁移过程,采用一维对流扩散方程计算氮、磷在土壤中的迁移过程。利用室内人工降雨资料对模型进行了率定及验证。结果表明,模型可以较好地模拟地表径流中氮、磷浓度,率定期与验证期模型效率系数均在0.89以上。根据坡地氮、磷流失机理,分析了降雨强度与地表坡度对坡面径流中氮、磷浓度的影响。     

降雨条件下土坡变形机制的离心模型试验研究

自行研制了离心场降雨模拟设备,进行了降雨条件下边坡的离心模型试验。试验模型在离心机中加载到50g,然后开始降雨。采用非接触位移测量系统测量了试验过程中边坡的位移场变化,通过T5张力计测量边坡中典型点的吸力变化。试验结果表明,边坡的位移随降雨量的增大逐渐发展,发生明显变形的区域也逐渐变大,主要集中在边坡表面。边坡某处应变迅速变化的时刻与土体含水率迅速增大的时刻相一致。边坡某点的应变随降雨量的增加不断增大,并存在2个拐点,形成湿润锋和稳定锋2个锋面,并把边坡分成3个区域,通过锋面的变化反映降雨条件下边坡的变形过程。     

概念性水文模型多目标参数自动优选方法研究

以三水源新安江模型为例，研究探讨了概念性水文模型多目标参数自动优选方法。目标函数综合考虑了水量平衡、确定性系数、洪峰和枯水流量过程。通过对目标函数的不同组合方式，分别率定模型参数和分析比较结果。研究表明，多目标参数自动优选方法综合考虑了水文过程的各种要素，优于传统的单目标优选结果，具有较高的模拟预报精度。     

降雨条件下浅层滑坡稳定性探讨

降雨条件下浅层滑坡是一种常见、多发的地质灾害现象,为了解边坡稳定性随降雨入渗过程的变化情况,以Green-Ampt入渗模型为基础,并考虑了动水压力的作用,建立了降雨入渗条件下浅层滑坡的概念模型,分别推导了降雨前有、无地下水位条件下的边坡安全系数与降雨时间的关系表达式。从分析结果中可以看出,对于这两种情况下边坡稳定性发生突变的主要原因归结于：前者为在湿润锋与地下水位面接触的短时间内,滑带处的孔隙水压力迅速增高;后者为滑带在浸水饱和情况下,岩土体的强度迅速降低。在此基础上,根据降雨过程中边坡是否达到饱和,提出边坡饱和临界时间的概念,考虑了初始降雨强度小于土壤入渗能力的情况。这个时间可以作为一个参数指标用于浅层滑坡的预警。     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.     

基于无限边坡算法的降雨型滑坡预警系统的模型试验研究

滑坡预警系统是减少降雨型滑坡灾害的重要手段,其中针对具体单个滑坡失稳的预警系统,尽管具有较好的物理判断依据,但由于其构造机制较为复杂,目前仍然比较少见。基于无限边坡算法构建了较为简单的实验室降雨型滑坡技术性预警系统,并详细介绍了该系统的预警思路、预警时间计算原理、信息交流及反馈的实现。通过模型试验结果考察该预警系统在估算不同降雨强度及不同初始含水状态下滑坡失稳时间的表现,并对模型试验结果、预警能力进行分析。结果表明,基于无限边坡算法的预警系统的预警能力尽管受到降雨侵蚀、滑动面位置、初始含水状态的影响,但仍然具有较好的准确性。     

Calibration of cyclic constitutive models by oscillating functions

Most structures are subjected to more cyclic loads during their life time than static loads. These cyclic action could be a result of either natural or man-made activities and may lead to soil failure. In order to understand the response of the foundation and its interaction with these complex cyclic loadings, various researchers have over the years developed different constitutive models. Although a lot of research is being carried out on these relatively new models, little or no details exist in literature about the model-based identification of the cyclic constitutive parameters which to a large extent govern the quality of the model output. This could be attributed to the difficulties and complexities of the inverse modeling of such complex phenomena. A variety of optimisation strategies are available for the solution of the sum of least-squares problems as usually done in the field of model calibration. However, for the back analysis (calibration) of the soil response to oscillatory load functions, this article gives insight into the model calibration challenges and also puts forward a method for the inverse modeling of cyclic loaded foundation response such that high-quality solutions are obtained with minimum computational effort.     

降雨入渗影响下边坡中的非饱和渗流特性

为了分析降雨入渗影响下非饱和土坡渗流特性,利用自制降雨模拟系统和实时监测系统,对降雨诱发非饱和土坡失稳过程进行全方位、多参量的实时监测,研究不同降雨条件下,不同坡度、不同压实度边坡坡体不同位置雨水入渗率和湿润峰的实变规律.结果表明:降雨入渗条件下,陡坡和高压实度土体不利于雨水入渗,而缓坡和低密实度土体入渗率变化快;实际土体吸力和含水量实时变化规律不同步,提出试验湿润峰概念,含水率（吸力）湿润峰点可按含水率（吸力）实时曲线的过渡区和雨后残余含水率（吸力）的线性交叉点确定;考虑单向吸湿或脱湿路径下土体含水率和吸力具有唯一对应关系,含水率湿润峰点与吸力湿润峰点的绝对值时差即为形成湿润峰所需时间;对比湿润峰实测值与Lumb半经验值散点分布规律,基于Lumb湿润峰深度计算公式提出非线性修正表达式.