Updated normalized load-settlement model for full-scale footings on granular soils

The design of spread footings on granular soils is generally governed by serviceability requirements. Recent studies have utilized databases of load tests to investigate the use of normalized load-settlement curves to model the behavior of footings on sands. A major limitation of available databases is that they are based primarily on data from plate load tests or footings that have an equivalent width smaller than 1.0 m. There is a need to confirm the applicability of these curves to footings of practical scale. The main objective of this paper is to update available normalized load-settlement curves using point measurements of settlement and load from full-scale footings. Bayesian techniques are employed in the updating process. Results indicate that the updated normalized load-settlement relationship is slightly more conservative but less uncertain than the current relationship. Results from an illustrative example involving serviceability limit state reliability analyses using footings with widths ranging from 1.5 to 3.0 m indicated that the updated relationship resulted in a slightly higher reliability level compared to the prior relationship.     

基于Copula函数的CFG桩复合地基载荷-变形曲线的概率分析

CFG桩(cement-fly ash-gravel pile)复合地基是一种重要的地基处理形式,在日益增加的大面积住宅和商业开发中作用越来越突出,然而该种桩型的加卸荷-沉降变形特性仍然需深入研究,尤其在概率评估方面。根据北京星光影视股份有限公司生产科研基地项目工地中的21根CFG桩单桩静载试验和32个复合地基静载试验的原位加卸载测试成果,采用两参数的双曲线或幂曲线回归拟合了每一条加荷-变形曲线。由于土体的内在各向异性和其强度的变异性,评估整个场地的加荷-变形曲线时,其回归参数表现出了较大的离散性。将一个场地的多组回归参数组成一个随机向量,其加载-位移曲线的不确定性可由简单的两变量随机向量体现,引入双变量联结函数（Copula）描述随机回归参数间的相依性。最后,考虑正常使用极限状态,采用基于Copula函数的模拟模型计算了CFG桩复合地基的可靠度指标。研究结果有助于改进CFG桩复合地基的概率设计与评估。     

基于Copula函数的基桩荷载-位移双曲线概率分析

提出了基于Copula函数的基桩荷载-位移双曲线概率分析方法。首先将基桩标准化荷载-位移双曲线模型不确定性转化为双曲线参数不确定性,然后在Copula理论框架下建立了双曲线参数的联合分布函数。最后以钻孔现浇灌注桩试验数据为例证明了所提方法的有效性,并进行了基桩正常使用极限状态可靠度分析。结果表明：Copula函数是构造基桩标准化荷载-位移双曲线参数联合分布函数一种有效的方法,它能够更加准确地实现基桩荷载-位移双曲线的随机模拟,从而得到更为合理的可靠度结果。钻孔现浇灌注桩双曲线模型中两个参数间具有较强的负相关关系,忽略了这种负相关性将会高估基桩的失效概率。此外,常用的Gaussian Copula函数并不是拟合双曲线模型中两个参数间相关结构最优的Copula函数,采用Gaussian Copula函数将会明显低估基桩的失效概率。     

Probabilistic analysis of strip footings resting on a spatially random soil using subset simulation approach

The failure probability of geotechnical structures with spatially varying soil properties is generally computed using Monte Carlo simulation (MCS) methodology. This approach is well known to be very time-consuming when dealing with small failure probabilities. One alternative to MCS is the subset simulation approach. This approach was mainly used in the literature in cases where the uncertain parameters are modelled by random variables. In this article, it is employed in the case where the uncertain parameters are modelled by random fields. This is illustrated through the probabilistic analysis at the serviceability limit state (SLS) of a strip footing resting on a soil with a spatially varying Young's modulus. The probabilistic numerical results have shown that the probability of exceeding a tolerable vertical displacement (P _e) calculated by subset simulation is very close to that computed by MCS methodology but with a significant reduction in the number of realisations. A parametric study to investigate the effect of the soil variability (coefficient of variation and the horizontal and vertical autocorrelation lengths of the Young's modulus) on P _e was presented and discussed. Finally, a reliability-based design of strip footings was presented. It allows one to obtain the probabilistic footing breadth for a given soil variability.     

