Rectangular Foundations Research Articles

Load carrying capacity of rectangular foundation on geogrid reinforced sloped sandy soil

A slope near the construction area is a problem for the geotechnical engineers. The paper studies the effect of reinforcing soil near slopes. Laboratory model has been designed and manufactured. The investigated parameters include vertical static (monotonic) loading, geogrid reinforcement, inclination of the slope of soil and the distance from the edge of slope to edge of foundation. The experimental results showed that the presence of a geogrid layer in sloped soil increased the foundation bearing capacity by a percent depending on the slope angle and the distance from edge of slope to the edge of foundation.

Bearing capacity of embedded foundations using quasi-kinematic limit analysis

Bearing capacity of rectangular foundations, with varying aspect ratios (1 ≤ L/B ≤ 5) and embedded at shallow to medium depths (D/B ≤ 5), has been evaluated by using the three-dimensional cell-based smoothed finite elements quasi-kinematic limit analysis. The results have also been obtained for circular and strip foundations by performing exclusively the axisymmetric and plane strain analyses. The associated optimization problem has been solved by employing the semidefinite programming (SDP). Shape factors (sc, sq and sγ) and depth factors (dc, dq and dγ) are given as a function of soil internal friction angle (ϕ). The shape factors have been expressed as a function of L/B, on the other hand, the depth factors have been given as a function of D/B and L/B. A thorough comparison of the results has been made with the different solutions available in literature. The variations of (i) power dissipation function, (ii) maximum plastic shear strain rates, and (iii) the nodal velocities patterns, have also been examined to interpret the failure mechanism.

Mechanisms beneath rectangular shallow foundations on sands: vertical loading

This paper details analysis of deformation behaviour of silica and carbonate sands under a rectangular foundation subject to uniaxial vertical load based on results from a series of centrifuge model tests. A multiscale particle image velocimetry/digital image correlation (PIV/DIC) technique was used to record and analyse the foundation tests with high resolution and measurement precision. Cone penetrometer and pressuremeter tests provide in situ soil characterisation of the tested sand sample in the centrifuge environment. The soil behaviour is analysed through foundation load–settlement response and the observed soil deformation measurements. Different soil deformation mechanisms and strain behaviours were observed in the different sands tested, and the particle shape effect is considered, with data from scanning electron microscopy, to explain the differences. The results and analyses contribute towards better understanding of different soil behaviours under shallow foundations in different sands.

CPT-Based Nonlinear Stress–Strain Approach for Evaluating Foundation Settlement: Analytical and Numerical Analysis

Due to complexities in soil–foundation interaction and nonlinear behavior of subsoil, considerable uncertainty is involved in the foundation settlement evaluation. In the present paper, a new analytical approach is proposed to estimate the foundation settlement based on soil behavior classification charts developed from CPT records. The approach is founded on the Janbu nonlinear stress–strain method. However, instead of using fixed parameters in the Janbu method, the variable coefficients are used depending on geomaterial properties. Also, in the proposed approach, the scale effect is taken into account for foundation width considering soil stiffness. The proposed procedure is calibrated and verified by a data bank containing 46 case histories including 22 square, 17 circular and 7 rectangular foundations with widths varying between 0.3 and 2.4 m in conjunction with CPT data. Furthermore, the numerical finite difference analysis using a CPT-based stress characteristics method is carried out to validate the proposed approach for the prediction of foundation settlement. The accuracy of the calculations done by the proposed and some available common methods is investigated. Comparisons based on statistical and probabilistic methods apparently reveal that the proposed approach calculates the foundation settlement promisingly.

Influence of fabric anisotropy on seismic response of circular foundation

Earthquake induced foundation failure has occurred in a number of events worldwide, such as the 1964 Niigata earthquake and 1995 Kobe earthquake. Fabric anisotropy has been considered as one of the factors that affect liquefaction characteristics. In this study, dynamic centrifuge tests were conducted for studying the influence of sand fabric anisotropy on seismic response of circular foundations. For this purpose, sub-angular Toyoura sand was used as the most anisotropic material, while sub-rounded Nevada sand was used for the comparison tests. Each group of tests were carried out in both dry and saturated conditions.These tests are considered complementary to similar centrifuge tests that the authors performed using rectangular foundations. The tests show that sand fabric anisotropy has significant impact on the seismic response of circular foundations as well, especially in saturated conditions. Specifically, as the deposition angle of the sand layer increased, the data show a remarkable decrease in acceleration amplitude concurrently with a considerable decrease of pore pressure ratio and foundation settlement. These effects were more pronounced in the sub-angular Toyoura sand. These effects of increased deposition angle are consistent with the corresponding decrease of bearing capacity and increase of footing settlements in static centrifuge tests from the literature.

