Reliability-based design of spread footings on clays reinforced with aggregate piers

ABSTRACT

The economical and safe design of footings supported on aggregate-pier-reinforced clay could benefit from the implementation of a reliability-based approach that incorporates the different sources of uncertainty. Monte Carlo simulations are conducted to quantify the probability distribution of the ultimate bearing capacity for practical design scenarios. A reliability analysis is then conducted to propose design charts that yield the required factor of safety as a function of the major input parameters. The novelty in the proposed methodology is the incorporation of a lower bound shear strength that is based on the remoulded undrained shear strength in the reliability analysis.     

Bearing capacity of two close strip footings on soft clay reinforced with geotextile

For many years ago, the beneficial effects of using reinforcement to improve the property of soil have been demonstrated. Over the last three decades, the use of polymeric reinforcement such as geotextile has increased in geotechnical engineering. Among the possible applications, earth reinforcement techniques have become useful and economical techniques to solve many problems in geotechnical engineering practice, such as improve the bearing capacity and settlement characteristics of the footing. This research presents the effect of geotextile inclusion on the bearing capacity of two close strip footings located at the surface of soft clay. A broad series of finite element analysis were performed on two footings with width of 1 and 2 m using two-dimensional plane strain model using the computer code Plaxis (ver 8). Only one type of soft clay was used for the analysis, and the soil was represented by two yielding criteria including hardening soil model and Mohr–Coulomb model, while reinforcement was represented by elastic element, and at the interface between the reinforcements and soft clay, interface elements have been used. A wide range of boundary conditions, including unreinforced and reinforced cases, was analyzed by varying parameters such as number of geotextile layers, vertical spacing of layers, depth to topmost layer of geotextile, tensile stiffness of geotextile layers, and distance of between two footings. From numerical results, the bearing capacity ratio and the interference factor of the foundations have been estimated. On the basis of the analysis performed in this research, it can be concluded that there is a best distance between footings and optimum depth for topmost layer to achieve maximum bearing capacity for closely spaced strip footings. The bearing capacity was also found to increase with increasing number of reinforcement layers if the reinforcements were placed within a range of effective depths. In addition, the analysis indicated that increasing reinforcement stiffness beyond a threshold value does not result in a further increase in the bearing capacity.     

Reliability Analysis of Excavation Induced Basal Heave

The present study deals with the reliability analysis of basal heave caused by excavation considering uncertainty in the soil properties. The case study considered in the present work has been analyzed deterministically by Hsieh et al. (Can Geotech J 45:788–799, 2008). Taiwan building code is adopted in the method for analyzing the basal heave failure. The random variables (undrained shear strength and total unit weight of clay) are assumed to be normally distributed and uncorrelated. A series of parametric studies have been conducted to calculate the reliability index on the basis of the matrix formulation for the second moment method by Hasofer and Lind (J Eng Mech ASCE 100(1):111–121, 1974) considering different coefficient of variation of undrained shear strength and total unit weight of clay layers. It has been found that for a particular value of coefficient of variation of total unit weight, the reliability index with respect to occurrence of basal heave failure decreases with increase in the coefficient of variation of undrained shear strength. Moreover, the reliability index also decreases when the coefficient of variation of total unit weight increases. It has also been found that the probability of basal heave failure is lower with respect to factor of safety equals to 1.2, as compared to factor of safety equals to 1.0. Sensitivity analysis shows that the undrained shear strength of the bottommost layer and total unit weight of the second layer are the most significant random variables affecting the reliability index. Guidelines are provided for reliability based design where, for ‘target’ reliability index of 2.5 and 3.0, the factor of safety can be chosen such that all the related uncertainties are taken into account, especially with regard to undrained shear strength of the bottommost layer and total unit weight of the second layer. Design guidelines have been provided for this purpose.     