Interference effect of two nearby strip footings on layered soil: theory of elasticity approach

In recent times, rapid urbanisation coupled with scarcity of land forces several structures to come up ever closer to each other, which may sometime cause severe damage to the structures from both strength and serviceability point of view, and therefore, a need is felt to devise simplified methods to capture the effect of footing interference. In the present study, an attempt has been made to model the settlement behaviour of two strip footings placed in close spacing on layered soil deposit consisting of a strong top layer underlying a weak bottom layer. Theory of elasticity is employed to derive the governing differential equations and subsequently solved by the finite difference method. The perfectly rough strip footings are considered to be resting on the surface of two-layer soil system, and the soil is assumed to behave as linear elastic material under a range of static foundation load. The effect of various parameters such as the elastic moduli and thickness of two layers, clear spacing between the footings and footing load on the settlement behaviour of closely spaced footings has been determined. The variation of vertical normal stress at the interface of two different soil layers as well as at the base of the failure domain also forms an important part of this study. The results are presented in terms of settlement ratio (ξ_δ), and their variation is obtained with the change in clear spacing between two footings. The present theoretical investigation indicates that the settlement of closely spaced footings is found to be higher than that of single isolated footing, which further reduces with increase in the spacing between the footings.     

Settlement of Shallow Foundations on Cohesionless Soils Based on SPT Value Using Multi-Objective Feature Selection

Accurate prediction of settlement for shallow footings on cohesionless soil is a complex geotechnical problem due to large uncertainties associated with soil. Prediction of the settlement of shallow footings on cohesionless soil is based on in situ tests as it is difficult to find out the properties of soil in the laboratory and standard penetration test (SPT) is the most often used in situ test. In data driven modelling, it is very difficult to choose the optimal input parameters, which will govern the model efficiency along with a better generalization. Feature subset selection involves minimization of both prediction error and the number of features, which are in general mutual conflicting objectives. In this study, a multi-objective optimization technique is used, where a non-dominated sorting genetic algorithm (NSGA II) is combined with a learning algorithm (neural network) to develop a prediction model based on SPT data based on the Pareto optimal front. Pareto optimal front gives the user freedom to choose a model in terms of accuracy and model complexity. It is also shown how NSGA II can be effectively applied to select the optimal parameters and besides minimizing the error rate. The developed model is compared with existing models in terms of different statistical criteria and found to be more efficient.     

Estimating liquefaction-induced settlement of shallow foundations by numerical approach

Occurrence of liquefaction in saturated sand deposits underlying foundation of structure can cause a wide range of structural damages starting from minor settlement, and ending to general failure due to loss of bearing capacity. If the bearing capacity failure is not the problem, reliable estimation of the liquefaction-induced settlement will be of prime importance in assessment of the overall performance of the structure. Currently, there are few procedures with limited application in practice for estimation of settlement of foundations on liquefied ground. Therefore, development of a general relationship is important from the practical viewpoint. In this paper, the dynamic response of shallow foundations on liquefied soils is studied using a 3D fully coupled dynamic analysis. For verification of the numerical model, simulation of a centrifuge experiment is carried out and the analysis results are compared with the experimental measurements. The results of centrifuge experiment are taken from the literature for the purpose of comparison and the experiment has not been performed by the authors. After verification of the numerical model, a practical relationship for estimation of liquefaction-induced settlement of rigid footings on homogeneous loose to medium fine sand is proposed based on the results of a comprehensive parametric study. In the interpretation process, the soil layer thickness in which the liquefaction takes place is found to be a key parameter, since by normalization with respect to this parameter, effects of a number of other parameters can be eliminated.     

