Least‐square support vector machine applied to settlement of shallow foundations on cohesionless soils

This paper examines the potential of least‐square support vector machine (LSVVM) in the prediction of settlement of shallow foundation on cohesionless soil. In LSSVM, Vapnik's ε‐insensitive loss function has been replaced by a cost function that corresponds to a form of ridge regression. The LSSVM involves equality instead of inequality constraints and works with a least‐squares cost function. The five input variables used for the LSSVM for the prediction of settlement are footing width (B), footing length (L), footing net applied pressure (P), average standard penetration test value (N) and footing embedment depth (d). Comparison between LSSVM and some of the traditional interpretation methods are also presented. LSSVM has been used to compute error bar. The results presented in this paper clearly highlight that the LSSVM is a robust tool for prediction of settlement of shallow foundation on cohesionless soil. Copyright © 2008 John Wiley & Sons, Ltd.     

Relevance vector machine applied to settlement of shallow foundation on cohesionless soils

The settlement of shallow foundation on cohesionless soil is a key parameter in the design of shallow foundation. The recently introduced relevance vector machine (RVM) technique is applied to predict the settlement of shallow foundation on cohesionless soils. RVM allows computation of the prediction intervals, taking into account the uncertainties of both the parameters and the data. It provides much sparser regressors without compromising performance, and kernel bases give a small but worthwhile improvement in performance. It also estimates the prediction variance. This study shows that compared to the available methods, RVM is better at determining the settlement of shallow foundation on cohesionless soil.     

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.     

公路软基沉降预测的支持向量机模型

提出了基于支持向量机（SVM）模型对公路软基沉降进行预测的一种新方法,工程实例预测结果表明,在同样的训练均方误差下,SVM模型预测能力要优于BP神经网络模型,同时该模型能够综合利用分级加载过程中的沉降观测数据作为训练样本集,比仅依靠预压期内部分实测沉降数据的双曲线法更能反映地基土的变形趋势。因此,将建立的SVM模型应用于公路软基沉降预测能够更准确地反映实际沉降过程     

Relevance vector machine applied to slope stability analysis

This paper examines the potential of relevance vector machine (RVM) in slope stability analysis. The nonlinear relationship between slope stability and its influence factors is presented by the relevance vector learning mechanism based on a kernel‐based Bayesian framework. The six input variables used for the RVM for the prediction of stability slope are density (γ), friction angle (C), friction coefficient (?), slope angle (?_r), slope height (H), and pore water pressure (r_u). Comparison of RVM with some other methods is also presented. RVM has been used to compute the error bar. The results presented in this paper clearly highlight that the RVM is a robust tool for the prediction of slope stability. The experimental results show the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of statistical learning algorithms to ultimate bearing capacity of shallow foundation on cohesionless soil

This study employs two statistical learning algorithms (Support Vector Machine (SVM) and Relevance Vector Machine (RVM)) for the determination of ultimate bearing capacity (q_u) of shallow foundation on cohesionless soil. SVM is firmly based on the theory of statistical learning, uses regression technique by introducing varepsilon‐insensitive loss function. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. It also gives variance of predicted data. The inputs of models are width of footing (B), depth of footing (D), footing geometry (L/B), unit weight of sand (γ) and angle of shearing resistance (?). Equations have been developed for the determination of q_u of shallow foundation on cohesionless soil based on the SVM and RVM models. Sensitivity analysis has also been carried out to determine the effect of each input parameter. This study shows that the developed SVM and RVM are robust models for the prediction of q_u of shallow foundation on cohesionless soil. Copyright © 2010 John Wiley & Sons, Ltd.     