Load-displacement uncertainty of vertically loaded shallow footings on sands and effects on probabilistic settlement estimation

This article focuses on the statistical characterisation and stochastic modelling of the load-displacement behaviour of shallow footings on cohesionless soils and on the probabilistic estimation of settlement for serviceability limit state design (LSD). The study relies on a field database of 30 full-scale footings subjected to vertical loading with cone penetration testing data available for each site. The performance of three load-displacement models in replicating field data is assessed comparatively through statistical analysis. Load-displacement uncertainty is subsequently modelled probabilistically to perform Monte Carlo Simulation (MCS)-based estimation of footing settlement using the best-performing power law model. The dependence among load-displacement model parameters is investigated and replicated using copula theory. Samples are generated to account for parametric uncertainties in model inputs. The simulation output samples of settlement are examined statistically in order to assess the relevance of parametric and load-displacement uncertainties in settlement estimation, as well as the importance of accounting for correlation between power law model parameters. A simple analytical model for the estimation of settlement at any target reliability level is obtained on the basis of the outputs of MCS. The model can be practically implemented in geotechnical LSD at serviceability limit states.     

Probabilistical distribution statistical analysis of Tianjin soft soil indices

In the design of soft ground treatment, the soft soil indices are the basic design parameter, and their changes have a strong geographical feature and significant uncertainty. Today, the soft soil indices statistical analysis content is mainly in the correlation and distribution regularity of physico-mechanical indices, which lack systematic study in different regions for different types of soft soils, and the statistical samples are from indoor tests and in-situ tests, without considering the impact of different test methods. In this paper, taking the soft soil in Tianjin as an independent statistical unit body, based on studying the change confines, variability, correlation, probabilistical distribution model of soil indices, some statistical relationship empirical formulas and probabilistical distribution models for physical indices, compression index, strength index were obtained; moreover, the correlation of shear strength results by straight shear test, triaxial test, vane shear test are analyzed; and a method for using random factor to evaluate the uncertainty involved in different test methods of soft soil parameters is proposed. The study results provide a basis and reference for defining the values of geotechnical parameters for soft soil.     

Strength and Compressibility Characteristics of a Soft Clay Subjected to Ground Treatment

The compressibility properties, undrained shear strength, and stress history are essential for reliable calculations of settlement and bearing capacity of soft soils. However, it is sometimes a challenge to determine representative parameters for very soft and high plasticity clays, which are often found in Brazilian coastal areas. In this study an extensive site investigation was planned aiming to interpret the behaviour of a trial embankment on stabilized soft ground. The site investigation was carried out in a test area located in the west of city of Rio de Janeiro, consisted of three clusters in which standard penetration tests, vane shear tests, and piezocone tests (CPTu) were performed. A number of correlations was developed and compared with empirical equations in order to verify their reliability. The results of these tests made it possible to define geotechnical parameters of the soft clay to use in the numerical and analytical computations of the embankment on reinforced ground.     

天津软土土性指标概率分布统计分析

软土土性指标作为软基处理设计的基本参数,其变化具有很强的地域特征和显著的不确定性。目前,对软土土性指标统计分析集中在软土物理力学指标的相互关系和分布规律等方面,采用的样本为室内试验和原位测试数据,没有考虑不同试验方法对土性指标不确定性分析的影响。将天津软土作为一个独立的统计单元体,研究了该地区软土物理力学指标的变化范围、变异性、指标间的相互关系和各指标的概率分布模型,得到了天津软土物理指标与压缩指标、强度指标间的统计关系经验公式以及土性指标的概率分布模型;并分析了直剪试验、三轴试验、十字板剪切试验3种不同方法抗剪强度试验结果的相互关系,提出了利用随机因子分析法对试验方法不确定性进行概率评定。研究成果为软土地区工程土工参数的取值提供了依据和参考。     

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.     

Effects of anisotropy in correlation structure on the stability of an undrained clay slope

Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.     

