Incorporating set-up into LRFD method for drilled shafts

The increase of pile resistance with time is referred to as ‘set-up’. This behaviour of driven piles has been widely discussed in many studies by researchers. Meanwhile, there has been little, if any, information regarding this aspect for drilled shafts. Performing a bearing capacity test for a shaft over time, however, requires higher costs and more complicated rigs compared to a driven pile. A database including results from five Osterberg cell-tested drilled shafts conducted at two different stages is considered, from which the set-up effect is statistically analysed. The reliability-based analysis technique using Monte Carlo simulation (MCS) is used to develop separate resistance factors to account for different degrees of uncertainties associated with the predicted reference resistance and the predicted set-up resistance in the framework of the load and resistance factor design (LRFD) method. By incorporating set-up into design, shaft length or number of shafts can be reduced and economical design of drilled shafts can be achieved.     

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.     

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.     

Numerical integration method for computing reliability index of geotechnical system

To account for the uncertainties in the design of a geotechnical system, reliability-based design approach is often adopted, in which the main task is to evaluate reliability index of the system based on a performance function (or limit state function). In this paper, we propose a new method for computing the reliability index, based upon the numerical integration of the cumulative distribution function (CDF) of the performance function. This numerical integration method requires only a deterministic evaluation of the system performance and the joint probability of the uncertain input parameters. The effectiveness and the efficiency of the proposed method, measured in terms of the accuracy and the computational effort, respectively, are demonstrated with two geotechnical problems: a drilled shaft in sand and a semi-gravity retaining wall. The new method is found valid regardless of the type of distribution of uncertain input parameters, whether the correlations exist among these input parameters, whether the system involves single or multiple failure modes, and how the performance function is formulated.     

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.     

Characterization and Estimation of Geotechnical Variability in Ankara Clay: A Case History

An important component in reliability-based design is the geotechnical property variability. Generic estimates are used often, but calibration to a local geologic setting is preferable. In this case history, a methodology is shown that employs local geotechnical data to estimate the total variability, using Ankara Clay for illustration. A literature review is used to estimate the inherent variability, which is modeled as a random field with coefficient of variation (COV) and scale of fluctuation. The resulting inherent variability COVs are much smaller than the generic ranges. Local correlations between various laboratory and field tests and soil strength and compressibility parameters then are developed to quantify the transformation uncertainties. The various sources of uncertainty are combined through a second-moment method to estimate the total geotechnical variability as a function of the test type and correlation used. The results show: (1) the COVs for direct laboratory measurements are significantly smaller than those obtained through correlations, and (2) depending on the geotechnical data available, the local COVs can be very different from the generic guidelines. These could lead to unconservative designs. These issues are illustrated by a simple design example.     

Simplified procedure for reliability-based robust geotechnical design of drilled shafts in clay using spreadsheet

This paper provides a simplified procedure for reliability-based robust geotechnical design (RGD) using spreadsheet. In the RGD methodology, design robustness is achieved by adjusting “design parameters” without reducing the uncertainties in noise factors. This design approach generally involves a multi-objective optimisation, which is computationally challenging. To improve the efficiency of the RGD methodology, the design robustness is evaluated in terms of sensitivity index and the safety requirement is evaluated using mean value first order second moment (MFOSM). To ease the concern that the reliability index obtained with MFOSM may not be sufficiently accurate, a mapping function that relates MFOSM to a more accurate method such as first order reliability method is introduced. To further improve the efficiency of the proposed simplified RGD method, a new simplified procedure along with a more accurate robustness measure is developed that eliminates the need for multi-objective optimisation. With these modifications, the proposed simplified RGD method can efficiently be implemented in a single Excel spreadsheet. The proposed simplified method, which goes beyond any existing reliability-based RGD methods in terms of ease of use and computational efficiency, is illustrated in this paper with an example of robust design of drilled shaft in clay.     

土工试验规范变更对膨胀计算和判定的影响

对土工试验方法标准的新旧规范中无荷膨胀率和有荷膨胀率的变化内容进行对比分析,发现两者的计算公式发生显著变化,新规范的计算结果与旧规范相比,膨胀率明显变大,膨胀量随之增大,这将对工程勘察、设计、施工等产生明显影响。以某工程为例,新规范计算后地层总膨胀量由旧规范的16.7 mm变为51.8 mm,增加了2倍左右,地基土的胀缩等级由Ⅰ级变为Ⅱ级,地基基础设计等级由丙级变为乙级,地基处理措施和施工方案随之也发生改变。因此,工程技术人员对此应综合考虑,严谨对待。     

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (q_c) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ q_c data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.     