Reliability assessment of serviceability performance of braced retaining walls using a neural network approach

In urban environments, one major concern with deep excavations in soft clay is the potentially large ground deformations in and around the excavation. Excessive movements can damage adjacent buildings and utilities. There are many uncertainties associated with the calculation of the ultimate or serviceability performance of a braced excavation system. These include the variabilities of the loadings, geotechnical soil properties, and engineering and geometrical properties of the wall. A risk‐based approach to serviceability performance failure is necessary to incorporate systematically the uncertainties associated with the various design parameters. This paper demonstrates the use of an integrated neural network–reliability method to assess the risk of serviceability failure through the calculation of the reliability index. By first performing a series of parametric studies using the finite element method and then approximating the non‐linear limit state surface (the boundary separating the safe and ‘failure’ domains) through a neural network model, the reliability index can be determined with the aid of a spreadsheet. Two illustrative examples are presented to show how the serviceability performance for braced excavation problems can be assessed using the reliability index. Copyright © 2005 John Wiley & Sons, Ltd.     

Calibration and assessment of reliability-based serviceability limit state procedures for foundation engineering

This paper uses an existing reliability-based serviceability limit state (RBSLS) procedure to illustrate some of the critical elements in the calibration of RBSLS models and to serve as guide for future calibration work. The impact of copula model selection and therefore correlation structure of bearing pressure-displacement model parameters on reliability is assessed. Then, a framework for evaluating bearing pressure-displacement normalisation techniques is presented as a revision to the existing RBSLS procedure proposed. The reliability of the revised RBSLS procedure is then evaluated by comparing its accuracy to newly conducted, full-scale loading tests of spread footings on aggregate pier-reinforced ground. It is shown that the new RBSLS procedure produces a more accurate estimate of the actual reliability and validates the proposed framework.     

戈壁地基扩底掏挖基础抗拔试验及其位移计算

在甘肃和新疆7个戈壁碎石土场地完成了46个扩底掏挖基础抗拔现场试验,分析了基础抗拔荷载-位移曲线的阶段特征,应用L1-L2方法确定了所有基础抗拔承载力和位移。采用归一化荷载-位移双曲线模型对实测荷载-位移曲线进行拟合,得到了各试验基础归一化荷载-位移双曲线模型拟合参数取值及其统计规律,给出了同时考虑抗拔基础极限承载力计算理论模型误差和归一化荷载-位移双曲线模型不确定性时基础荷载和位移的计算方法。结果表明：戈壁碎石土扩底掏挖基础抗拔荷载-位移曲线呈初始弹性直线段、弹塑性曲线过渡段和直线破坏的3阶段变化规律,归一化荷载-位移双曲线模型可较好拟合基础实测荷载-位移曲线,归一化荷载-位移双曲线模型不确定性可转化为该双曲线模型拟合参数的不确定性,基于强度和变形统一的工程设计更有利于工程安全。     

Probabilistic analysis of responses of cantilever wall-supported excavations in sands considering vertical spatial variability

The influence of vertical spatial variability of sands on the excavation-induced lateral wall deflection and bending moment of excavations supported by cantilever retaining walls is investigated in this paper. Herein, the random finite element method (RFEM) is adopted to explicitly study the effect of one-dimensional spatial variability of internal friction angle of sands on the predicted wall and ground responses. The RFEM analysis consists of three components: (1) finite element method for analyzing lateral wall deflection and bending moment, (2) random field theory implemented with Monte Carlo simulation (MCS), and (3) statistical interpretation of MCS results through confidence intervals. This study reveals the importance of random field modeling in coping with the spatial variability of sands in the problem of supported excavations: (1) neglecting spatial variability of soil property will cause an overestimation of the variation in the predicted wall deflection and bending moment; (2) the estimated probability of failure based on a well-established serviceability limit state may be overestimated or underestimated depending on the chosen limiting lateral wall deflection. This study further investigates the effect of the number of MCS on the confidence intervals of the predicted statistics of the maximum lateral wall deflection and the maximum bending moment. The results also demonstrate that the confidence interval analysis of the predicted statistics of the maximum lateral wall deflection and the maximum bending moment provides a rational tool for interpreting the statistical data from RFEM.     