孔隙比对砂类土抗剪强度影响的定量分析

砂类土的密实程度是影响其抗剪强度的重要指标,然而已有研究并没有直观给出砂类土抗剪强度随孔隙比变化的定量规律。控制砂类土的初始孔隙比得到土体所需的抗剪强度,这在土工相似模型试验中具有一定的应用前景。基于砂土的临界状态理论,本文建立了砂类土抗剪强度与孔隙比关系的理论表达式。针对尾矿库现场取回的铜、钨尾砂开展了直剪试验和固结试验,并利用所推导的理论表达式对尾砂在不同状态时的抗剪强度进行了分析。结果表明,随着孔隙比的增加,砂类土的抗剪强度非线性减小,孔隙比越大时抗剪强度减小的幅度越平缓。试验结果证实砂类土抗剪强度与孔隙比关系的理论表达式能够合理描述尾砂在不同孔隙比下的抗剪强度。     

Seismic reliability-based analysis and GIS mapping of cyclic mobility of clayey soils of Mumbai city,India

Cyclic mobility is a mechanism of ground failure due to lateral spreading of soils during an earthquake that usually occurs in soft or medium stiff saturated soils. The simplified procedures developed by the researchers give a factor of safety for judging the cyclic mobility potential. However, the simplified procedures do not take into account the uncertainty in the parameters required to estimate the cyclic stresses in the soil. In this study, a reliability framework based on the simplified procedure, considering the parameter uncertainty, has been proposed for computing the probability of cyclic mobility of clay deposits for a metro city of India, i.e., Mumbai city (latitudes 18°53′N–19°19′N and longitudes 72°47′E–72°58′E). Extensive geotechnical borehole data from 1028 boreholes across 50 locations in the city area of 390 km² and laboratory test data are collected and analyzed thoroughly. A correlation between undrained shear strength (Su) and other parameters such as natural water content (w), SPT N value, liquid limit (LL) and plasticity index (PI) has been established for Mumbai city and has been used in the proposed approach. The sensitivity analysis of the proposed approach predicts that Su has significant influence in the evaluation of the cyclic mobility. Cyclic mobility hazard maps are prepared using the geo-statistical analysis tool in GIS, and it shows that the clayey soils at few locations have a 60–90 % probability of cyclic mobility for a moment magnitude (M _w) of an earthquake of 7.5. These hazard maps can be used by the geotechnical engineers for the cyclic mobility hazard assessment of Mumbai city.     

珠江口海洋软土不排水抗剪强度及循环弱化特性试验研究

为了获得广东珠江口海洋软土的不排水抗剪强度,分别开展了不固结不排水剪切和固结不排水剪切三轴试验、无侧限抗压试验、现场取土离心机正常固结模型地基的T-bar静力贯入试验以及现场十字板剪切试验和静力触探试验（CPT）,并采用土力学经验公式进行计算,确定了珠江口海洋软土不排水抗剪强度沿深度的分布规律,并综合评价了各种方法的有效性。为了获得该区域软土的循环弱化规律,分别开展了循环动三轴试验、现场取土离心机正常固结模型地基的T-bar循环贯入试验和现场单桩水平循环加载试验,揭示了软土循环动模量比与循环次数之间的双对数线性关系,获得了3种试验条件下珠江口海洋软土的循环弱化因子。其研究结果可为该区域海洋建筑物设计提供直接依据,也可为其他类型工程提供借鉴。     

有限数据条件下边坡可靠度分析的Bootstrap方法

基于Bootstrap抽样技术提出了有限数据条件下边坡可靠度分析方法。简要介绍了传统的边坡可靠度分析方法。采用Bootstrap方法模拟了抗剪强度参数概率分布函数的统计不确定性。以无限边坡为例研究了抗剪强度分布参数和分布类型不确定性对边坡可靠度的影响规律。结果表明：基于有限数据估计的样本均值、样本标准差和AIC值具有较大的变异性,这种变异性进一步导致了抗剪强度参数概率分布函数存在明显的统计不确定性。在考虑抗剪强度参数概率分布函数的统计不确定性时,边坡可靠度指标应为具有一定置信度水平的置信区间,而不是传统可靠度分析中的固定值。边坡可靠度指标的置信区间变化范围随安全系数的增加而增大,同时考虑分布参数和分布类型不确定性计算的可靠度指标具有更大的变异性和更宽的置信区间变化范围。Bootstrap方法为有限数据条件下抗剪强度参数概率分布函数统计不确定性的模拟以及边坡可靠度的评估提供了一条有效的途径。     