Numerical simulation study of eye-shaped foundation pit

In order to study the stability of the “eye-shaped” foundation pit support, the rectang ular and the “eye-shaped” deep foundation pit are studied by using the numerical simulation sof tware Midas GTS NX. The results show that the rectangular deep foundation pit is subjected to lateral extrusion and the maximum lateral displacement exceeds 6m. In practical engineering, t he foundation pit has been destroyed and collapsed. Therefore, the safety of rectangular deep fo undation pit without internal support is very poor. For the “eye-shaped” foundation pit, the lat eral displacement at different vertical depths shows obvious characteristics of soil layer, in whi ch the silty clay layer increases sharply, which is a weak layer liable to damage. The tight effec t of middle weathered rock is remarkable due to different strength of silty clay layer and weath ered rock layer, and the negative displacement at the top appears. The lateral displacement of t he wall in the transverse inner wall region is significantly smaller than that in the circular arch r egion. The maximum lateral displacement of the wall is 2.96 cm at the intersection of the two “arches” in the transverse region and the vertical one at the silty clay layer. Along the depth of e xcavation, the uplift value is excavated by 1> excavation and 3> excavation 2. The research res ults fully prove that the eye-shaped foundation pit has good stability and the deformation is con trolled within a reasonable range.

Two-dimensional generalized finite integral transform method for new analytic bending solutions of orthotropic rectangular thin foundation plates

In this paper, a two-dimensional generalized finite integral transform method is developed for new analytic bending solutions of orthotropic rectangular thin foundation plates. The vibrating beam functions are adopted as the integral kernels to construct the integral transform pairs. By imposing the transform to the governing equation, utilizing some inherent properties of the beam functions, the title problem is converted to that of solving a system of linear algebraic equations, by which the new analytic solutions are elegantly obtained in a straightforward way. Numerical examples validate the present method as well as the solutions yielded by satisfactory agreement with the literature and finite element analysis.

Effectiveness of Effective Area Method for Assessing Undrained Capacity of Shallow Rectangular Foundations

AbstractThis paper investigates the effectiveness of the effective area method (EAM) for assessing the undrained load-carrying capacity of rectangular foundations under combined vertical (V), horiz...

Non-singular boundary element method on impedances of three-dimensional rectangular foundations

A non-singular boundary element method, as well as Green's functions of distributed loads, is developed to calculate the impedances of three-dimensional rectangular foundations. Both the sources and the targets for boundary element method are on the true foundation interface, instead of an additional auxiliary interface for sources or for targets, and the gradient variation of Green's functions near the sources is smooth, which ensures the stability, precision and efficiency of the method. Foundation impedances in multi-layered half-space are concerned to consider the stratifications of the building sites. Compared to axisymmetric foundations, large calculation task and storage requirement are expected, so MPI parallelism for clustered computers is described and various techniques are used to reduce the computer task effectively. The method is immediately used for impedances of arbitrary-shaped foundations and other scattering problems associated with unbounded half-space.

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

SummaryA 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, sc and sq, 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 sγ, 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 sγ with L/B has been found to be quite similar to that of the factors sc and sq. 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.

Correction factors for SSI effects predicted by simplified models: 2D versus 3D rectangular embedded foundations

SummaryThe effects of soil‐structure interaction (SSI) are often studied using two‐dimensional (2D) or axisymmetric three‐dimensional (3D) models to avoid the high cost of the more realistic, fully 3D models, which require 2 to 3 orders of magnitude more computer time and storage. This paper analyzes the error and presents correction factors for system frequency, system damping, and peak amplitude of structural response computed using impedances for linear in‐plane 2D models with rectangular foundations, embedded in uniform or layered half‐space. They are computed by comparison with results for 3D rectangular foundations with the same vertical cross‐section and different aspect ratios. The structure is represented by a single degree‐of‐freedom oscillator. Correction factors are presented for a range of the model parameters. The results show that in‐plane 2D approximations overestimate the SSI effects, exaggerating the frequency shift, the radiation damping, and the reduction of the peak amplitude. The errors are larger for stiffer, taller, and heavier structures, deeper foundations, and deeper soil layer. For example, for a stiff structure like Millikan library (NS response; length‐to‐width ratio ≈ 1), the error is 6.5% in system frequency, 44% in system damping, and 140% in peak amplitude. The antiplane 2D approximation has an opposite effect on system frequency and the same effect on system damping and peak relative response. Linear response analysis of a case study shows that the NEHRP‐2015 provisions for reduction of base shear force due to SSI may be unsafe for some structures. The presented correction factor diagrams can be used in practical design and other applications.