基于LSSVM与MCS的路基沉降可靠度分析

提出了一种计算路基沉降可靠度的新方法。基于FLAC中的修正剑桥模型,以最小二乘支持向量机为核心技术,结合蒙特卡罗法构建计算模型。由于修正剑桥模型参数较多,对模型参数进行了敏感性分析,将对沉降影响较大的参数确定为随机变量。选取训练样本对支持向量机进行训练,按照随机变量的概率分布进行抽样,馈送到最小二乘支持向量机得到相应的响应值,用Matlab编制程序完成可靠度计算,并进行了算例分析。计算结果表明,蒙特卡罗法结合支持向量机的沉降可靠度计算方法应用于公路软基沉降可靠度计算是可行的。     

Numerical Study of Behavior of Circular Footing on Geogrid-Reinforced Sand Under Static and Dynamic Loading

A series of axi-symmetry models using finite element analyses were performed to investigate the behavior of circular footings over reinforced sand under static and dynamic loading. Geogrid was modeled as an elastic element and the soil was modeled using hardening soil model which use an elasto-plastic hyperbolic stress–strain relation. Several parameters including number of geogrid layers, depth to the first geogrid layer, spacing between layers and load amplitude of dynamic loading are selected in this paper to investigate the influence of these parameters on the performance of reinforced systems under both static and dynamic loads. The numerical studies demonstrated that the presence of geogrid in sand makes the relationship between contact pressure and settlement of reinforced system nearly linear until reaching the failure stage. The rate of footing settlement decreases as the number of loading cycles increases and the optimum values of the depth of first geogrid layer and spacing between layers is found 20% of the footing diameter. Some significant observations on the performance of footing-geogrid systems with change of the values of parametric study are presented in this paper.     

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.     

嵌岩抗拔桩作用机制研究

嵌岩抗拔桩广泛应用于现代化建设的各个领域,但就其作用机制研究来说还有待进一步完善,关于其荷载传递特性、侧阻力分布规律及其影响因素等还存在许多模糊认识。以剪滞模型为基础,通过理论分析和验算,讨论了抗拔桩侧阻力分布规律、荷载-变位特性。结果表明：当抗拔荷载低于弹性极限抗拔时,桩侧阻力呈指数规律分布,荷载-变位曲线呈线性变化;当抗拔荷载大于弹性极限抗拔荷载时,桩侧阻力分为两段,其中脱黏段上侧阻力均匀分布,黏结段上侧阻力呈指数规律分布,荷载-变位曲线呈非线性规律变化。     

Factors Affecting Differential Settlements of Framed Structures

The estimation of settlements, differential settlements and relative rotations on critical positions of the foundation is indispensable when carrying out analyses of both ultimate and serviceability limit states. The use of finite element method is recommended in cases where soil?Cstructure interaction is expected to be significant. The scope of this paper is a contribution to the investigation of general trends in the effects of main parameters on the interaction. A typical five-span frame building with varying rigidity was examined by using finite element numerical method under 2-D conditions. Soil below the foundation was simulated as linearly elastic or elastoplastic medium. The effects of superstructure and foundation rigidity are closely related to the effect of soil deformability thereby analyses were performed in terms of relative rigidity factors. The effects of specific foundation types, namely isolated footings, flexible and rigid mat, were investigated in detail. The conclusions were focused on the development of normalized differential settlements, on the influence of the relative rigidity factor as well as on the determination of those cases where the interaction approach is necessary to be used for the analysis.     

考虑参数和模型不确定性的基桩正常使用极限状态可靠度分析

考虑承载力计算模型和荷载不确定性,利用可靠度分析方法和概率统计理论,推导出承载能力极限状态（ULS）和正常使用极限状态（SLS）下可靠度指标的计算公式,给出了两种极限状态下可靠度指标间的线性关系式,研究了桩顶容许沉降 随机性对正常使用极限状态可靠度分析结果的影响。研究结果表明,土体类别和桩型对正常使用极限状态模型因子影响很小;正常使用极限状态下基桩可靠度指标随承载力计算模型和荷载不确定性的增大而减小,但减小幅度逐渐降低,且可靠度指标总变化量不大,工程应用中可忽略承载力计算模型和荷载不确定性在可靠度分析中的影响; 随机性对正常使用极限状态可靠性分析结果的影响很大,随 的增加,正常使用极限状态模型因子和可靠度指标逐渐增大,而模型因子变异性逐渐减小,但桩本身性质并没有任何改变,只是所允许的沉降条件不同。研究结果可为规范修订和工程应用提供参考。     