Reliability analysis of the bearing failure problem considering uncertain stochastic parameters

The consideration of uncertainties plays an increasing role in the design of geotechnical structures. An important procedure in the uncertainty analysis is the reliability assessment whereby the required statistical quantities and distributions are assumed to be known exactly. Due to small sample observations and missing information this is not the case in practical applications and uncertainties in the stochastic parameters themselves have to be considered. In our study we estimate the parameter variation of soil properties by statistical procedures and perform an extended reliability analysis of a shallow foundation considering these uncertainties. We propose a novel approach based on a Taylor series expansion which enables the estimation of the failure probability variation very efficiently.     

临近边坡的条形基础地基极限承载力数值分析

建筑物或构筑物基础临近边坡置放的情况在实际工程中十分普遍,但目前对于临近边坡基础的地基承载力及破坏模式尚缺乏深入研究。采用不连续布局优化（DLO）极限分析法建立数值模型,分析边坡几何尺寸、土体参数和基础位置对临坡条形基础的极限承载力和边坡破坏模式的影响,并对国内外现行规范推荐的计算方法进行评价。结果表明：极限承载力随边坡高度和边坡倾斜角的增大而减小,当坡高超过临界高度后,极限承载力将不受其影响;极限承载力随土体黏聚力和内摩擦角的增大而提高,滑动面随黏聚力的增大而变浅,随内摩擦角的增大而变深;极限承载力随基础与坡肩相对距离的增大而提高,当基础置放位置超过某临界距离后极限承载力不受边坡影响。在土体强度高、坡角较大时,《建筑地基基础设计规范》规定的临坡基础最小置放距离偏于危险,设计时仍需考虑边坡对承载力的减损作用;在土体强度较低、坡角较小时,规范规定值偏于保守。美国AASHTO规范对边坡地基极限承载力的取值在砂土边坡时较为可靠,但其仅适用于坡面破坏模式的情况;饱和黏土边坡的承载力曲线有悖于理论解,对临界距离的规定同样存在低估。     

Reliability-based robust design for reinforcement of jointed rock slope

Traditional reliability-based design methodologies often involve selection of design which is of lowest cost and satisfies safety requirements. But, this design is sensitive to variation in statistics of input parameters (noise parameters) and might become unsatisfactory if an underestimation of coefficient of variation of input parameters is made. A relatively new design methodology known as robust geotechnical design (RGD) is applied for the case of reinforcement of rock slope using end-anchored rock bolts. This ensures selection of a cost-effective and safe design for which probability of failure (P_f) of reinforced rock slope is least sensitive to the noise parameters. Reliability-based RGD approach involves evaluation of P_f for each design with different possible noise parameters. Finding P_f for the complex geotechnical structure is computationally expensive, and thus an augmented radial basis function-based response surface is used as a surrogate to the finite element model of rock slope. This response surface, being very efficient, also performs well for a range of values of noise parameters. Later, minimum distance algorithm is applied to obtain a cost-effective and robust design. Finally, a comparison is made in the costs between two robust designs obtained for different target probability of failure for the same rock slope.     

A generalized surrogate response aided-subset simulation approach for efficient geotechnical reliability-based design

This paper aims to develop an efficient geotechnical reliability-based design (RBD) approach using Monte Carlo simulation (MCS). The proposed approach combines a recently developed MCS-based RBD approach, namely expanded RBD approach, with an advanced MCS method called “Subset Simulation (SS)” to improve the computation efficiency at small probability levels that are often concerned in geotechnical design practice. To facilitate the integration of SS and expanded RBD, a generalized surrogate response f is proposed to define the driving variable, which is a key parameter in SS, for expanded RBD of geotechnical structures (e.g., soil retaining structures and foundations). With the aid of the proposed surrogate response, failure probabilities of all the possible designs in a prescribed design space are calculated from a single run of SS. Equations are derived for integration of the surrogate response-aided SS and expanded RBD, and are illustrated using an embedded sheet pile wall design example and two drilled shaft design examples. Results show that the proposed approach provides reasonable estimates of failure probabilities of different designs using a single run of the surrogate response-aided SS, and significantly improves the computational efficiency at small probabilities levels in comparison with direct MCS-based expanded RBD. The surrogate response-aided SS is able to, simultaneously, approach the failure domains of all the possible designs in the design space by a single run of simulation and to generate more complete design information, which subsequently yields feasible designs with a wide range of combinations of design parameters. This is mainly attributed to the strong correlation between the surrogate response and target response (e.g., factor of safety) of different designs concerned in geotechnical RBD.     