深海浅表层沉积物不排水剪切强度的多探头原位测试系统及评价方法研究

海洋工程建设已步入深海,但与之匹配的浅表层沉积物不排水剪切强度原位测试技术尚不成熟。为此,本文开发了可用于评估深海浅表层沉积物土力学性质的多探头原位测试系统,包括锥形触探仪、球形贯入仪和十字板剪切仪,可实现对深海沉积物土力学性质的快速、准确和智能化评价。进一步,通过CEL大变形数值模拟和足尺土工模型试验确定锥形触探仪的锥尖阻力系数,基于离心模型试验给出球形贯入仪的贯入阻力系数,从而完善深海浅表层沉积物不排水剪切强度的评价方法;在此基础上,探讨3种特定仪器各自适合的强度测试区间。结果表明:对于深海浅表层沉积物不排水剪切强度的评估,锥形触探仪和球形贯入仪的阻力系数建议分别取值为9.5和11.1。     

Dynamic Properties of Soft Clay and Loose Sand from Seismic Centrifuge Tests

Appropriate evaluation of shear modulus and damping characteristics of soils subjected to dynamic loading is key to accurate seismic response analysis and soil modeling programs. Dynamic centrifuge experiments were conducted at C-CORE (Memorial University of Newfoundland) centrifuge center to investigate the dynamic properties and seismic response of soft clay and dry loose sand strata. Soft clay with shear strength of about 30 kPa and well graded silica sand at about 35% relative density were employed in a rigid container to simulate local site effects. Several earthquake-like shaking events were applied to the model to evaluate variation of shear modulus and damping ratio with shear strain amplitude and confining pressure, and to assess their effects on site response. The estimated modulus reduction and damping ratio were compared to the predictions of empirical formulae and resonant column tests for both soft clay and loose sand. The evaluated shear modulus and damping ratio were found to be dependent on confining pressure in both soil types. Modulus variation in both soils agreed well with the empirical curves and resonant column test results. However, the sand modulus values were slightly higher than the empirical relations and resonant column tests. This discrepancy is attributed to higher stress and densification of sand during large amplitude shaking applied to the model. The damping ratio at shear strains lower than 0.5% was in reasonable agreement with the empirical curves and the resonant column tests in both clay and sand models, but was generally higher at shear strain larger than 0.5%.     

倾斜基岩上的边坡破坏模式和稳定性分析

应用离心模型试验对工程中被颇为关注的带有与边坡走向一致的倾斜基岩面,且在该基岩面存在软弱夹层的边坡的稳定性和破坏模式进行了比较详细地研究,并用极限平衡分析方法对试验结果进行了计算分析。模型试验结果表明,该类边坡失稳时,紧贴岩面的软弱夹层就成为滑动破坏面,因而边坡整体沿基岩面向下滑动,且侧向水平位移各处基本一致,表现出典型的平移滑动破坏模式。将稳定安全系数的实测结果与按平移滑动破坏模式的极限平衡分析方法的计算结果相比较后发现,两者相当地吻合,证实了按平移滑动破坏模式所作的极限平衡分析,能良好地预测边坡平移滑动破坏情形下的稳定安全系数。     

Prediction of undrained shear strength using extreme gradient boosting and random forest based on Bayesian optimization

