Reliability of shallow foundations designed to Eurocode 7

Eurocode 7, the new European standard for geotechnical design, is based on the limit state design method, with partial factors and characteristic parameter values. An objective of the Eurocodes is that the chosen partial factors should achieve reliability levels for a structure close to a prescribed target value. The target ultimate limit state reliability index for a medium risk structure for 50 years is 3.8. This paper examines the reliability of an inclined-eccentrically and vertically loaded square foundation designed using all three Design Approaches in Eurocode 7 with the recommended partial factor values given in EN1997-1. The reliabilities obtained using the three Design Approaches are compared with the target reliability value and the reliabilities of traditional designs using overall factors of safety. The paper provides evidence that Eurocode 7 gives more consistent reliabilities for a greater range of parameter values than the traditional allowable stress method and demonstrates the importance of selecting appropriate characteristic values.     

Honing safety and reliability aspects for the second generation of Eurocode 7

ABSTRACT

Ten years after their publication, the Eurocodes, including Eurocode 7 for Geotechnical design, are being revised taking into account experiences with their use and developments in design concepts and practices since their publication to produce a second generation of the Eurocodes. The objectives for this second generation of Eurocode 7 are to improve its ease of use, harmonise its structure with the other Eurocodes, reduce the number of nationally determined parameters, include measures for robustness and include sections on topics not covered in the current Eurocode 7, such as numerical methods, reinforced soil and ground improvement. The evolution of Eurocode 7 aims to hone its safety and risk assessment aspects by developing the concept of Geotechnical Categories, expanding the supervision, monitoring and maintenance requirements, and explicitly allowing for reliability differentiation.     

路堤边坡稳定可靠度计算中的模型不确定性分析

基于均质路堤边坡Monte Carlo法的稳定可靠度计算,分析了临界滑面搜索策略和稳定分析方法两类模型不确定性对边坡可靠度的影响特性,讨论了边坡失效概率随土工参数变异性的变化规律。研究表明,选用不同的临界滑面搜索策略所得可靠度结果差异不大,参数滑面法（overall slope）的失效概率略大于均值滑面法（global minimum）,但差别对边坡稳定性分析没有实质性影响;土性参数变异水平是影响边坡可靠度的最重要因素,边坡在相同设计参数安全系数下的可靠度指标随参数变异性增大而急剧降低;不同稳定性分析方法对应的安全系数概率密度函数曲线形态基本一致,但失效概率差异明显,因此目标可靠度指标取值应与稳定性分析方法相适应。提出的考虑土工参数变异水平的安全系数取值修正原则,对改进确定性设计的边坡稳定分析技术有积极意义。     

Probabilistic comparative analysis between design rules of a shallow foundation safety

ABSTRACT

A fact that is generally overlooked in many geotechnical uncertainty analyses is that input data of the model may be correlated. While this correlation may influence the system response, epistemic uncertainties i.e. lack of knowledge of this correlation appears as a risk factor. This paper discusses how a negative correlation between cohesion (c’) and friction angle (Ø’) with their associated uncertainties can influence both the bearing resistance of a shallow strip foundation footing and the estimation of its safety. A probabilistic approach that considers both the negative correlation and the uncertainty is used in this work as a reference. This method is compared to Eurocode 7 variants that do not for the correlation. These variants, resistance and material factoring methods appears to be more or less conservative depending on the negative correlation degree between (c’–Ø), their associated uncertainties and soil configurations. Finally, the proposed probabilistic comparison shows that the material factoring method is more conservative than the resistance one.     

The need for judgement in geotechnical reliability studies

ABSTRACT

A core principle of geotechnical engineering practice is the need to exercise judgement in evaluating soil and site conditions and in performing analyses. The requirement for considering judgement applies equally to performing deterministic or probabilistic analyses. In addition, for probabilistic analyses, choices must be made among the possible methods of analysis and the method of characterising variables. Consequently, geotechnical reliability studies inevitably involve significant uncertainties, and judgement is needed to perform reliability analyses and to evaluate the results. Two case histories, briefly described here, show that judgement and experience are essential prerequisites for meaningful assessment of geotechnical reliability.     

Numerical evaluation of the bearing capacity factor N’c of circular and ring footings

Ring footings are widely used to support structures like silos and storage tanks. Analytical design of safe and economical shallow footings requires the knowledge of the bearing capacity factors N’_c and N’_γ. The geotechnical design Eurocode 7 provides such factors only for simple geometric shapes like squares, circles or rectangles. Furthermore the N’_γ factor has been extensively carried out but the research on the N’_c factor hasn’t yet been performed. Thus, the present study aims to provide the first numerical N’_c values of a ring footing laying on general c-φ Mohr-Coulomb soil. The results, carried out by using FLAC code, indicate that for rough footings there is an optimal ring which is also dependent of the friction φ. The optimal value of r_i/r₀ is found to be almost equal to 0.26, 0.33 and 0.46 corresponding respectively to a low, medium and high friction soil. The results also indicate that the soil dilation angle influences the value of N’_c when the soil displays high non-associativity for large internal friction angle values. The computational results are presented in the form of design tables and graphs, and compared with previous published results available in the literature.     

