The Effect of Spatial Correlation of Cone Tip Resistance on the Bearing Capacity of Shallow Foundations

The effect of directional behaviour of correlation structure of cone tip resistance on the bearing capacity of shallow strip footing resting on cohesionless soil deposit in 2-D random field is analysed using probabilistic approach. The results obtained from the analysis show that the assumption of perfect (or infinite) correlation of cone tip resistance data leads to lower values of probability of failure. In contrast, the isotropic assumption of correlation behaviour based on vertical scale of fluctuation leads to higher values of probability of failure. The results also show that the transformation model would play a major role in the evaluation of variability of design property. In conclusion, the need for a proper evaluation methodology for calculation of correlation lengths of soil properties and their influence in foundation design is highlighted.     

A reliability analysis framework coupled with statistical uncertainty characterization for geotechnical engineering

Reliability analysis plays an important role in the risk management of geotechnical engineering.For the random field-based method,it is expected that the uncertainty characterization of geo-material param-eters and the realization of random field can be integrated effectively.Moreover,as the increase in mea-sured data size is generally difficult in the field investigation of geotechnical engineering due to limitation of budget and time etc.,the statistical uncertainty resulting from sparse data should be paid great attention.Therefore,taking the determination of hyper-parameters for Bayesian-based conditional random field as the breakthrough,this study proposed a reliability analysis framework to achieve the expectation above.In this proposed reliability analysis framework,the present characterization method of statistical uncertainty is improved by setting the lognormal distribution as the prior distribution of scale of fluctuation(SOF).Subsequently,the performance of statistical uncertainty characterization method is tested by a set of unconfined compressive strength(UCS)database about rocks.Then,a case study about the stability analysis of slope is employed to demonstrate the beneficial effect of the pro-posed reliability analysis framework.It is found that the uncertainty in both the realization of random field and the reliability analysis results can be significantly mitigated by the proposed reliability analysis framework.     

基于GIS的甘肃北山花岗岩裂隙密度地质统计分析

以甘肃北山花岗岩中发育的构造裂隙(主要指节理)为研究对象,采用高精度GPS、罗盘等对其进行现场测量,获取裂隙的迹长及产状信息,并将信息导入ArcGIS平台建立裂隙属性数据库; 进而应用地质统计分析理论,以裂隙面密度P21为地质统计分析的区域性变量,探索花岗岩岩体裂隙空间分布特征; 然后借助ArcGIS软件平台建立变异函数模型,利用地质统计学的普通克里金插值方法得到整个区域的面密度预测分布图。结果表明:芨芨槽块段所测某区域裂隙面密度值的半变异函数变程值在20～30m之间,NS和EW方向有明显差异,由此知该区域裂隙面密度分布具有显著空间自相关性,但分布特征不均匀; 此结论对北山花岗岩裂隙空间分布特征的深入研究以及三维裂隙网络建模具有重要参考价值。     

Reliability analysis of piles in spatially varying soils considering multiple failure modes

In most limit state design codes, the serviceability limit checks for drilled shafts still use deterministic approaches. Moreover, different limit states are usually considered separately. This paper develops a probabilistic framework to assess the serviceability performance with the consideration of soil spatial variability in reliability analysis. Specifically, the performance of a drilled shaft is defined in terms of the vertical settlement, lateral deflection, and angular distortion at the top of the shaft, corresponding to three limit states in the reliability analysis. Failure is defined as the event that the displacements exceed the corresponding tolerable displacements. The spatial variability of soil properties is considered using random field modeling. To illustrate the proposed framework, this study assesses the reliability of each limit state and the system reliability of a numerical example of a drilled shaft. The results show the system reliability should be considered for the serviceability performance. The importance measures of the random variables indicate that the external loads, the performance criteria, the model errors of load transfer curves and soil strength parameter are the most important factors in reliability analysis. Moreover, it is shown that the correlation length and coefficient of variation of soil strength can exert significant impacts on the calculated failure probability.     