Filtering action of embedded massive foundations: New analytical expressions and evidence from 2 instrumented buildings

SummaryThis paper deals with the effect of the foundation mass on the filtering action exerted by embedded foundations. The system under examination comprises a rigid rectangular foundation embedded in a homogeneous isotropic viscoelastic half‐space under harmonic shear waves propagating vertically. The problem is addressed both theoretically and numerically by means of a hybrid approach, where the foundation mass is explicitly included in the kinematic interaction between the foundation and the surrounding soil, thus referring to a “quasi‐kinematic” interaction problem. Based on the results of an extensive parametric study, it is shown that the filtering problem depends essentially on three dimensionless parameters, i.e.: the dimensionless frequency of the input motion, the foundation width‐to‐embedment depth ratio, and the foundation‐to‐soil mass density ratio. In complements to the translational and rotational kinematic interaction factors that are commonly adopted to quantify the filtering effect of rigid massless foundations on the free‐field motion, an additional kinematic interaction factor is introduced, referring to the horizontal motion at the top of a rigid massive foundation. New analytical expressions for the above kinematic interaction factors are proposed and compared with foundation‐to‐free‐field transfer functions computed from available earthquake recordings on two instrumented buildings in LA (California) and Thessaloniki (Greece). Results indicate that the foundation mass can have a strong beneficial effect on the filtering action with increasing foundation‐to‐soil mass density and foundation width‐to‐embedment depth ratios.

Spatial distribution of Winkler spring stiffness for rectangular mat foundation analysis

Structural design of mat foundations of buildings is often done by performing static analysis of a slab resting on vertical uncoupled Winkler springs. It is already well established that the simplifying assumption of a uniform modulus of subgrade reaction throughout the mat foundation leads to inaccurate results that significantly underestimate the bending moments in the mat. This paper examines the spatial variation of the Winkler spring stiffness constants that is necessary for the mat-on-springs analysis to produce the same slab deflections and bending moment diagrams as finite element analysis that treats the soil as continuum. For this purpose, three-dimensional parametric analyses of slabs resting on elastic soil are performed using the finite element method for various values of soil elastic properties, slab geometrical characteristics and column load configurations. The finite element analysis results were used for back-calculating analytically the equivalent Winkler spring constants at each node of the mat. Based on the numerical results, equations describing the spatial distribution of spring stiffness are proposed. The performance of the proposed equations is compared against existing spring stiffness spatial distribution approaches used in practice.

Application of ANN and ANFIS for Predicting the Ultimate Bearing Capacity of Eccentrically Loaded Rectangular Foundations

Extensive laboratory model tests were conducted on a rectangular embedded foundation resting over homogeneous sand bed and subjected to an eccentric load to determine the ultimate bearing capacity. Tests were conducted for foundations with width-to-length ratios (B/L) of zero (strip case), 0.333, 0.5, and 1. The depth of embedment varies from 0 to 1B with an increment of 0.5B; where B is the width of foundation and the eccentricity ratio (e/B) varies from 0 to 0.15 with an increment of 0.05. Based on the laboratory model test results, two different approaches are proposed to determine the ultimate bearing capacity. Firstly, a neural network model is developed to estimate the reduction factor. The reduction factor can be used to estimate the ultimate bearing capacity of an eccentrically loaded foundation from the ultimate bearing capacity of a centrally loaded foundation. A thorough sensitivity analysis was carried out to determine the important parameters affecting the reduction factor. Importance was given to the construction of neural interpretation diagram. Based on this diagram, whether direct or inverse relationships exist between the input and output parameters were determined. Secondly, an adaptive neuro-fuzzy interface system (ANFIS) is used to predict the ultimate bearing capacity. The neuro-fuzzy models combine the transparent, linguistic representation of a fuzzy system with learning ability of artificial neural networks (ANNs). The results from the ANN and ANFIS were compared with the laboratory model test results. It is clearly seen that the performance of the ANFIS model in our study is better than that of the ANN model.

Impedance functions of three-dimensional rectangular foundations embedded in multi-layered half-space

Although most of the building foundations are approximate to embedded three-dimensional rectangular foundations of different length-to-width ratios, the two-dimensional models or axis-symmetric models which ignore the influence of length-to-width ratios, are usually used for dynamic analysis due to less computational effort on impedance functions. The impedance functions of foundations characterized by different length-to-width ratios and depth-to-width ratios embedded in multi-layered half-space, are obtained by a boundary element method, combined with non-singular Green's functions of high efficiency. Results of high precision based on dense element meshing are presented on complete eight impedance functions (two horizontal, two coupled, two rocking, vertical and torsional impedance functions) for the practical values in the dynamic analysis of the buildings.