岩土工程最小勘探数据量确定方法

准确地确定岩土设计参数统计特征值诸如均值、标准差是岩土工程可靠度分析与设计的重要前提。在满足岩土设计参数统计特征值计算精度条件下,文中提出了岩土工程最小勘探数据量的确定方法,定义了相对误差和相对变异性指标衡量岩土设计参数统计特征值计算准确性。系统地分析了静力触探试验数据量对砂土有效内摩擦角统计特征值计算精度的影响,并且根据相对误差和相对变异性指标确定了静力触探最小勘探数据量。研究结果表明,由静力触探试验间接估计砂土有效内摩擦角时均值相对误差较低,砂土有效内摩擦角相对变异性指标随静力触探试验数据量的增加而降低,即由认知不足引起的不确定性占总变异性的比值随静力触探试验数据量的增加而减小;当砂土有效内摩擦角容许相对变异性指标小于0.2时砂土有效内摩擦角在最大变异（COV=20%）与最小变异性（COV=5%）范围内,满足预定要求所需的最小静力触探试验数据量为10～100;若容许相对变异性指标小于0.3,所需的最小静力触探试验数据量为5～43。此外,间接估计岩土设计参数时经验回归模型不确定性对最小勘探数据量有显著影响。静力触探试验最小勘探数据量随经验回归模型不确定性的增大而增加,在确定岩土设计参数统计特征值时应尽量广泛收集勘探数据并选择精度较高的计算模型。     

Uncertainty in spatial average undrained shear strength with a site-specific transformation model

ABSTRACT

Transformation models are used to infer geotechnical properties from indirect measurements. A site-specific transformation model can be calibrated with direct and indirect measurements from a site. When such a model is used, then spatial variability, measurement errors and statistical uncertainty propagate into the uncertainty of the spatial average, which is the variable of interest in most geotechnical analyses. This research shows how all components enter the total uncertainty of a transformation model for undrained shear strength from cone resistance. A method is proposed to estimate the uncertainty in the spatial average undrained shear strength, particularly focusing on the role of averaging of all spatially variable error components. The main finding is that if a considerable share of the measurement and transformation errors is random or spatially variable, the uncertainty estimates can be considerably lower compared to methods proposed earlier, and hence, characteristic values can be considerably higher.     

钻孔岩心红外光谱-便携式XRF-磁化率测试在攀西太和钒钛磁铁矿床勘查中的应用

近年来,红外光谱技术因其可以绿色、快速、无损、精确探测矿物和提高勘查效率而备受关注。攀西超大型太和钒钛磁铁矿床位于镁铁质-超镁铁质层状岩体中,该矿床的典型矿物的红外光谱特征研究相对缺乏,制约了勘查效率的提高。本文应用便携式傅里叶变换红外光谱仪对四川太和钒钛磁铁矿床钻孔ZK1307岩心开展热红外光谱测试工作,并辅以便携式X射线荧光光谱（XRF）元素含量分析和磁化率值的综合分析,参考岩心编录情况,分析研究了钻孔岩性-矿物组合-元素含量-磁化率之间的对应关系。研究表明：热红外光谱可以实现快速、无损对辉石特征吸收峰的信息提取,识别含磁铁辉石岩体分布范围,快速界定含矿岩体;太合矿床Fe、Ti、V元素含量可以用磁化率值进行线性拟合,较高的Fe、Ti、V金属元素含量和磁化率值可作为判断地质体矿化的指示信息。     

The geological and geotechnical design model in tunnel design: estimation of its reliability through the R-Index

ABSTRACT

In this paper recent improvements of the R-Index method are presented, based on its application on several projects in various geological and geotechnical contexts. The R-Index derives from a probabilistic procedure conceived for estimating the reliability level of the Geological and Geotechnical Design Model used to design underground structures, especially tunnels. The R-Index takes into account the geological complexity of a site and recommended empirical scores (based on expert judgement) for different quality levels of geological surveys and geotechnical and geophysical investigations.     

