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.     

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.     

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 In LSSVM, Vapnik's ε‐insensitive loss function has been replaced by a cost function that corresponds to a form of ridge regression.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.     

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.     

Settlement of a soil stratum subjected to an earthquake

A settlement analysis of a cohesionless soil layer subjected to an earthquake is presented. A theoretical solution utilizing Bessel functions and based on the so-called densification model for amplitudes has been obtained. This permits to calculate the settlement under cyclic loading. The simplified formula is also presented which allows for the fast and straightforward estimation of settlement. A numerical example is included giving the comparison of results obtained by different methods.     

Developing artificial neural network models to predict allowable bearing capacity and elastic settlement of shallow foundation in Sharjah,United Arab Emirates

This research proposes the use of artificial neural network to predict the allowable bearing capacity and elastic settlement of shallow foundation on granular soils in Sharjah, United Arab Emirates. Data obtained from existing soil reports of 600 boreholes were used to train and validate the model. Three parameters (footing width, effective unit weight, and SPT blow count) are considered to have the most significant impact on the magnitude of allowable bearing capacity and elastic settlement of shallow foundations, and thus were used as the model inputs. Throughout the study, depth of footing was limited to 1.5 m below existing ground level and water table depth taken at the level of the footing. Performance comparison of the developed models (in terms of coefficient of determination, root mean square error, and mean absolute error) revealed that the developed artificial neural network models could be effectively used for predicting the allowable bearing capacity and elastic settlement. As such, the developed models can be used at the preliminary stage of estimating the allowable bearing capacity and settlements of shallow foundations on granular soils, instead of the conventional methods.     

Application of Relevance Vector Machine for Prediction of Ultimate Capacity of Driven Piles in Cohesionless Soils

This paper examines the potential of relevance vector machine (RVM) in prediction of ultimate capacity of driven piles in cohesionless soils. RVM is a Bayesian framework for regression and classification with analogous sparsity properties to the support vector machine (SVM). In this study, RVM has been used as a regression tool. It can be seen as a probabilistic version of SVM. In this study, RVM model outperforms the artificial neural network (ANN) model based on root-mean-square-error (RMSE) and mean-absolute-error (MAE) performance criteria. It also estimates the prediction variance. An equation has been developed for the prediction of ultimate capacity of driven piles in cohesionless soils based on the RVM model. The results show that the RVM model has the potential to be a practical tool for the prediction of ultimate capacity of driven piles in cohesionless soils.     

Numerical investigation of the stabilisation behaviour of shallow foundations under alternate loading

This article presents a stability criterion for shallow foundations on sand for various loading conditions. By means of laboratory model tests, a behaviour called self-healing is shown. Numerical simulations of these tests prove the suitability of the employed numerical model. Based on this validation, a numerical parametric study is done to analyse the influence of loading condition and initial state of the soil on the self-healing. Main focus is on the rotational behaviour and settlement of the foundation. The observations and numerical results are discussed and an explanation is presented based on results of cyclic laboratory tests.     

考虑不完全土拱效应的浅层地基竖向应力计算

浅层岩溶土洞塌陷和浅埋隧道施工等时常会引发浅层地基出现局部沉陷,导致地基可能承受不完全土拱效应作用。如何定量分析不完全土拱效应对浅层地基竖向应力的影响尤为重要。统计了国内外浅层活动门试验,将浅层地基滑移面概化为塔形,同时考虑了浅层地基不同深度处土层差异沉降及主应力偏转过程。通过建立主应力偏转角与活动门相对位移之间的数量关系,量化了浅层地基不同深度对应的不完全土拱效应发挥程度,优化了考虑不完全土拱效应的浅层地基竖向应力计算方法。分析了主要参数对不完全土拱效应的影响,结果表明,随着浅层活动门高宽比及相对位移的增大,应力转移量增加,土体有效内摩擦角及滑移面倾角则相反。可为局部沉降作用下的浅层地基竖向应力计算提供理论指导。     

Use of evolutionary computing for modelling some complex problems in geotechnical engineering

In this paper, the feasibility of using evolutionary computing for solving some complex problems in geotechnical engineering is investigated. The paper presents a relatively new technique, i.e. evolutionary polynomial regression (EPR), for modelling three practical applications in geotechnical engineering including the settlement of shallow foundations on cohesionless soils, pullout capacity of small ground anchors and ultimate bearing capacity of pile foundations. The prediction results from the proposed EPR models are compared with those obtained from artificial neural network (ANN) models previously developed by the author, as well as some of the most commonly available methods. The results indicate that the proposed EPR models agree well with (or better than) the ANN models and significantly outperform the other existing methods. The advantage of EPR technique over ANNs is that EPR generates transparent and well-structured models in the form of simple and easy-to-use hand calculation formulae that can be readily used by practising engineers.     

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.     

A Simple Limit Equilibrium Approach for Calculation of Ultimate Bearing Capacity of Shallow Foundations on Two-Layered Granular Soils

The bearing capacity of shallow foundations in a non-homogeneous soil profile has been a challenging task in geotechnical engineering. In this paper, a limit equilibrium method is used for calculating bearing capacity factors of shallow foundations constructed on a two-layered granular soil profile. The main objective has been to determine the ultimate bearing capacity computed from equivalent bearing capacity factors N_q and N_γ and comparing that with numerical analysis using finite element methods. It will be shown that the data obtained form the developed method are well comparable with those obtained from FE approach, specially when the difference between shear strength parameters of layers is low which is a practical case for sedimentary soil profiles and also for artificially compacted soils. A computer program has been developed to investigate the influence of various parameters on bearing capacity factors.     