Nonlinearity analysis in studying shallow grid foundation

Simulating shallow grid foundation resting on a homogenous C & ϕ soil by different nonlinear finite element analysis types, and estimate the foundation geometry effects on choosing the nonlinear analysis accuracy and degree, will be the main two concerned points through this paper. Almost of the nonlinearity classified agent techniques were mentioned briefly. Through studding the interaction between foundation and soil where the expected penetration may occurs, small and large deformation analysis was performed with a good comparison between their results for various loading levels. The soil material nonlinearity was defined by hardening plasticity cap model while elasticity model was chosen for the foundation. Then the tested variables for grid foundation were performed again on a systemized rectangular raft foundation to discuss contrasts in relative stress distribution inside the soil for the two varied foundation geometries. ABAQUS cae V.6.9.1 was the F.E Program simulation.

An analytical solution for the undrained horizontal–torsional resistance of mudmats

Rectangular mudmat foundations are frequently used for supporting subsea structures for offshore oil and gas developments. The self-weight of the subsea structure and mudmat often mobilise a relatively small proportion of the vertical bearing capacity and horizontal–torsional sliding generally represents the governing load case. However, the effect of torsion on mudmat capacity is not explicitly considered in current guidelines for geotechnical design of offshore foundations. In this paper, upper-bound plastic limit analysis is used to develop explicit expressions for the combined horizontal and torsional capacity of skirted mudmats. The results of the limit analyses are compared with results from finite-element analysis, and with other published solutions. A method is proposed for estimating the translational sliding resistance from the interaction diagram for biaxial horizontal loading and a unique expression is proposed to define the normalised H–T failure envelope. The effects of foundation aspect ratio, foundation embedment ratio, skirt–soil interface roughness, direction of horizontal loading and degree of soil strength heterogeneity are investigated systematically.

Effect of interface condition on the undrained capacity of subsea mudmats under six-degree-of-freedom loading

The effect of soil–foundation interface condition on the undrained capacity of rectangular mudmat foundations under loading in six degrees of freedom is investigated. Undrained failure envelopes for mudmats with zero-tension interface have been derived from finite-element analyses, and compared with the solutions from traditional methods and established for an unlimited-tension interface condition. The zero-tension interface has minimal effect on failure envelopes in the absence of moment, but significantly reduces the load-carrying capacity of mudmats under all other load paths that include moment. The traditional method for predicting the capacity of shallow foundations under multi-directional loading generally predicts lower capacity under any combined loading condition in comparison with the finite-element results for mudmats with zero-tension interface. Algebraic expressions are proposed to describe failure envelopes for mudmats with zero-tension interface. The proposed expressions can be implemented in an automated calculation tool to enable essentially instantaneous generation of failure envelopes and optimisation of a foundation design as a function of foundation dimension or material factor.

Shape effects on undrained capacity of mudmat foundations under multi-directional loading

The results presented in this paper systematically quantify shape effects on undrained capacity of rectangular mudmat foundations under multi-directional loading for a practical range of soil shear strength heterogeneity. Mudmat foundations are extensively deployed to support infrastructure for subsea production systems, are typically rectangular in plan, ranging from square to a width-to-length aspect ratio of 0.2, and are subject to multi-directional loading from the attached pipelines and jumpers. The load-carrying capacity of rectangular mudmats on deposits with undrained shear strength linearly increasing with depth is analysed by the finite-element method, and presented in the form of ‘failure envelopes’. The results show that shape effects are significant and are dependent on the degree of soil strength heterogeneity and loading direction (relative to the orthogonal axes of the mudmat). General algebraic expressions are established that systematically define the coupled effects of width-to-length aspect ratio of the mudmats and the degree of strength heterogeneity of the subsoil. Expressions describing the uniaxial ultimate limit states and the normalised failure envelopes under multi-directional loading can be programmed into a calculation tool for automating optimised mudmat sizing for a range of foundation geometry and soil strength heterogeneity.

Capacity of rectangular mudmat foundations on clay under combined loading

Rectangular shallow foundations known as mudmats are commonly used in the offshore oil and gas industry. They are often subject to large horizontal forces that can also give rise to overturning and torsional moments. This paper focuses on analysing the ultimate capacity of a rigid rectangular mudmat resting on the surface of, or embedded in, homogeneous undrained clay. Realistic three-dimensional load combinations are applied, based on the combined horizontal, moment and torsional loading generated by a horizontal force applied within the envelope of the mudmat and the equipment that it supports. Analytical lower- and upper-bound plasticity calculations are performed for a surface footing under combined horizontal and torsional loading, while embedded footings and more complex loading arrangements are considered using three-dimensional finite-element limit analysis. The undrained soil is modelled as a rigid–plastic von Mises material, and the interface between the external sides of the mudmat and the soil is modelled with both unlimited and zero tension capacity. Design charts are presented and relationships between loading combinations and failure mechanisms are explored.