Geo-Characterization at selected accelerometric stations in Crete (Greece) and comparison of earthquake data recordings with EC8 elastic spectra

To estimate the seismic response according to Eurocode (EC8) and almost all other national codes, site conditions have to be properly characterized so that soil amplification and the corresponding peak ground motion can be calculated. In this work, different geophysical and geotechnical methods are combined in order to define the detailed ground conditions in selected sites of the Hellenic Accelerometric Network (HAN) in Crete. For this purpose, the geological information of the sites and shear wave velocity, calculated from surface wave measurements, is used. Additionally, ground acceleration data recorded through HAN have been utilized from intermediate depth earthquakes in the broader area of South Aegean Sea. Using the recorded ground motion data and the procedure defined in EC8, the corresponding elastic response spectrum is calculated for the selected sites. The resulting information is compared to the values defined in the corresponding EC8 spectrum for the seismic zone that includes the island of Crete. The comparison shows that accurate definition of ground type through geological, geotechnical and geophysical investigations is important. However, our current comparison focuses on the distribution of values rather than the absolute values of EC8-prescribed spectra, and the results should be considered in this context.     

边坡模糊可靠性分析隶属函数取值界限研究

针对岩土参数取值所具有的随机性、模糊性与区间性特征,建议采用隶属函数表征参数取值,分别构造了岩土参数三角形分布、正态分布与拟正态分布隶属函数,并建立了采用隶属函数取值界限表示的不同截集水平岩土参数区间值确定方法,提出分别采用均值加减2.5倍标准差与3倍标准差确定岩土参数三角形分布与拟正态分布隶属函数取值界限,进而以此为基础采用模糊点估计分析方法对工程算例进行分析,结果表明,在截集水平个数为11时,模糊点估计方法所得边坡稳定模糊可靠性指标与蒙特卡洛法所得随机概率可靠性指标精度相当,截集水平个数为9时,评价结果偏安全,建议在工程分析时,截集水平取0.1⁰.9间的9个,该方法计算过程直接简单,计算代价低,更具工程实用性。     

Determination of partial factors for the verification of the bearing capacity of shallow foundations under open channels

The limit state design method has been introduced into the design criteria for geotechnical structures. The current paper attempts to apply the reliability-based design method, at Level II, to the bearing capacity of the foundations of open channels from the viewpoint of the limit state design. To examine the applicability of the proposed procedure for practical structures, the reliability index is computed for evaluating the stability of the foundations of existing open channels designed by the conventional method. The conventional design procedure makes excessively safe side design. We applied the FORM to the existing open channels designed by the conventional design procedure, and consequently, large values of reliability index, 3 and 5 were obtained for clayey and sandy soils, respectively. Finally, the partial factors for the soil parameters have been determined, corresponding to the target reliability indices β _t =1, 3 and 4.     

MCS-based probabilistic design of embedded sheet pile walls

A probabilistic approach to the design of embedded sheet pile walls is developed in this paper. The approach is based on Monte Carlo simulation (MCS), and it is used to investigate the performance of the partial factors and different design approaches in Eurocode 7 in achieving the target degrees of reliability. The approach is illustrated through an embedded sheet pile wall design example that has been used in literature for the evaluation of Eurocode 7. The approach deals rationally with the correlated load and resistance, and it bypasses a difficult but frequently asked question in Eurocode 7 (i.e. should the passive earth pressure be considered as a load (i.e. action) or a resistance?). The probabilistic design approach (DA) is also used to explore the effects of the soil unit weight variability and uncertainties in over-digging depth and wall friction. The effects of uncertainties in over-digging depth and wall friction are found to be significant. It is also found that, although the soil unit weight variability is generally minor, its effect on the design of embedded sheet pile walls is significant and should be properly accounted for in the design. The MCS-based probabilistic DA proposed in this study provides a straightforward way for proper consideration of such variability with relative ease.     

Reliability analysis of shallow foundation in the vicinity of the existing buried conduit

ABSTRACT

The present study proposes reliability-based approach for assessing the performance of shallow foundation placed in the vicinity of an existing buried flexible pipe or utility tunnel. Performance function for the reliability analysis is defined in terms of % bearing capacity loss in the load carrying capacity of the shallow foundation due to the presence of buried flexible pipe or utility tunnel, and, allowable bearing capacity loss in load carrying capacity that can be tolerated. For the reliability analysis, an explicit functional relationship between input variables, such as geotechnical parameters of in situ soil as well as material properties of pipe, and, output response, i.e. % bearing capacity loss in load carrying capacity of foundation soil is needed. Using concept of response surface methodology (RSM) combined with the results of the numerical analysis; such an explicit functional relationship is easily established. Thereafter, reliability analysis can be performed, conveniently, using standard First Order Second Moment (FOSM) approach and performance of the foundation soil system with buried flexible pipe, present in the vicinity, can be assessed in terms of an index, popularly known as ‘reliability index (β)’.     