支持向量机方法在膨胀土分类中的应用

将支持向量机方法应用于膨胀土分类问题中,建立了膨胀土分类的支持向量机模型。以膨胀土实测数据为学习样本,经过训练,得到膨胀土的分类区间。应用该模型对剩余的膨胀土数据进行预测,预测结果表明支持向量机分类模型性能良好、预测精度高、简便易行,是膨胀土判别的一种有效方法,具有广阔的应用前景。     

Drained bearing response of shallow foundations on structured soils

This paper examines the drained bearing response of circular footings resting on structured soil deposits. Numerical simulations have been carried out using a finite element formulation of the Structured Cam Clay model. A parametric study was conducted by varying the parameters that govern the behaviour of structured soils and guidelines are given for designers to identify when effects of the soil structure are important. Under fully drained conditions, deformation within the structured soil supporting the footing usually occurs as a local or punching shear failure due to high compressibility of the structured soil and the mobilised bearing pressure increases with the footing movement, without reaching an ultimate value. A novel approximate method is presented to obtain the load–displacement response of a rigid circular footing resting on the surface of a structured soil deposit. This requires the properties of the soil in the reconstituted state and two additional parameters, which govern the natural structure of the soil. The proposed method has been applied to a published case study, where plate load test results are given for rigid circular steel plates resting on structured soil deposits. Fair agreement is observed between the computed and experimental results, suggesting the approximate method may be useful in design studies of foundations on structured soil deposits.     

Progressive failure analysis of shallow foundations on soils with strain-softening behaviour

This paper presents a finite element approach to analyse the response of shallow foundations on soils with strain-softening behaviour. In these soils, a progressive failure can occur owing to a reduction of strength with increasing the plastic strains induced by loading. The present approach allows this failure process to be properly simulated by using a non-local elasto-viscoplastic constitutive model in conjunction with a Mohr–Coulomb yield function in which the shear strength parameters are reduced with the accumulated deviatoric plastic strain. Another significant advantage of the method is that it requires few material parameters as input data, with most of these parameters that can be readily obtained from conventional geotechnical tests. To assess the reliability of the proposed approach, some comparisons with experimental results from physical model tests are shown. A fairly good agreement is found between simulated and observed results. Finally, the progressive failure process that occurs in a dense sand layer owing to loading is analysed in details, and the main aspects concerning the associated failure mechanism are highlighted.     

Application of a non-coaxial soil model in shallow foundations

The influence of a non-coaxial model for granular soils on shallow foundation analyses is investigated. The non-coaxial plasticity theory proposed by Rudnicki and Rice (J. Mech. Phys. Solids 1975, 23, 371–394) is integrated into a Drucker–Prager model with both perfect plasticity and strain hardening. This non-coaxial model is numerically implemented into the finite-element program ABAQUS using a substepping scheme with automatic error control. The influence of the non-coaxial model on footing settlement and bearing capacity is investigated under various loading and boundary conditions. Compared with the predictions using conventional coaxial models, the non-coaxial prediction results indicate that the settlement of a footing increases significantly when the non-coaxial component of plastic strain rate is taken into consideration, although ultimate footing bearing capacities are not affected significantly. The non-coaxial model has a different effect on footing settlements under different loading and boundary conditions. In general, the discrepancies between coaxial and non-coaxial predictions increase with increasing rotation of principal stresses of the soil mass beneath a footing. It can be concluded that if the non-coaxial component of plastic strain rate is neglected in shallow foundation problems using the finite-element method, the results tend to be non-conservative when designs are dominated by settlement of footings.     

Slope reliability analysis using a support vector machine

The first-order second-moment method (FOSM) reliability analysis is commonly used for slope stability analysis. It requires the values and partial derivatives of the performance function with respect to the random variables for the design. Such calculations can be cumbersome when the performance functions are implicit. Implicit performance functions are normally encountered when the slope is geologically complicated and the limit equilibrium method (LEM) is used for the stability analysis.

To address this issue, this paper presents a support vector machine (SVM)-based reliability analysis method which combines the SVM with the FOSM. This method employs the SVM method to approximate the implicit performance functions, thus arriving at SVM-based explicit performance functions. The SVM method uses a small set of the actual values of the performance functions obtained via the LEM for complicated slope engineering. Using the SVM model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis using the FOSM. Examples are given to illustrate the proposed SVM-based slope reliability analysis. The results show that the proposed approach is applicable to slope reliability analysis which involves implicit performance functions.     

