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 In LSSVM, Vapnik's ε‐insensitive loss function has been replaced by a cost function that corresponds to a form of ridge regression.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

Support vector machine applied to settlement of shallow foundations on cohesionless soils

The determination of settlement of shallow foundations on cohesionless soil is an important task in geotechnical engineering. Available methods for the determination of settlement are not reliable. In this study, the support vector machine (SVM), a novel type of learning algorithm based on statistical theory, has been used to predict the settlement of shallow foundations on cohesionless soil. SVM uses a regression technique by introducing an ε – insensitive loss function. A thorough sensitive analysis has been made to ascertain which parameters are having maximum influence on settlement. The study shows that SVM has the potential to be a useful and practical tool for prediction of settlement of shallow foundation on cohesionless soil.     

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.     

Seismic Bearing Capacity of Shallow Strip Footing with Coulomb Failure Mechanism using Limit Equilibrium Method

In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (q_uE) is expressed in terms of single coefficient N_γE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (d_f/B₀), seismic acceleration (k_h, k_v) are studied on the variation of seismic bearing capacity co-efficients.     

Bearing capacity of two interfering footings

By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξ_γ) was determined, where ξ_γ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξ_γ at S/B = 0 becomes equal to 2.0, and the maximum ξ_γ occurs at S/B = S_cr/B. For S/B?S_cr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>S_cr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξ_γ for S/B>S_cr/B. Copyright © 2007 John Wiley & Sons, Ltd.     

Bearing capacity of a strip foundation on a sand layer overlying a smooth rigid stratum

The effect of a smooth rigid stratum, located beneath a dense sand layer, on the bearing capacity and settlement of surface and shallow strip footings is investigated using an advanced experimental model. A theoretical analysis is presented for the bearing capacity of surface footings. The results indicate that the bearing capacity reaches a minimum value at a specific sand-layer thickness. Any increase in the layer thickness above this value causes an increase in the bearing capacity up to that corresponding to a continuous media.Notation H= thickness of the sand layer - B= foundation width - N _q and N = bearing capacity factors for a semi-infinite layer - N _qs and N _s= bearing capacity factors for a finite layer - H _o /B= limiting depth - D _r= relative density - = angle of soil internal friction - M= model width - D= depth of surcharge - q= bearing stress, pressure applied on the footing - q _u= bearing capacity - = unit weight of sand     

The variation of Nγ with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing–soil interface friction angle (δ) on the bearing capacity factor N_γ was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B_t from the footing edge. For a given footing width (B), the value of B_t increases continuously with a decrease in δ. For δ=0, no trapped wedge exists below the footing base, that is, B_t/B=0.5. On the contrary, with δ=?, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in ?. The magnitude of N_γ increases substantially with an increase in δ/?. The maximum depth of the plastic zone becomes higher for greater values of δ/?. The results from the present analysis were found to compare well with those reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Site characterization model using least‐square support vector machine and relevance vector machine based on corrected SPT data (Nc)

Statistical learning algorithms provide a viable framework for geotechnical engineering modeling. This paper describes two statistical learning algorithms applied for site characterization modeling based on standard penetration test (SPT) data. More than 2700 field SPT values (N) have been collected from 766 boreholes spread over an area of 220 sqkm area in Bangalore. To get N corrected value (N_c), N values have been corrected (N_c) for different parameters such as overburden stress, size of borehole, type of sampler, length of connecting rod, etc. In three‐dimensional site characterization model, the function N_c=N_c (X, Y, Z), where X, Y and Z are the coordinates of a point corresponding to N_c value, is to be approximated in which N_c value at any half‐space point in Bangalore can be determined. The first algorithm uses least‐square support vector machine (LSSVM), which is related to a ridge regression type of support vector machine. The second algorithm uses relevance vector machine (RVM), which combines the strengths of kernel‐based methods and Bayesian theory to establish the relationships between a set of input vectors and a desired output. The paper also presents the comparative study between the developed LSSVM and RVM model for site characterization. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Collapse loads for rectangular foundations by three-dimensional upper bound limit analysis using radial point interpolation method