Optimization of site exploration program for improved prediction of tunneling-induced ground settlement in clays

Excessive settlement caused by tunneling during construction often damages adjacent infrastructures and utilities. Such excessive settlement can also present a challenge in the maintenance of subways during their operation. Thus, it is important to be able to accurately predict tunneling-induced settlement. The uncertainties in geotechnical parameters, however, can lead to either an overestimation or an underestimation of the tunneling-induced settlement. Such uncertainties can arise from many sources such as spatial variability, measurement error, and model error; in this paper, the focus is on the geotechnical parameters characterization from site exploration. The goal here is to determine an optimal level of site exploration effort so that effective predictions of the tunneling-induced settlement in clays can be achieved. To this end, a Monte Carlo simulation-based numerical model of site exploration is first established to generate artificial test data. Then, a series of parametric analyses are performed to investigate the relationship between the level of site exploration effort and the accuracy of the tunneling-induced ground settlement prediction. Through the assumed different levels of site exploration effort, statistics of soil parameters are estimated using the maximum likelihood method and the tunneling-induced ground settlement is then analyzed using the probabilistic method, and finally the effect of site exploration effort is assessed. The knowledge generated from this series of analyses is then used to develop the proposed framework for selecting an optimal site exploration program for improved prediction of the tunneling-induced ground settlement in clays. Examples are presented to illustrate the proposed framework and demonstrate its effectiveness and significance.     

黄土地基掏挖扩底基础抗拔试验研究

随着西部电网建设的发展,越来越多的架空输电线路需经过黄土地区。输电线路杆塔基础抗拔能力通常是其设计控制条件。掏挖扩底基础因具有较好的抗拔承载性能而在黄土地区输电线路工程中得到广泛应用。根据甘肃黄土地区2个试验场地12个掏挖扩底基础实测上拔荷载位-移曲线,分别采用Chin双曲线模型以及初始直线斜率法、双直线交点法和L1-L2方法确定了基础抗拔极限承载力及其对应位移,得到了抗拔基础归一化荷载-位移曲线,采用归一化荷载-位移双曲线模型对试验结果进行拟合,给出了不同保证概率下基础荷载-位移预测曲线。结果表明：初始直线斜率法得到的承载力最小,双直线交点法次之,Chin数学模型法最大,宜采用L1-L2方法确定黄土地基掏挖扩底基础抗拔承载性能;荷载-位移曲线归一化处理可显著减小实测荷载-位移曲线的离散性,按双曲线拟合参数a、b均值确定的归一化荷载-位移曲线代表了试验平均值,而试验荷载-位移曲线刚度远大于95％保证概率的预测曲线。     

Prediction of Uplift Pile Displacement Based on Cone Penetration Tests (CPT)

Accurate prediction of uplift pile displacement is necessary to ensure appropriate structural and serviceability performance of civil projects. On the other hand, in recent years, machine-learning models have been applied to many geotechnical-engineering problems, with some degrees of success. The scope of this research includes three main stages: (1) the compilation of load–displacement data sets, obtained from the published literature, (2) analysis of machine learning models that predict the uplift pile displacement based on the cone penetration test data, and the relative importance of input parameters that have been evaluated using senility analysis by the artificial neural network, In addition, this paper also examines the different selection of input parameters and internal network parameters to obtain the optimum model, (3) A parametric study has also been performed for the input parameters to study the consistency of the suggested model. The statistical parameters and parametric study obtained in this research show the superiority of the current model. It is demonstrated that machine learning models such as ANN and GP models outperform the traditional methods, and provide accurate uplift pile displacement predictions.