Design of shallow foundations under tensile loading for transmission line towers: An overview

Tensioned foundations are common in civil engineering applications such as transmission towers, harbors, offshore structures, basement slabs under pressure, industrial equipment, etc. Procedures for the design of tensioned foundations are discussed in this paper, including specific recommendations for more common transmission tower foundations. Starting from a distinction between shallow and deep modes of failure, the paper presents the most common failure mechanisms for shallow failure in tension, including procedures for calculation of foundation tensile capacity under vertical and inclined loading. Emphasis is given to the influence of the strength of the compacted backfill compared to the strength of the natural soil, including presentation of results of full-scale loading tests.     

Modeling tunneling-induced ground surface settlement development using a wavelet smooth relevance vector machine

Accurate prediction of ground surface settlement is necessary for effectively controlling the settlement that develops during tunneling. Many models have been established for this purpose by extracting the relationship between the settlement and the factors that influence it. However, most of the models focused on the maximum ground surface settlement and do not involve dynamic and real-time predictions. This paper investigated how tunneling-induced ground surface settlement developed using a smooth relevance vector machine with a wavelet kernel (wsRVM). Various factors that affect this settlement, including geometrical, geological and shield operational parameters were considered. The model was applied to earth pressure balance (EPB) shield-driven tunnels. The results indicate that the prediction model performs well and that the distribution of the predictions can provide a measure of the prediction uncertainty. Unlike conventional methods that requireadditional efforts to determine relevant model parameters, the proposed method can optimize the parameters in the training process. The results of the parametric study conducted show that the model performance can be improved by the optimization and that the method can serve as a simple tool for practitioners to use in estimating ground surface settlement development during tunneling.     

Comparative study of the compression and uplift of shallow foundations

This paper compares the compression and uplift capacity of a strip foundation from numerical coupled analyses using the Modified Cam Clay (MCC) soil model. The focus is on the failure mechanism and pore pressure development in the soil. Triaxial compression and tension tests were first modelled to develop a rigorous understanding of the pore pressure responses; then, the compression and uplift of a strip foundation were modelled. The results show that the balance of excess pore pressures due to the changes in mean total stress and deviatoric stress during the compression and uplift of a strip foundation are different, although the ultimate undrained capacities are identical. Furthermore, the resistance and excess pore pressure responses during uplift differ from those in compression under the K₀-consolidated condition because of the elastic unloading. Although the failure mechanisms have identical shape and size between undrained compression and uplift, the pore pressure distribution in the soil is different and affects the load–displacement behaviours under partially drained compression and uplift.     

Support vector machines applied to uniaxial compressive strength prediction of jet grouting columns

Learning from data is a very attractive alternative to “manually” learning. Therefore, in the last decade the use of machine learning has spread rapidly throughout computer science and beyond. This approach, supported on advanced statistics analysis, is usually known as Data Mining (DM) and has been applied successfully in different knowledge domains. In the present study, we show that DM can make a great contribution in solving complex problems in civil engineering, namely in the field of geotechnical engineering. Particularly, the high learning capabilities of Support Vector Machines (SVMs) algorithm, characterized by it flexibility and non-linear capabilities, were applied in the prediction of the Uniaxial Compressive Strength (UCS) of Jet Grouting (JG) samples directly extracted from JG columns, usually known as soilcrete. JG technology is a soft-soil improvement method worldwide applied, extremely versatile and economically attractive when compared with other methods. However, even after many years of experience still lacks of accurate methods for JG columns design. Accordingly, in the present paper a novel approach (based on SVM algorithm) for UCS prediction of soilcrete mixtures is proposed supported on 472 results collected from different geotechnical works. Furthermore, a global sensitivity analysis is applied in order to explain and extract understandable knowledge from the proposed model. Such analysis allows one to identify the key variables in UCS prediction and to measure its effect. Finally, a tentative step toward a development of UCS prediction based on laboratory studies is presented and discussed.     