Spatial variability assessment of soil nutrients in an intense agricultural area,a case study of Rugao County in Yangtze River Delta Region,China

Topsoil samples (0–20 cm) (n = 237) were collected from Rugao County, China. Geostatistical variogram analysis, sequential Gaussian simulation (SGS), and principal component (PC) analysis were applied to assess spatial variability of soil nutrients, identify the possible areas of nutrient deficiency, and explore spatial scale of variability of soil nutrients in the county. High variability of soil nutrient such as soil organic matter (SOM), total nitrogen (TN), available P, K, Fe, Mn, Cu, Zn, and B concentrations were observed. Soil nutrient properties displayed significant differences in their spatial structures, with available Cu having strong spatial dependence, SOM and available P having weak spatial dependence, and other nutrient properties having moderate spatial dependence. The soil nutrient deficiency, defined here as measured nutrient concentrations which do not meet the advisory threshold values specific to the county for dominant crops, namely rice, wheat, and rape seeds, was observed in available K and Zn, and the deficient areas covered 38 and 11%, respectively. The first three PCs of the nine soil nutrient properties explained 62.40% of the total variance. TN and SOM with higher loadings on PC1 are closely related to soil texture derived from different parent materials. The PC2 combined intermediate response variables such as available Zn and P that are likely to be controlled by land use and soil pH. Available B has the highest loading on PC3 and its variability of concentrations may be primarily ascribed to localized anthropogenic influence. The amelioration of soil physical properties (i.e. soil texture) and soil pH may improve the availability of soil nutrients and the sustainability of the agricultural system of Rugao County.     

Geostatistical approach for identification of transmissivity structure at Dulliu area in Taiwan

 A thorough understanding of the characteristics of transmissivity makes groundwater deterministic models more accurate. These transmissivity data characteristics occasionally possess a complicated spatial variation over an investigated site. This study presents both geostatistical estimation and conditional simulation methods to generate spatial transmissivity maps. The measured transmissivity data from the Dulliu area in Yun-Lin county, Taiwan, is used as the case study. The spatial transmissivity maps are simulated by using sequential Gaussian simulation (SGS), and estimated by using natural log ordinary kriging and ordinary kriging. Estimation and simulation results indicate that SGS can reproduce the spatial structure of the investigated data. Furthermore, displaying a low spatial variability does not allow the ordinary kriging and natural log kriging estimates to fit the spatial structure and small-scale variation for the investigated data. The maps of kriging estimates are smoother than those of other simulations. A SGS with multiple realizations has significant advantages over ordinary kriging and even natural log kriging techniques at a site with a high variation in investigated data. These results are displayed in geographic information systems (GIS) as basic information for further groundwater study. Received: 27 August 1999 · Accepted: 22 February 2000     

On the estimation of scale of fluctuation in geostatistics

Describing how soil properties vary spatially is of particular importance in stochastic analyses of geotechnical problems, because spatial variability has a significant influence on local material and global geotechnical response. In particular, the scale of fluctuation θ is a key parameter in the correlation model used to represent the spatial variability of a site through a random field. It is, therefore, of fundamental importance to accurately estimate θ in order to best model the actual soil heterogeneity. In this paper, two methodologies are investigated to assess their abilities to estimate the vertical and horizontal scales of fluctuation of a particular site using in situ cone penetration test (CPT) data. The first method belongs to the family of more traditional approaches, which are based on best fitting a theoretical correlation model to available CPT data. The second method involves a new strategy which combines information from conditional random fields with the traditional approach. Both methods are applied to a case study involving the estimation of θ at three two-dimensional sections across a site and the results obtained show general agreement between the two methods, suggesting a similar level of accuracy between the new and traditional approaches. However, in order to further assess the relative accuracy of estimates provided by each method, a second numerical analysis is proposed. The results confirm the general consistency observed in the case study calculations, particularly in the vertical direction where a large amount of data are available. Interestingly, for the horizontal direction, where data are typically scarce, some additional improvement in terms of relative error is obtained with the new approach.     