Mapping horizontal displacement of soil nail walls using machine learning approaches

Machine learning (ML) approaches have stormed nearly all engineering fields since recent years. However, the situation is somehow subtle in civil engineering practice, especially in the sub-field of geotechnical engineering where data from real-life projects are usually scarce, which in turn prevents development of meaningful mapping tools based on ML techniques. This study first shares a database containing a total of 376 measured horizontal displacements from instrumented soil nail walls reported in the literature. Then, these data are utilized to develop three types of ML models for mapping the wall horizontal displacement along depth, including artificial neural network (ANN), random forest (RF), and support vector machine (SVM). The uncertainties of the ANN, RF, and SVM models are then quantitatively evaluated using bias statistics where bias is defined as the ratio of measured to predicted horizontal displacement. The three ML models are proved to be accurate on average with medium dispersions in prediction, which outperform the existing simple empirical regression models. Probability distribution functions for those biases are also characterized. This study demonstrates that introduction of machine learning approaches into the reliability-based design framework for soil nail walls and other geotechnical structures is promising.

     

Response surface-based robust geotechnical design of supported excavation – spreadsheet-based solution

ABSTRACT

The robust geotechnical design (RGD) approach which involves optimization to obtain a design that is safe, cost-efficient, and robust in the face of uncertainties, can be computationally challenging for complex geotechnical structures. In this study, the RGD approach has become practical by introducing a response surface as a surrogate to finite element- or finite difference-based computer code that is used for analyzing the system, and developing a fast algorithm for the optimization process. For demonstration purposes, a real-world supported excavation project is designed using this modified RGD approach and it is compared with the one designed by a local expert.     

EN1997－1设计方法与国内规范设计方法对比

系统研究掌握国外标准规范,是企业跨出国门走向海外市场的第一步,也是增强国际竞争力的关键。同时,修订与完善国内现行规范,必须借鉴与吸收国际标准的先进经验。介绍了欧洲规范EN1997－1[1]设计原理,包括作用、效应、抗力与极限状态验算不等式,分析3种设计方法的取值特点与应用现状。以《建筑地基基础设计规范》[2]为例,对比分析中欧岩土工程设计规范中设计方法的异同点及国内规范存在的问题。以一浅基础设计实例,说明欧洲规范3种设计方法与国内规范设计方法设计结果的差异,并在该基础之上,提出改进国内规范设计方法的几点建议。     

The displacement computation and construction pre-control of a foundation pit in Shanghai utilizing FEM and intelligent methods

Controlling the displacements of foundation pit walls and supporting structures is one of the most effective measures for ensuring safety of foundation pit construction. Because of this, the accurate displacement computation of foundation pit walls and supporting structures is paid great attention by geotechnical scientists and engineers. In this paper, the three-dimensional displacement field of Deping Station foundation pit, which is part of Shanghai Track Traffic Line 6 project, is computed by means of ANSYS software. Artificial neural networks (ANNs) are a broad category of computer algorithms which have the ability to learn some target values (desired output) from a set of chosen input data that has been introduced to the network. The ANNs have very excellent ability in simulating nonlinear and complicated problems. In the current paper, the authors try to combine FEM method with ANNs so as to improve the computational accuracy. Basing on the computed results, fuzzy control theory is applied to construction pre-control. The application effect is satisfactory. The research result of current paper is very helpful for geotechnical construction and the development of geotechnical theory.     

Ring foundation on elastic subgrade: an analytical solution for computer modelling using the Lagrangian multiplier method

In the practice of geotechnical engineering, the case of a ring footing carrying a set of concentrated point loads is a common problem. At times, the induced vertical and angular displacements for the ring footing need to be evaluated at a relatively precise level. By making use of the governing set of equations derived for the case of a general curved beam, expressions that can be easily implemented in modern computing software are derived for the vertical and angular displacements of a ring footing of rectangular cross section as functions of the radial position. The loading case considered is a vertical point load, and the soil is modelled as elastic. Estimates of the displacements have been shown for a common range of practical applications. The behaviour for a set of concentrated loads may be evaluated using the derived equations through direct superposition. Nonlinear finite element analysis is used to evaluate the vertical deflection and angular twist of the ring foundation. Numerical analysis performed for three ring foundations with different radii and cross sections is reported to validate the accuracy of the derived analytical solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of Fuzzy Set Theory to Rock Engineering Classification Systems: An Illustration of the Rock Mass Excavability Index

The characterization of rock masses is one of the integral aspects of rock engineering. Over the years, many classification systems have been developed for characterization and design purposes in mining and civil engineering practices. However, the strength and weak points of such rating-based classifications have always been questionable. Such classification systems assign quantifiable values to predefined classified geotechnical parameters of rock mass. This results in subjective uncertainties, leading to the misuse of such classifications in practical applications. Fuzzy set theory is an effective tool to overcome such uncertainties by using membership functions and an inference system. This study illustrates the potential application of fuzzy set theory in assisting engineers in the rock engineering decision processes for which subjectivity plays an important role. So, the basic principles of fuzzy set theory are described and then it was applied to rock mass excavability (RME) classification to verify the applicability of fuzzy rock engineering classifications. It was concluded that fuzzy set theory has an acceptable reliability to be employed for all rock engineering classification systems.     

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。