Reliability of shallow foundations designed against bearing failure using LRFD

Worldwide, there is growing interest in the development of a rational reliability-based geotechnical design code. The reasons for this interest are at least two-fold; first, geotechnical engineers face significantly more uncertainties than those faced in other fields of engineering, therefore there is a need to properly characterize and deal with these uncertainties. Second, for decades, structural engineers have used a reliability-based design code, and there is a need to develop the same for geotechnical engineers, in order that the two groups can ‘speak the same language’. This paper develops a theoretical model to predict the probability that a shallow foundation will exceed its supporting soil's bearing capacity. The footing is designed using characteristic soil properties (cohesion and friction angle) derived from a single sample, or ‘core’, taken in the vicinity of the footing, and used in a load and resistance factor design approach. The theory predicting failure probability is validated using a two-dimensional random finite element method analysis of a strip footing. Agreement between theory and simulation is found to be very good. Therefore, the theory can be used with confidence to perform risk assessments of foundation designs and develop resistance factors for use in code provisions.     

Predicted ultimate capacity of laterally loaded piles in clay using support vector machine

The determination of ultimate capacity of laterally loaded pile in clay is a key parameter for designing the laterally loaded pile. The available methods for determination of ultimate resistance of pile in clay are not reliable. This study investigates the potential of a support vector machine (SVM)-based approach to predict the ultimate capacity of laterally loaded pile in clay. The SVM, which is firmly based on statistical learning theory, uses a regression technique by introducing an ?-insensitive loss function. A sensitivity analysis has been carried out to determine the relative importance of the factors affecting ultimate capacity. The results show that SVM has the potential to be a practical tool for prediction of the ultimate capacity of pile in clay.     

岩爆分类的支持向量机方法

针对岩爆分类问题,提出了基于支持向量机的分类方法。通过对影响岩爆因素的分析,运用支持向量机理论建立岩爆类别的支持向量机模型。结果表明,基于支持向量机的岩爆分类方法具有较高的准确率,该方法是科学可行的,具有广泛的应用前景。     

基于范例推理的公路隧道拱顶变形时序支持向量机外延预测

针对公路隧道拱顶变形预测模型的普适性与外推预测的准确性,提出了基于人工智能推理的隧道工程属性（地理位置、监测位置、隧道高宽比、围岩级别和埋深）与拱顶变形时序曲线原子矩阵的相似范例检索方法,并在深入分析了获取的相似范例特征的基础上,进一步以LPG新核函数支持向量机建立先验知识的预测模型。应用该方法对通渝隧道工程K19+994断面拱顶下沉进行了预测与评估。结果表明,对于不同隧道间或同一隧道不同区段预判拱顶变形或收敛,基于范例推理能够获知良好的先验背景知识,且以此进行的支持向量机预测模型学习的回归内插（1～14步序）的平均相对误差为1.36%,而一次性外推预测15 d内的8个变形值（16～30步序）的平均相对精度为97.28%,证实了方法的可靠性     

Reliability with respect to settlement limit-states of shallow foundations on linearly-deformable subsoil

A step by step procedure for applying the response surface and SORM methods in estimating the reliability index associated with exceeding a certain allowable settlement level by a shallow foundation is presented in this paper. Two random variables, the Young modulus and Poisson's ratio, of lognormal and beta distribution respectively, in a single soil layer are taken into account. A linearly-deformable model of soil is assumed which is most frequently used in engineering practice when the serviceability limit state is considered. The main problem encountered in using the response surface methodology was the existence of false design points that prevented coordinate calculations of the real ones. Two procedures were employed. The first one consisted of widening the area covered by the response surface (polynomial of the second degree) with an additional “oedometric” term. Inserting the oedometric term improves the quality of the fitting and enables one to extend the range of approximation. The latter added a barrier to prevent the procedure from moving into the false design point region. Moreover, the paper presents the effect of random variation of the Young modulus E and Poisson's ratio ν as well as their mutual correlation, on the reliability index associated with exceeding the assumed level of a shallow foundation settlement.