A three-dimensional kinematic limit analysis approach based on the radial point interpolation method (RPIM) has been used to compute collapse loads for rectangular foundations. The analysis is based on the Mohr-Coulomb yield criterion and the associated flow rule. It is understood that the internal plastic power dissipation function and flow rule constraints can be expressed entirely in terms of plastic strain rates without involving stresses. The optimization problem has been solved on basis of the semidefinite programming (SDP) by using highly efficient primal-dual interior point solver MOSEK in MATLAB. The results have been presented in terms of the variation of the shape factors with changes in the aspect ratio (L/B) of the footing for different values of soil internal friction angle (ϕ). Computations have revealed that the shape factors, s_c and s_q, due to effects of cohesion and surcharge increase continuously with (1) decrease in L/B and (2) increase in ϕ. On the other hand, the shape factor s_γ, due to the effect of soil unit weight, increases very marginally with an increase in L/B up to (1) ϕ = 25° for a rough footing and (2) ϕ = 35° for a smooth footing. Thereafter, for greater values of ϕ, the variation of s_γ with L/B has been found to be quite similar to that of the factors s_c and s_q. The variations of (1) nodal velocity patterns, (2) plastic power dissipation, and (3) maximum plastic shear strain rates have also been examined to interpret the associated failure mechanism.     

Determination of stability of slope using Minimax Probability Machine

This article examines the capability of Minimax Probability Machine (MPM) for the determination of stability of slope. MPM is constructed within a probabilistic framework. This study uses MPM as classification and regression tools. Unit weight (γ), cohesion (c), angle of internal friction (φ), slope angle (β), height (H) and pore water pressure coefficient (r_u) have been used as inputs of the MPM model. The outputs of MPM are stability status of slope and factor of safety (F). The results of MPM have been compared with the artificial neural network models. The experimental results demonstrate that the developed MPM is a promising tool for the determination of stability of slope.     

Behaviour of model footing on pond ash

This paper focuses on the effective utilization of pond ash, as foundation medium. A series of laboratory model tests have been carried out using square, rectangular and strip footings on pond ash. The effects of dry density, degree of saturation of pond ash, size and shape of footing on ultimate bearing capacity of shallow foundations are presented in this paper. Local shear failure of a square footing on pond ash at 37% moisture content (optimum moisture content) is observed up to the values of dry density 11.20 kN/m³ and general shear failure takes place at the values of dry density 11.48 kN/m³ and 11.70 kN/m³. Effects of degree of saturation on ultimate bearing capacity were studied. Experimental results show that degree of saturation significantly affects the ultimate bearing capacity of strip footing. The effect of footing length to width ratio (L/B), on increase in ultimate bearing capacity of pond ash, is insignificant for L/B ≥ 10 in case of rectangular footings. The effects of size of footing on ultimate bearing capacity for all shapes of footings viz., square, rectangular and strip footings are highlighted.     

Estimation of Pullout Capacity of Vertical Plate Anchors in Cohesionless Soil Using MARS

Vertical plate anchors provide an economical solution to safely resist the large horizontal forces experienced by the foundation of different structures such as bulkheads, sheet piles, retaining walls and so forth. This paper develops a multivariate adaptive regression spline (MARS) model-based approach for the determination of horizontal pullout capacity (P _u ) of vertical plate anchors buried in cohesionless soil by utilizing experimental results reported by different researchers. Based on the collection of forty different pullout experimental test results reported in the literature for anchors buried in loose to dense cohesionless soil with an embedment ratio ranges from 1 to 5, a predictive approach for P _u of vertical plate anchors has been developed in terms of non-dimensional pullout coefficient (M _γq ). The capability of the proposed MARS model for estimating the values of M _γq is examined by comparing the results obtained in the present study with those methods available in the literature. Using different statistical error measure criteria, this study indicates that the present approach is efficient in estimating the horizontal pullout capacity of vertical plate anchors as compared to other methods. The sensitivity analysis indicates that the embedment ratio (H/h, where H = embedment depth of anchor, and h = height of anchor) and internal friction angle (?) of soil mass are the two most important parameters for the evaluation of non-dimensional pullout coefficient (M _γq ) using the proposed MARS model.     