Spatial variability of soil available Zn and Cu in paddy rice fields of China

As a source of nutrient supplements, the deficiency or excess of micronutrients in soil is directly connected to the plant uptake and, thereby, status of micronutrients in the human population. Proper management of micronutrients requires an understanding of the variations of soil micronutrients across the fields. This study is to investigate the spatial patterns of soil available Zn and Cu in paddy rice fields. Four hundred and sixty three soil samples were taken in Hangzhou–Jiaxing–Huzhou (HJH) watershed in Zhejiang Province, China, and available Zn and Cu were analyzed using an atomic adsorption spectrometer. Geostatistical semivariograms analysis indicated that the available Zn and Cu were best fitted to a spherical model with a range of 40.5 and 210.4 km, respectively. There were moderate spatial dependences for Zn and Cu over a long distance and the dependence were attributed to soil types and anthropogenic activities. The overlay analysis of spatial patterns and soil types gave us greater understanding about how intrinsic factors affect the spatial variation of available micronutrients. Based on the above, macroscopically regionalized management of soil available micronutrients and the implications to potential risk were discussed.     

Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations

ABSTRACT

Field data is commonly used to determine soil parameters for geotechnical analysis. Bayesian analysis allows combining field data with other information on soil parameters in a consistent manner. We show that the spatial variability of the soil properties and the associated measurements can be captured through two different modelling approaches. In the first approach, a single random variable (RV) represents the soil property within the area of interest, while the second approach models the spatial variability explicitly with a random field (RF). We apply the Bayesian concept exemplarily to the reliability assessment of a shallow foundation in a silty soil with spatially variable data. We show that the simpler RV approach is applicable in cases where the measurements do not influence the correlation structure of the soil property at the vicinity of the foundation. In other cases, it is expected to underestimate the reliability, and a RF model is required to obtain accurate results.     

Generation of correlated properties in heterogeneous porous media

The spatial distribution of rock properties in porous media, such as permeability and porosity, often is strongly variable. Therefore, these properties usefully may be considered as a random field. However, this variability is correlated frequently on length scales comparable to geological lengths (for example, scales of sand bodies or facies). To solve various engineering problems (for example, in the oil recovery process) numerical models of a porous medium often are used. A need exists then to understand correlated random fields and to generate them over discretized numerical grids. The paper describes the general mathematical methods required to do this, with one particular method (the nearest neighbor model) described in detail. How parameters of the mathematical model may be related to rock property statistics for the nearest neighbor model is shown. The method is described in detail in one, two, and three dimensions. Examples are given of how model parameters may be determined from real data.     

农田土壤水分和盐分空间分布的指示克立格分析评价

运用非参数地质统计学的多元指示克立格法,结合单元指示克立格法,对黄河河套灌区55hm2的盐渍化土地上两个比较关键时期的土壤水分和盐分进行空间分布的分析,给出了同一时期土壤水盐和不同时期土壤盐分满足一定标准的综合概率图,并借助该案例详细介绍了多元指示克立格的原理、步骤及应用范围。指示克立格方法为不同尺度(从农田到区域)上水土资源质量的评价提供了新的方法,能为水土资源的现代决策管理提供指导。     

Effect of sample location on the reliability based design of pad foundations

Site investigations that aim to sufficiently characterize a soil profile for foundation design, typically consist of a combination of in situ and laboratory tests. The number of tests and/or soil samples is generally determined by the budget and time considerations placed upon the investigation. Therefore, it is necessary to plan the locations of such tests to provide the most suitable information for use in design. This is considered the sampling strategy. However, the spatial variability of soil properties increases the complexity of this exercise. Results presented in this paper identify the errors associated with using soil properties from a single sample location on a pad foundation designed for settlement. Sample locations are distributed around the site to identify the most appropriate sample location and the relative benefits of taking soil samples closer to the center of the proposed footing. The variability of the underlying soil profile is also shown to a have a significant effect on the errors due to sampling location. Such effects have been shown in terms of the statistical properties of the soil profile. The performance of several common settlement relationships to design a foundation based on the results of a single sample location have also been examined.