Reliability based assessment of axial pile bearing capacity: static analysis,SPT and CPT-based methods

ABSTRACT

Since piles are one of the major geotechnical foundation systems, estimation of their axial bearing capacity is of great importance. Employing different design methods, resulting in a wide range of bearing capacity estimations, complicates the selection of an appropriate design scheme and confirms the existence of model error along with the inherent soil variability in bearing capacity prediction. This paper tends to evaluate different predictive methods in Reliability-Based Design (RBD) framework. In this regard, different static analyses, SPT and CPT-based methods are considered to evaluate which approaches collectively and which method individually, have more reliable predictions for compiled data bank. In order to assess reliability indices and resistance factors, two approaches have been considered, i.e. First Order Second Moment method (FOSM) and First Order Reliability Method (FORM). To investigate the reliability indices for different methods in both RBD approaches, various safety factors and loading ratios have been considered. Also, the Load and Resistance Factor Design (LRFD) resistance factors are calibrated for different target reliability indices and loading ratios. Results show that CPT-based methods are more reliable among other methods. Furthermore, the estimated efficiency ratio, i.e. the ratio of resistance factor to resistance bias factor, confirms this agreement.     

西安黄土土性相关距离的统计分布特性研究

土性指标概率模型参数的确定是进行岩土工程可靠度分析和设计的基础。为了更好地推行岩土工程可靠度设计,应该首先建立地区土性参数的概率模型。作为反映土性指标自相关特性的相关距离,研究其区域分布特性,建立其概率分布模型是必要的。本文收集了西安黄土的176个钻孔CPT数据,利用其端阻值qc作为样本,采用递推空间法计算了各层西安黄土的相关距离。研究了计算结果的统计特性,并对其均值进行了单侧置信区间估计,提出了各层西安黄土相关距离的代表值。建立了西安各层黄土相关距离的概率模型,对模型参数进行了估计,采用皮尔逊-卡方检验法对模型进行了拟合优度检验,检验结果认为其符合Beta分布。     

Bayesian soil assessments combining prior with posterior censored samples

The geotechnical engineer is often faced with the problem of how to assess the statistical properties of a soil parameter on the basis of a sample measured in-situ or in the laboratory with the defect that some values have been replaced by interval bounds because the corresponding soil parameter values have turned out to exceed the capacity of the measuring instrument. Given such a censored sample the problem is to estimate the mean value, variance and certain fractiles of the distribution of the soil parameter as it would be measured by an instrument of unrestricted range. In many situations only a small censored sample is given. To estimate the characteristic value defined as a lower fractile value corresponding to a codified probability value, the geotechnical engineer is thus urged to supplement the information from the measurements at the actual location by considering whatever prior knowledge is available about the soil parameter distribution. The present paper shows how a characteristic value by computer calculations can be assessed systematically from the actual sample of censored data supplemented with prior information from a soil parameter data base.     

Effect of sampling plan and trend removal on residual uncertainty

ABSTRACT

The ground is one of the most highly variable of all engineering materials. As a result, geotechnical designs depend upon a site investigation to estimate the ability of the ground to perform acceptably. For example, when a shallow foundation is being proportioned to avoid a bearing capacity failure under a certain applied load, the frictional and cohesive properties of the ground under the foundation must first be estimated through a site investigation. Questions which arise are: How does the quality and intensity of the site investigation affect the design? Is more investigation cost effective? If the site is sampled at one location and the foundation placed at a different location, how does this mismatch affect the target design and the reliability of the final foundation? By modelling the ground as a spatially variable material, questions such as the above can be investigated through Monte Carlo simulation and sometimes theoretical probabilistic models. Using such tools, this paper looks specifically at how the intensity (frequency and spatial distribution) of a site sampling plan, and how the samples are used, affects the understanding of the ground properties under a foundation. Interestingly, it is found that removing the sample mean outperforms removing the best linear unbiased estimate (BLUE) when the actual field correlation length is small but the BLUE correlation length is assumed equal to the field size. Recommendations are made regarding number of samples and the type of trend to best characterise the field.

Abbreviations: BLUE: best linear unbiased estimate; MCS: Monte Carlo simulation; LAS: local average subdivision     

A Factor Strength Approach for the Design of Rock Fall and Debris Flow Barriers

This paper discusses the applicability and the limitations of an approach to the limit states design of flexible barrier in which the soil/rock strength are factored as required in the European construction code. It shows as this approach has different implications if it is applied to the same kind of structure when loaded by different phenomena (rockfall and debris flow in particular). Flexible barriers are common countermeasures to protect from rockfall hazard and to restrain debris flow events. Even if an intense scientific production has demonstrated the difference between the two phenomena, the protection systems are still often designed in the same way. Additionally, the Eurocode 7 (EC7), which is the European Standard concerning geotechnical design, has not been conformed to these kinds of structures and consequently a relationship between the reliability of the system and the partial factors does not exist. Since most of the parameters that rule these systems are not even considered in the code, the Authors propose the study of two cases, in which rockfall and debris flow occur, respectively, to analyse the applicability and the limitations of EC7 principles to design the suitable kind of structure.