Determination of ultimate capacity of driven piles in cohesionless soil: A Multivariate Adaptive Regression Spline approach

The determination of ultimate capacity (Q) of driven piles in cohesionless soil is an important task in geotechnical engineering. This article adopts Multivariate Adaptive Regression Spline (MARS) for prediction Q of driven piles in cohesionless soil. MARS uses length (L), angle of shear resistance of the soil around the shaft (?_shaft), angle of shear resistance of the soil at the tip of the pile (?_tip), area (A), and effective vertical stress at the tip of the pile as input variables. Q is the output of MARS. The results of MARS are compared with that of the Generalized Regression Neural Network model. An equation has been also presented based on the developed MARS. The results show the strong potential of MARS to be applied to geotechnical engineering as a regression tool. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Machine learning techniques applied to prediction of residual strength of clay

Stability with first time or reactivated landslides depends upon the residual shear strength of soil. This paper describes prediction of the residual strength of soil based on index properties using two machine learning techniques. Different Artificial Neural Network (ANN) models and Support Vector Machine (SVM) techniques have been used. SVM aims at minimizing a bound on the generalization error of a model rather than at minimizing the error on the training data only. The ANN models along with their generalizations capabilities are presented here for comparisons. This study also highlights the capability of SVM model over ANN models for the prediction of the residual strength of soil. Based on different statistical parameters, the SVM model is found to be better than the developed ANN models. A model equation has been developed for prediction of the residual strength based on the SVM for practicing geotechnical engineers. Sensitivity analyses have been also performed to investigate the effects of different index properties on the residual strength of soil.     

Stratigraphic delineation by three-dimensional clustering of piezocone data

Piezocone soundings are a fast and economical approach for geotechnical site characterization, providing three separate and continuous channels of data with depth, including: tip resistance q _T, porewater pressure u ₂ and sleeve friction f _s. Literally hundreds to thousands of data points are collected by a single sounding. Since these readings are functions of both soil type and soil behaviour, they can be used for the delineation of soil stratigraphy.

One way to process large amounts of data involves clustering. Cluster analysis is an efficient statistical way to analyse the stratigraphic vertical profiling of geomaterials and means to detect the inherent similarity between data sets and group them together. Clustering in previous geotechnical research was based on only two channels of piezocone data (q _T and u₂). The method works well for soils that are under the groundwater table and was applied to soundings in clay deposits.

In the present paper, a new cluster analysis approach is developed based on all three channels of data, thus extending the method to soils above the water table and applicable to sands, silts, and clays. Example soil profiles derived by three-channel cluster analysis are presented herein and compared with conventional soil boring and sampling data.     

Relations between load and settlement of circular foundations on or in a dense sand expressed by a function of diameter and depth

When load acts on a circular foundation on or in a dense sand, average contact pressure on the lower surface of the foundation is q and settlement of the foundation is s. Diameter and depth of the foundation are B and D_f. When the sand, B and D_f are given, we can know the relation between q and s/B by, e.g. a loading test, i.e. the relation is determined by B and D_f for the sand. Using the results of numerical analyses, we express a relation between q and s/B up to s=0.1B by functions of a single variable which is a linear combination of B and D_f. Consequently when two foundations have different B's and different D_f's but have the same value of the variable, the relations are the same. Then we examine whether the functions can express the results of eleven tests of model foundations of wide range of B and/or D_f. In all the tests, the relations are expressed with sufficient accuracy. Copyright © 2005 John Wiley & Sons, Ltd.     

Ultimate bearing capacity of equally spaced multiple strip footings on cohesionless soils without surcharge

The ultimate bearing capacity of a group of equally spaced multiple rough strip footings was determined due to the contribution of soil unit weight. The analysis was performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. Along the interfaces of all the triangular elements, velocity discontinuities were considered. The value of ξ_γ was found to increase continuously with a decrease in S/B, where (i) ξ_γ is the ratio of the failure load of an interfering strip footing of a given width (B) to that of a single isolated strip footing having the same width and (ii) S is the clear spacing between any two adjacent footings. The effect of the variation of spacing on ξ_γ was found to be very extensive for small values of S/B; ξ_γ approaches infinity at S/B=0. In all the cases, the velocity discontinuities were found to exist generally in a zone only around the footing edge. Copyright © 2008 John Wiley & Sons, Ltd.