Accurate assessment of undrained shear strength(USS)for soft sensitive clays is a great concern in geotechnical engineering practice.This study applies novel data-driven extreme gradient boosting(XGBoost)and random forest(RF)ensemble learning methods for capturing the relationships between the USS and various basic soil parameters.Based on the soil data sets from TC304 database,a general approach is developed to predict the USS of soft clays using the two machine learning methods above,where five feature variables including the preconsolidation stress(PS),vertical effective stress(VES),liquid limit(LL),plastic limit(PL)and natural water content(W)are adopted.To reduce the dependence on the rule of thumb and inefficient brute-force search,the Bayesian optimization method is applied to determine the appropriate model hyper-parameters of both XGBoost and RF.The developed models are comprehensively compared with three comparison machine learning methods and two transformation models with respect to predictive accuracy and robustness under 5-fold cross-validation(CV).It is shown that XGBoost-based and RF-based methods outperform these approaches.Besides,the XGBoostbased model provides feature importance ranks,which makes it a promising tool in the prediction of geotechnical parameters and enhances the interpretability of model.     

柱下独立基础稳健性设计与分析

岩土工程随机参数统计特征的不确定性,使得岩土工程可靠度设计存在一定风险。岩土工程稳健性设计能够充分考虑随机参数的不确定性结合结构安全性、稳健性和经济性实现最优设计。针对随机参数统计特征的不确定性对柱下独立基础设计的影响,基于可靠度理论和岩土工程稳健性设计方法,考虑岩土参数、混凝土和钢筋材料力学参数统计特征不确定性的影响,以独立基础几何尺寸作为可控设计参数进行设计分析。将独立基础地基承载力、地基变形、基础结构冲切破坏和基础弯曲破坏4种失效模式视为串联系统,进行多失效模式下的结构体系稳健性设计,分析了多失效模式下结构几何参数与结构体系可靠度的关系。结合稳健性和经济性,进行了独立基础多目标优化设计,确定柱下独立基础设计的最优解。     

Undrained Shear Strength in Cohesive Soils Estimated by Directional Modes of In-Situ Shear Wave Velocity

The estimated undrained shear strength (s_u) is often not a unique value because it can be evaluated by various test types and/or procedures, such as different failure modes, shear strain rates, and boundary conditions. This study explores (1) the relationship between reference undrained shear strength and in situ shear wave velocity in terms of the effective overburden stress, and (2) the independent relationships to evaluate the undrained shear strength with special consideration of different directional and polarization modes (VH, HV, HH shear waves), which has not been reported. This evaluation is done via a worldwide database compiled from 43 well-documented geotechnical test sites associated with soft ground. Finally, new correlation models are proposed to estimate the undrained shear strength based on the in situ shear wave velocity as well as the plasticity index or the overconsolidation ratio. The application of the shear wave velocity–undrained shear strength relation is illustrated through two independent case studies. The proposed relationships are expected to contribute to reasonable estimates of undrained shear strength as well as offer practical guidance on even extrapolation beyond the data that is available to geotechnical engineers.     

NGI‐ADP: Anisotropic shear strength model for clay

Many geotechnical problems involve undrained behavior of clay and the capacity in undrained loading. Most constitutive models used today are effective stress based and only indirectly obtain values for the undrained shear strength. To match the design profiles of undrained shear strengths, in active (A), direct simple shear (D) and passive (P) modes of loading are complicated. This paper presents the elastoplastic constitutive model NGI‐ADP which is based on the undrained shear strength approach with direct input of shear strengths. Consequently, exact match with design undrained shear strengths profiles is obtained and the well‐known anisotropy of undrained shear strength and stiffness is accounted for in the constitutive model. A non‐linear stress path‐dependent hardening relationship is used, defined from direct input of failure strains in the three directions of shearing represented by triaxial compression, direct simple shear and triaxial extension. With its clear input parameters the model has significant advantages for design analysis of undrained problems. The constitutive model is implemented, into finite element codes, with an implicit integration scheme. Its performance is demonstrated by a finite element analysis of a bearing capacity problem. Copyright © 2011 John Wiley & Sons, Ltd.