Reliability of Conventional Settlement Evaluation for Circular Foundations on Stone Columns

The unit cell idealization has been long adopted in the settlement prediction of stone column-reinforced soils. This paper tests the accuracy of this modeling concept against trusted settlement values of engineering foundations. It is believed that in order to bestow the outcome of this study adequate generality different soil properties and foundation geometries need to be considered. It was, nevertheless, found impracticable to collect field settlement records for all the analyzed cases. The authors, therefore, appealed to the back analysis concept to construct a reliable mathematical model, calibrated against settlement records of full-scale field load test. This model, which is capable of reproducing the real field settlements, is then employed as a generic tool to obtain trusted settlement values for a variety of cases with essential geometrical similarity. The investigation revealed that the unit cell analysis may, in some cases, lead to erroneous estimation for the settlements of foundations with limited extents. Correction factors, dependent on the treated soil properties as well as the foundation size, are introduced.     

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     

横-竖立体加筋地基中附加应力的分析计算

建立了横-竖立体加筋（H-V筋）地基的有限元模型,通过分析地基中的竖向应力分布、水平向位移分布以及筋-土界面相互作用,发现横-竖立体加筋地基中的竖向应力在筋材下方出现扩散和重分布,并逐渐向土体下部传递,使得土体中整体的应力分布更加均匀;同时,横-竖筋材中的竖筋类似于一个侧壁,其提供的垂直侧向力约束了介于竖筋间的土体,限制了土体的侧向水平位移,使得地基中筋材上部土体的侧向水平位移变小。基于有限元模拟对横-竖立体加筋地基加固机制的认识,将横-竖立体筋视为作用在地基上的一维弹性地基梁,通过弹性地基梁理论,根据弗拉曼解推导求解了横-竖立体加筋地基中任意一点竖向附加应力的计算表达式。将模型计算结果与有限元模拟所得结果进行对比发现两者吻合良好。     

Analysis of rigid rafts supported by granular piles

Solutions for the magnitude and rate of settlement of rigid foundations supported by soil reinforced with granular piles are presented. An analytic solution using the theory of elasticity is developed for the settlement of the foundation and expressions for evaluating the moment and shear distributions across the foundation are given. A solution for the increase of the rate of settlement due to the presence of the granular piles has been found by a numerical solution of Biot's equations of consolidation.     

Allowable Bearing Capacity of Shallow Foundations Based on Shear Wave Velocity

Firstly, the historical background is presented for the determination of ultimate bearing capacity of shallow foundations. The principles of plastic equilibrium used in the classical formulation of the ultimate bearing capacity are reviewed, followed by a discussion about the sources of approximations inherent in the classical theory. Secondly, based on a variety of case histories of site investigations, including extensive bore hole data, laboratory testing and geophysical prospecting, an empirical formulation is proposed for the determination of allowable bearing capacity of shallow foundations. The proposed expression corroborates consistently with the results of the classical theory and is proven to be reliable and safe, also from the view point of maximum allowable settlements. It consists of only two soil parameters, namely, the in-situ measured shear wave velocity, and the unit weight. The unit weight may be also determined with sufficient accuracy, by means of another empirical expression, using the P-wave velocity. It is indicated that once the shear and P-wave velocities are measured in-situ by an appropriate geophysical survey, the allowable bearing capacity is determined reliably through a single step operation. Such an approach, is considerably cost and time-saving, in practice.     

Dewatering induced subsidence during excavation in a Shanghai soft deposit

Foundation dewatering has become a major cause of land subsidence in Shanghai. The burial depth of foundations in relation to geotechnical construction works is less than 75 m, and the corresponding groundwater includes phreatic, low-pressure artesian, and the first confined aquifers. Based on the geological and hydrogeological conditions beneath Shanghai, methods of dewatering may be divided into three modes and further five patterns according to the insertion depth of the dewatering-retaining system. The most common dewatering mode aims to reduce the water pressure in the confined aquifer by setting the dewatering wells inside the pit, whilst the retaining walls are buried in the confined aquifer and partially cut off the confined aquifer layer. To predict the settlement due to foundation dewatering, numerical models are generally adopted, which are similar to those used to predict land subsidence induced by regional groundwater withdrawal; however, since foundation dewatering is conducted along with the setting of retaining walls and foundation pit excavation, which differs from regional groundwater withdrawal, interactions between the retaining wall-dewatering well, the dewatering-excavation, and dewatering-recharge are important factors affecting the analytical model. Since the grading of the shallow soil layers is different, stratified settlement characteristics of the shallow soil strata and seepage erosion, which results in additional deformation, need to be given particular consideration.     

Stochastic model for settlement: footings on cohesionless soil

In this paper, given an estimate of the bearing capacity of the soil, by treating settlement at a given load as a random variable and the evolution of settlement of footing on cohesionless soil with the increasing load as a stochastic process, a tri-level homogeneous Markov chain (TLHMC) model is proposed for prediction of settlement. Comparison of the predicted mean and bounds on settlements, obtained using TLHMC, with the respective field values obtained from literature shows that the stochastic evolution can be modelled using TLHMC with a correlation coefficient of 0.90. A methodology for reliability-based design of footings is also presented and its use is demonstrated through a numerical example.     

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.